Message/Author 


I am running a CFA using ML estimation. The default output provided Chisquare, Loglikelihood, Information Criteria, and RMSEA. I am interested in other fit indices such as SRMR and the SatorraBentler SCALED chisquare. I assume that I can use the formula in the Categorical analysis section of this list to calculate TLI and CFI. I am particularly interested in the SRMR as Hu and Bentler (Dec. 1998  Psych Mehtods) recommend it as it is sensitive to model misspecification and less sensitive to distribution and sample size. Is it possible to instruct Mplus to provide this as well as the SCALED chisquare? Thanks. 


You can obtain the SatorraBentler SCALED chisquare by asking for ESTIMATOR=MLM in the ANALYSIS command. You can use the formula in the Categorical analysis section of this list to calculate TLI and CFI. You would need to calculate SRMR using the formula in the Hu and Bentler article. This measure is not yet available in Mplus. 


I have a very practical question: I use datafiles with a unique respondent identifier. Is there a way to save this variable as well (i.e., together with calculated factor scores) to the output file (type= FSCORES) without having to insert it in the list of analysis variables? 


There is no way to do this at the present time. And it should not be inserted in the list of analysis variables or it will be considered as part of the analysis. We will be adding this feature in Version 2. 


Hello, I appreciated Linda Muthen's note of Thursday, March 9, 2000 indicating that the SatorraBentler Scaled T model fit statistic is equivalent to the MLM chisquare option in Mplus. I have a similar question: Is the MLMV chisquare fit option in Mplus equivalent to the SatorraBentler Adjusted T statistic reported in Bentler & Dudgeon's 1996 Annual Review of Psychology Article? A simulation study conducted by Rachel Fouladi at UT Austin reported at AERA a few years ago noted that this test statistic performed especially well in small samples (bootstrapping also performed well; it would be nice to see this added to Mplus in future releases). Thanks a lot, Tor Neilands UT Austin 


No, MLMV is not the same as the SatorraBentler Adjusted T statistic reported in Bentle & Dudgeon's 1996 Annual Review of Psychology Article. 


Is there a way to calculate TLI and CFI for a multigroup analysis using output from Mplus? 


You can find the formulas under the Mplus Discussion topic Categorical Data Modeling, Fit Measures for Categorical Outcomes. The formulas are the same for categorical or continuous outcomes. 

Anonymous posted on Thursday, June 14, 2001  8:35 pm



Why is the CFI index that I calculated from LISREL and MPLUS on the same data set different? I am purplexed at the difference. 

Anonymous posted on Thursday, June 14, 2001  8:37 pm



Is there another fit index (like GFI, NFI,....)available other than CFI available in MPLUS? 


If you have a model without a mean structure, they should be the same. Do you obtain the same chisquare and degrees of freedom? Mplus uses the formula used in Hu and Bentler (1999). If this is still unclear, send both outputs to support@statmodel.com and I will look at them 


TLI, RMSEA, SRMR, and WRMR are also available in Version 2. 


Would it be possible to get a copy of Yu and Muthen's (2001) Technical report on model fit indices? 


Please email bmuthen@ucla.edu to request the paper. 

Chuck Green posted on Wednesday, August 27, 2003  5:43 pm



Hello, I have run a three factor confirmatory model. When I used the MLR estimator to correct for violations of normality etc., I found that the significance test and confidence interval associated with the RMSEA fit index were not given in the output, as they are under ML estimation of continuous data. How might I go about calculating this? Chuck Green University of Houston 


These values have not been developed yet. That is why they are not there. 

Chuck Green posted on Monday, September 01, 2003  12:13 am



In reading your manual, I noted that the MLR estimator was listed as only being available for mixture modeling. As I understood it MLR produces the YuanBentler T2* statisic (Yuan & Bentler, 2000; 1999). I have implemented it with nonnormal data with missing values for a confirmatory data analysis. In examining nested comparisons I have used your manual's equations for producing the chisquare distributed values. I admit, however, to being somewhat disconcerted by the manual only mentioning the use of MLR for mixture analyses. Have I erred in using this estimator for a straight forward CFA with TYPE = MISSING? Chuck Green University of Houston 


There is an Addendum to the Mpus User's Guide which is available at www.statmodel.com under Product Support. If you look at the table on page 35, I think this will answer your question. This table has changed from the Version 2 user's guide. 

Chuck Green posted on Monday, September 01, 2003  5:23 am



Excellent. Many Thanks. 

Anonymous posted on Thursday, November 27, 2003  2:31 pm



If you compare two models: the first one has six latent factors which are allowed to covariate; and the second has the same six factors to all load on a general latent factor. Is it possible that the generalfactormodel has a better fit than the covariancemodel? The indicators are categorial; estimator is WLSMV. Thanks! 

bmuthen posted on Friday, November 28, 2003  4:23 pm



The second model, the general factor model, imposes restrictions on the factor covariance matrix of the first model and therefore should fit worse, although perhaps not significantly so. If the p value of the WLMSV chisquare test is better for the second model it could indicate that the second model is well fitting so that the fewer parameters make up for the worse fit. 

Anonymous posted on Monday, January 26, 2004  6:20 am



I am running a CFA on a sixfactor model consisting of 67 dichotomous items (WLSMV). The CFA (.776) and the TLI (.938) differ much from each other. I`m not sure about any reasons for this result. 


I'd need to know more to comment on this. Why don't you send the full output to support@statmodel.com. 


I am a new user of MPLUS, having moved from EQS. Although I am familiar with the SatorraBentler robust chisquare statistic (equivalent to your MLM estimator) I am not familiar with your MLMV estimator. Under what conditions is the second better than the first? Are these equivalent with respect to MLSM vs MLSMV in the case of categorical dependent variables? 

bmuthen posted on Thursday, April 22, 2004  6:31 pm



Welcome over to Mplus. The MLMV estimator adjusts not only the mean but also the variance to better approximate a chisquare distribution for the test statistic. This is written about by Satorra in his series of articles. We have found in simulations that MLMV tends to overadjust a bit with nonnormal continuous outcomes and that therefore MLM is better. My paper with du Toit and Spisic on categorical outcomes and WLSM and WLSMV (analogous to MLM and MLMV but for weighted least squares) shows through simulations that in contrast to the continuous outcome case that WLSMV works better than WLSM. You can do your own simulations in Mplus to see if you are convinced. 


I'm now using Mplus V3 where the main attraction (over V2) is the ability to model Poisson dependent variables. I have traffic accident count data which I'm modelling in a path analysis, previously I declared them as categorical (values limited to 0, 1 or 2). In order to compare the count output with the categorical output, I have specified MLR estimation for both. However, I do not get a test statistic (YuanBentler T2 as stated in the manual), I get AIC, BIC etc but I am unsure how to judge and compare the two fits and adequacy of the fit. 


You cannot get chisquare test statistics with Poisson because a mean and covariance structure does not capture the full model. Means and coviariaces are not sufficient statistics with Poisson variables. Raw data are needed because higher order moment information is needed for estimation. 

bmuthen posted on Tuesday, May 18, 2004  5:47 pm



Just to add to the previous reply  a general approach to getting a chisquare test of a path model is to use 2 times the difference of the log likelihoods, comparing the path model to a justidentified path model (all paths included). This comparison is essentially what is done by the weighted least squares approach, although not using likelihoods. Using ML in version 3, the log likelihood difference approach can be used both with categorical and count outcomes and therefore chisquares can be compared when treating the outcomes differently. Note, however, that this tests only the restrictions imposed by the path model and doesn't test the model against the data  and the latter fit may differ when treating the outcomes differently. The dilemma of model testing against the data is discussed for categorical outcomes in my 1993 BollenLong chapter on Goodness of fit (see the reference section on the Mplus web site). 

Anonymous posted on Tuesday, May 25, 2004  1:01 am



Hi, Dr. Muthen, If RMSEA is 0.084 and GFI is 0.90 in my MIMIC model, can I continue with my analysis or I need to do something to improve the model fit first before going on? Thanks a lot. 


This does not sound like good model fit. Following are some suggestions I posted earlier: A MIMIC model is a CFA model with covariates. You want to investigate your measurement model to be sure it is well fitting before adding covariates. EFA is a good way to start looking at any factor model. You can see whether your factor indicators behave the way you think they should or that you have unexpected cross loadings. An EFA can be followed by an EFA in a CFA framework to investigate significance of factor loadings. The Day 1 handout from our short courses goes through a series of steps from EFA to a final wellfitting simple structure CFA before turning to MIMIC and multiple group analysis. You might find this handout useful. See our website for details about obtaining course handouts. 

Anonymous posted on Tuesday, May 25, 2004  3:35 pm



Thank you. But if my scale is unidimensional, does EFA help to investigate corss loading? By the way, does 'cross loading' mean that one item in the scale has high loading for more than one factor? Thanks. 


You may think that your scale is unidimensional. EFA can confirm that. You may find through EFA that your items do not behave as you believe they will. Yes, that is what the cross loading means. 

Anonymous posted on Wednesday, May 26, 2004  5:10 am



Linda, you are right. I did find two latent factors derived and 5 items with cross loading in my scale which was supposed to be unidimensional. Then I guess I might need to use two latent variables model instead single latent variable model. For items with cross loading, how should I handle with them and interprete them? Thanks a lot. 


You can handle them by allowing them to be factor indicators for both factors. The interpretation would depend on the meaning of the items. Were they designed to load on both factors? If not, why do they? If there is not a good reason, perhaps they should be eliminated. 

Anonymous posted on Wednesday, May 26, 2004  4:14 pm



Thank you, Linda. Your comments are very helpful. I don't think they were designed to load on two latent factors, but one actually. From the item wording redundant information can be observed in the scale. But because I want to examine DIF for each item, I don't know whethe I can eliminate them or not. If the items with cross loading were eliminated, I guess my research topic would be a little different. By the way, is there any criteria or rule of thumb for deciding cross loading? Both loadings are higher than 0.4 or 0.5? Many thanks. 


You can do an EFA in a CFA framework. Then you get standard errors and can assess significance. 

Anonymous posted on Thursday, May 27, 2004  6:53 pm



Hi, Linda, I am not sure whether I understand "do an EFA in a CFA framework" correctly. Does it mean that doing an EFA on items of each factor specified by CFA? Thank you. 

bmuthen posted on Thursday, May 27, 2004  7:01 pm



No, it means doing a CFA where you set up the same model as used in the EFA  the advantage being that you get SEs and MIs. The handout for Day 1 of the Mplus Short Courses shows how. 

Anonymous posted on Monday, December 13, 2004  6:11 pm



I am looking for references for interpreting firstorder derivatives of parameters (TECH2) output. Thank you. 


I don't know of any references for interpreting firstorder derivatives. Perhaps an SEM textbook would address this. If you are using them for model modification, I would suggest using modification indices as they have a simple interpretation, the drop in chisquare if that parameter is free. 


What a wonderful forum! I feel very fortunate to have such a renowned expert available to answer my questions! I'm running a CFA with 24 binary outcomes (true/false responses) and one latent factor using WLS estimation. Am I correct in my understanding that the chisquare test of model fit probably isn't the best one to use because of problems with nonnormal data and that chisquare df with WLS does not represent interpretable information? Also, I'm not sure how to interpret SRMR with tetrachoric correlations. Is the value of .234 reliable? If so, do you believe it represents a better indication of fit than RMSEA (.028) for this anaysis? Finally, what do you think would be the best way to compare nested models? Are chisquare difference comparisons appropriate with tetrachoric correlations, or should I use CFI? Thank you very much! 


You might find the following publication helpful: Yu, C.Y. (2002). Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes. Doctoral dissertation, University of California, Los Angeles. It can be downloaded from the Mplus website from Mplus Papers. This dissertation examines the behavior of the fit measures you are asking about for categorical outcomes. I believe your reference to degrees of freedom and weighted least squares estimation refers to the fact that for the WLSMV estimator, the degrees of freedom are not computed in the regular way. This does not make the chisquare untrustworthy. In fact, WLSMV is the Mplus default. I recommend that you use that not WLS. The degrees of freedom for WLS and WLSM are computed in the regular way. I would compare nested models using chisquare difference testing. I'm not sure how two CFI values can be compared. 


Hi, I'm running a CFA, and I'm not getting an overall chisquare value (it just has a zero there) or RMSEA (missing altogether). I'm wondering what the cause of this would be. Thanks! 


I would need to see the output to know for sure. You should send it to support@statmodel.com along with your license number. Did your model converge? What are your degrees of freedom? 

Anonymous posted on Thursday, March 24, 2005  3:19 pm



I am running what I think is a simple regression analysis. The output shows a good model fit but I am not getting critical values. I am using Analysis: type=general missing h1; !iterations=2000; PARAMETERIZATION=THETA; estimator= WLSMV; Model: PERSISTE on support social academic sregl extra sregef expect seffic assert placemt faminc72; persistence is a categorical outcome. What am I doing incorrectly? 


You should get a pvalue for your chisquare. I assume you are given that you say you get good model fit. What do you mean by critical values? 

Anonymous posted on Wednesday, April 06, 2005  4:00 pm



I'm running a CFA model with the factors I got from EFA. Three factors from 14 binary variables, obtained from EFA. But the test of model fit for CFA shows that the model is not a good fit. ChiSquare of model fit: Value 165.523* Degrees of freedom 51** Pvalue 0.00000 RMESA is 0.035, which is ok according to the 0.06 criteria. May I ask what should I do next? Thank you very much! 


It sounds like there may have been important crossloadings on some of your items that you have fixed to zero in your simple structure CFA. Or perhaps you have a very large sample which makes the chisquare test of fit overly sensitive. I would look at modification indices and also the other fit measures, for example, CFI. 

Anonymous posted on Friday, May 27, 2005  3:56 pm



Dear Dr. Muthen, I am running CFA and MIMIC models, and checking the fitness of the models: while the CFI/TLI are around 0.93, and RMSEA close to 0.06, the pvalue for Chisquare Test of Model Fit is 0.0000. It seems there is a paradox: while the CFI/TLI and RMSEA indicate the models fit the data well, the Chisquare Test does not. Is it right? How to interpret these indices? Thank you very much. 


The issue here is that chisquare is a test of exact fit. This makes it sensitive to sample size. With large samples, there is a lot of power to reject the null hypotheses. You can do a sensitivity test by freeing parameters until you obtain an acceptable chisquare. Then compare the original parameter estimates etc. to the new ones. If they are close to the same, then you can conlcude that chisquare was too sensitive. If they are not close, you can conclude that chisquare was correct about model fit. 


I have a set of CFA models that are all giving RMSEA of <.05 but TLI and CFI well below .95 (they range between .84 and .87). Beyond the fact that my models don't fit as well as they might, is there anything else I can conclude from the discrepancy between these different fit statistics? 

bmuthen posted on Monday, August 08, 2005  7:18 pm



I don't think so. The level of agreement between fit indices seems to depend very much on the data, the model, and the kind and degree of model misspecification. I think Yu's dissertation illustrates that (see a pdf at this web site), for example when studying the HolzingerSwineford data. 


In my experience this (Mark Torrance's problem) can happen because of the null model fit. The incremental fit indices (CFI, IFI, etc) compare the model with the null model. If the correlations between the variables are low, then the null model is not very bad, and that means that the incremental fit indices don't show much improvement. To get some idea, run a model in which the model: statements are all empty. This will estimate the null model  have a look at the RMSEA. Ideally, this should indicate dreadful fit. If it's not appalling, the null model isn't so bad. Sometimes this can happen with questionnaire data where the questionnnaire items are poor. There is so much error in each measure, that the correlations between them are low. This has come up occasionally on semnet, so it might be worth searching the archives there. Most recently there was a posting by Stan Mulaik. (An example of the opposite problem is discussed in Browne MW, MacCallum RC, Kim CT, Andersen BL, Glaser R: When fit indices and residuals are incompatible. Psychological Methods 2002, 7:403421.) JM 


Dear Dr. Muthen, I am reviewing an article that uses Mplus v3.11. Could you please help me with these abbreviations of model fit: CFI TLI RMSEA WRMR What do these abbreviations stand for? It would be a great help to me and to the author of the article for me to know. I was delighted to find this website. Thank you very much, Joan Gerring, M.D. Johns Hopkins School of Medicine 

bmuthen posted on Thursday, August 11, 2005  8:01 pm



See Technical Appendices in the left margin of the Mplus home page  Appendix 5 discusses these indices (comparative fit index, TuckerLewis fit index, Root Mean Square Error of Approximation, and Weighted Root Mean Square Residual). 

ChingLin posted on Tuesday, September 20, 2005  3:44 pm



Hi, I am trying to use MIMIC on DIF detection. I get some results from the outputs of Mplus. There are degrees of freedom (df) of the DIF model and the Baseline model,respectively, but i have not idea about how the df was calculated ? Is there any papers discuss about the df of the MIMIC model? Thanks for any comment. 


It would depend on which estimator you are using. I think you can find this informaton in the Technical Appenices on the website. 


Hi, I ran across this site while looking for information. I am running a CFA using MPlus and based on results from EFA. My SRMR and RMSEA values are within the acceptable range (according to Hu & Bentler), but my CFI is low (.80). The modification indices do not seem to indicate anything troublesome. My sample is 394 for a 40 item scale, where only 36 items loaded above .40 on one factor (and were therefore included in the CFA analysis) it's a 3factor model based on several EFA rules and parenting theory. I'm wondering how to interpret the low CFI value against the other cutoffs. The scale is a 4point Likert scale. Any recommendations? 


CFI is usually a pretty reliable fit index. I assume that your chisquare value also indicates poor model fit. I am surprised that you see no large modification indices. You can send your input, data, output, and Mplus license number to support@statmodel.com if you would like me to look at it. 

Anonymous posted on Friday, October 28, 2005  12:43 pm



Hello. I am trying to compare Model A with 5 correlated firstorder factors with a Model B, a 4factor model that has 4 of the same correlated firstorder factors from Model A but excludes the items that load on the 5th factor in Model A (because these items are potentially problematic in certain ways). Chisquare difference is inappropriate here because the models are not nested, correct? I know that information theorybased indices like AIC are appropriate for comparing models, regardless of whether the models are nested. However, is it meaningful to use AIC or similar indices when one model includes some indicators that are not in the other model? I can't seem to find the answer to this anywhere. If yes, then I am all set. If no, then is there any meaningful way to compare Model A and Model B? Thanks for your time. 


I think one generally wants to have the same set of observed variables when comparing two models in order to see which model fits better. In your case, you have different sets of observed variables. What would be the question you are trying to answer by comparing the two models? 

Anonymous posted on Friday, October 28, 2005  2:28 pm



The instrument was designed to tap 5 distinct constructs  4 of them behavior difficulties, 1 of them prosocial behavior. There is some concern that the items for the prosocial factor represent more of a method factor than a symptom dimension (they are reversescored; almost all the other items are not reversescored). Because of this and also because this particular factor is also conceptually distinct from the other 4 factors (the "total" score for the scale is based solely on the items from the 4 behavior difficulties factors), I want to compare the 5factor model to a 4factor model that just includes the behavior difficulties factors. Can this be done in a meaningful way? 


What would the question be that you are asking? If I had the same set of observed variables, I would ask which model fits the data better? The four factor model or the five factor model? I think it will help to formulate the question that you are asking. Then you can decide if it can be answered in a meaningful way. 

Anonymous posted on Friday, October 28, 2005  6:09 pm



The question is which model fits better, the 5factor model for the 25item data (5 indicators per factor) or the 4factor model for the 20item data; also 5 indicators per factor). The latter model excludes those last 5 indicators (the 5th factor) because they seem to represent a method factor (all 5 items are reversescored) rather than a symptom factor. I understand that typically we compare model fit for different models using the same observed data. Is there a meaningful way to compare these models given that they are based on data sets with different numbers variables? Does it make sense to use all 25 items for the 4factor model but just not let the last 5 items load on any factor? If so, what about other parameters associated with these items besides factor loadings? Or, would it be better to test a 6factor model, where the 6th factor is a method factor, and have reversescored items load on the appropriate symptom factor and on the method factor? If so, would it be more appropriate to estimate the correlations between the method factor and each of the 5 symptom factors, or would it be better to constrain the correlation between the 6th factor and each of the 5 symptoms factors to be zero? Thanks again. 


I don't know of a meaningful way although there certainly may be one. There's a lot I don't know. If I were in this situation, I would probably go back to an EFA to help understand if my variables are behaving the way they were intended to behave. But maybe you have already done that. For example, see if they load on the factors they were developed to load on or if there are unintended cross loadings that can or if there is a methods factor. 


Thanks for previous help. I'm stuck again... I'm performing a series of CFAs in v3.12 with type=complex to make the analysis clusterrobust. This requires MLR. I want to perform chisquare difference tests and have looked at the method for doing this for MLM and MLR that's outlined on Mplus web pages. I understand how this works with MLM, because this gives me SatorraBentler ChiSquare. However, MLR gives YuanBentler T2* rather than SB. Do I just treat this as if it were the SB chisquare, and if not, how do I set about doing my difference test? 


You can follow the same steps as with MLM. 

jim posted on Wednesday, February 22, 2006  7:04 pm



Hello. I need to run a multiplegroup CFA and my continuous data is nonnormal. I was planning to use my LISREL software, but found out that LISREL does not compute the SatorraBentler adjusted fit indices (they do if you have a singlegroup but not multiple groups). Since my data is nonnormal, I want to use this adjustment when running my multiplegroup analysis. From what I have read about MPLUS, you have the SatorraBentler estimator (MLM) and MPLUS produces fit indices (CFI, RMSEA). Now I just need to know if these fit indices are adjusted for nonnormality if MLM is used as the estimator in a multiplegroup model. Can you let me know if MPLUS is capable of this so I can get it ordered ASAP if it is. 


Mplus does compute the SatorraBentler chisquare for multiple group analysis. A better choice might be MLR. 

jim posted on Thursday, February 23, 2006  4:45 pm



Thanks, Linda, for the feedback. Does MPLUS adjust the fit indices (CFI, RMSEA) along with producing the SB chisquare for multiplegroup procedures? Also, why do you say that MLR might be a better choice? 


Yes, all fit indices are available for multiple group. In some situations we have seen MLR behave better than MLM, for example, with complex survey data. In Version 4, MLM will not be available for these situations. 


I've been using clustered CFA with FIML missingdata handling to evaluate a conceptuallyderived model of patients' evaluations of physicians' endoflife care. The dataset includes 801 patients clustered under 92 physicians. Indicators are dichotomous, and I used the default WLSMV estimator and the default parameter constraints. To assess fit, I used the following criteria: normed chisquare (chisquare/df) <3.00 CFI and TLI >0.95 RMSEA <0.06 WRMR <1.00. The original conceptual model included 29 indicators, 5 1storder latent variables, and 1 2ndorder latent variable. All fit statistics except WRMR (1.017) met the fit criteria. Modification indices were all <8.00. Elimination of 3 indicators with low coverage (0.233, 0.263, 0.317) and two additional indicators that contributed to correlated residuals produced a 24indicator model that met the fit criteria. I have two questions: (1) Do you think the normed chisquare is a reasonable "substitute" for the actual chisquare test of model fit. (The models I've produced with our datasets typically do not produce chisquare tests that come even close to nonsignificance.) (2) I've read some comments about the WRMR that suggest that under some circumstances, it has performed less well than hoped. Does this suggest that I should perhaps disregard the WRMR and accept my original 29indicator model as "good enough"? (chisquare/df = 93.155/44 = 2.12; CFI = 0.995; TLI = 0.998; RMSEA = 0.037; WRMR = 1.017) Thanks. 


1. I would not use the normed chisquare. I would do a sensitivity analysis by freeing parameters until I get good fit. I would then compare my original estimates to their counterparts in the mew analysis and see if they remain the same. If so, I would assume that chisquare was too sensitive and go with my original model. If the original parameter estimates changed dramatically, I would assume my original model does not fit. 2. I wouldn't worry about WRMR if all else is okay. 


Chisquare diff testing with WLSM I'm doing CFAs with categorical data and the WLSM estimator. How should a chisquare difference test be performed, taking the scaling correction factor into account? There are refs to the webpages but I can't find any specific procedures. Is the procedure similar to that described for MLM/MLR ( http://www.statmodel.com/chidiff.shtml )? Thanks 


You would use the same procedure as for MLM and MLR. 


Hi I am trying to do CFA and EFA with 60 observed variables. I have a lot of missing values within my categorical observed variables. I am using the TYPE=MISSING in analysis and F1 by (my observed variables); but in the output the no. of observations doesn't give show the correct no. representing all the cases in my dataset(i.e. only 226 is shown as oppose to 452). I am not sure if this is ok and if this means that it is not doing list wise deletion, at the same time give me a FIML analyses output. Your response will be highly appreciated. Thank you. 


If you are using TYPE=MISSING; and you don't see the correct number of observations, it is likely that you are reading your data incorrectly. You either have more variable names in the NAMES statement or you are reading your data free format and you have blanks in your data. If this information is not sufficient to help you, please send your input, data, output, and license number to support@statmodel.com. 


Thank you so much. I found the mistake! 


Hi I'm running a overall model and I need these informations : RMSEA CFI and Chisquare. Is it possible? Here my input : variable: name are id sexe age1age3 p y1y3 x1x3 n1n3 v1v3; usevariables are y1y3 n1n3; useobservations are sexe eq 2; classes = c(3); missing = . ; analysis: type = mixture missing; starts = 500 10; model: %overall% i1 s1  y1@0 y2@1 y3@2; i2 s2  n1@0 n2@1 n3@2; Thank you so much! Annie 


With mixtures, it is not relevant to test model fit using the mean and covariance structure usually considered in SEM and on which conventional SEM fit indices are based. This is because mean vectors and covariance matrices are not sufficient statistics  the model implies restrictions beyond the secondorder moments and needs raw data to be estimated. Instead, fit is judged by "neighboring models". For example, first do a 1class conventional growth model and then do a 2class model  then compare loglikelihoods using Chisquare. See Muthen (2004) in the Kaplan handbook on our web site for further info on model choice. 


Hi, I have this model : VARIABLE: NAMES ARE u1 x1 x3; NOMINAL IS u1; MODEL: u1#1 u1#2 ON x1 x3; Is it possible to have statistic fits (chisquare, rmsea,...) whit this king of model? Thank you Annie 


The model is just identified so you will not get fit statistics. With nominal outcomes, you will not get chisquare even if the model has degrees of freedom because means, variances, and covariances are not sufficient for model estimation. 


Thank you, My problem is that I want to compare two classifications. I did an analysis to know how many classes are in my data. And I'm not sure about 4 or 5 classes. I did logistic regression on the two classifications but I need statistic fits to choose the best one! Do you have any suggestion? Annie 


If you are trying to determine the number of classes, you should be looking at BIC, loglikelihoods, and other measures. Under recent papers, you will find a paper by Bengt Muthen in a book edited by David Kaplan. This outlines how to determine the number of classes. 

Matt Moehr posted on Friday, November 10, 2006  2:40 pm



I'm stuck between using an age covariate (MIMIC) and a multiple group analysis of factor invariance based on age groups. The crux of the problem is that I would like to have age (in months) actually be a continuous variable in the model. See the explanation below, but here's my current strategy: Model 1. VARIABLES: NAMES ARE x1x9; ANALYSIS: TYPE=missing; MODEL: F1 BY x1x9; Then I covary by age, Model 2. VARIABLES: NAMES ARE age x1x9; MODEL: F1 BY x1x9; F1 ON age; Using the estimates from Model 1, I fix the loadings and residuals in Model 2. (Is this analogous to invariance?) Model 3. MODEL: F1 BY x1@1 x2@.798 ... x9@.774; x1@.415 x2@.798 ... x9@.774; F1 ON age; I apparently needed to fix the loadings to recover the model fit from Model 1. ..........chi^2 (df) Model 1 29.9 (27) p=.33 Model 2 53.2 (35) p=.03 Model 3 58.7 (52) p=.23 Is this a valid approach? Is there a way to make age as a "continuous group" variable to test invariance in the more traditional way? 

Matt Moehr posted on Friday, November 10, 2006  2:42 pm



Background: This is a study of 36 year old children examining the development of certain cognitive attributes. The use of a single factor or multiple factors is a hotly debated subject, but my colleagues have a paper in press where the 1factor model above seems to be well supported. Now we would like to show that this factor has some sort of predictive capabilities. But in order to relate the cognitive factor to educational or behavioral outcomes we need to "control" for age. I realize this could/should be done as a multigroup analysis of measurement invariance, but there are two problems with that: 1) the younger the kids the more missing data there is, and 2) I don't really want to impose an arbitrary developmental cutoff point (say 3&4 year olds vs. 5&6). Both technical and theoretical comments are welcomed. Thanks, matt 


You can approach measurement invariance in two ways  a CFA with a covariate (MIMIC model) or multiple group analysis. If you use a CFA with a covariate, you can assess only intercept invariance using direct effects. Factor loading invariance cannot be studied. In our experience, factor loading invariance is most often not a problem. It is intercept invariance. You can use multiple group analysis to study both intercept and factor loading invariance. However, you will have to make some decision about age groups. The approach you suggest above is not how measurement invariance is generally looked at. See the discussion of testing for measurement invariance in Chapter 13 in the Mplus User's Guide. It comes at the end of the discussion of multiple group analysis. 

yshing posted on Wednesday, December 13, 2006  8:25 am



Is a negative AIC value produced in M+ plausible? I understand that in M+ the way AIC is computed is by taking the loglikelihood of the better model (2*logL+2*free parameter). My loglikelihood turned out to be positive hence leading to a negative AIC value. What does this indicate? The other fit indices look reasonable. 


This is unusual but possible. Sometimes the loglikelihood can be positive resulting in a negative AIC. If you want me to look at this further, send your input, data, output, and license number to support@statmodel.com. 


Hello, Using the maximum likelihood robust estimator, is it possible to get a confidence interval for the RMSEA? Thanks in advance for your answer. 


Not at this time. 


Hello, when using MLR Mplus gives me the YB\chi^2, right? Is the calculation of the fit indices like TLI and CFI based on the YB\chi^2? Thanks in advance! 


The chisquare for MLR is asymptotically equivalent to the YuanBentler T2* test statistic. CFI and TLI are based on whichever type of chisquare is given. 


Hello, I am using Mplus for a CFA with ordinal data (4point Likert scale) for my dissertation. The distributions are also rather skewed. I am looking for ways to assess model fit. I understand that the cutoff criteria for various fit indices suggested by Hu and Bentler (1999) refer to normal data, and that Yu (2002) extends their findings for nonnormal and categorical (binary) data, the latter using WLSMV as the estimator. I was wondering whether this research generalizes to WLSMV estimation based on ordinal data, and if it would make sense to work with the cutoff criteria Yu (2002) suggests for binary (unequal proportions) data. Has anything been published about the performance of fit indexes and cutoff critera with WLSMV estimation and ordinal data? Thank you very much, Julia 


I don't know of any study of fit statistics for ordinal dependent variables. The cutoffs for binary dependent variables are very similar to those for continuous dependent variables. I would think they are similar for ordinal. You would have to do a Monte Carlo simulation study to answer this question. 

Alex posted on Monday, June 04, 2007  7:22 pm



Greetings, Is it possible to obtain the 95% confidence interval for the RMSEA using MLR and/or WLSMV ? Is it is, how ? Thank you 


Not at this time. If this has been defined in the literature, we are not aware of it. 

David Bard posted on Thursday, August 02, 2007  10:40 pm



In the June 13th response to Espen Røysamb, I see that a WLSM difference test is performed in like manner to that of MLR & MLM. I have two related questions: 1. I've noticed the scaling parameter in WLSM does not [always?] equal the ratio of the WLS chisquare and the WLSM chisquare (as would be true for MLR & MLM). How is this scaling parameter calculated? Is it possible to calculate this parameter by hand using Mplus output (I'm trying to use it in a simulation study where the Difftest calculations are too difficult to capture)? 2. For judging significance of any of these difference tests (MLR,MLM,WLSM), do you use the difference in the adjusted degrees of freedom or the unadjusted degrees of freedom? 


Dear Dr. Muthen I just ran CFA with 24 variables and got a three factors solution (EFA on the same variable showed around 6 factors solution but those factors make so sense for interpretation). Now my model fits all goodness of fit indices but one which is Chisquare fit. 1. Is there any way you can suggest which could improve my model (I've taken into account modification indices)? 2. Will my model be considered bad if it does not fit chisquare? And how does not fitting chisquare effect the model? 3. Correlation between my factors in EFA was quite low (0.30.5) but is it quite high when I do CFA (0.70.8). Why is that? Also, do you think I could use factors, with such high correlation, as independent variables when doing regression analysis? Many thanks, Joanna 


Harma: One suggestion is to do a sensitivity analysis by freeing parameters until chisquare shows good fit and seeing if this changes the original results. If it does, I would worry about model fit. The correlations go up because you go from EFA to simple structure CFA. I wouldn't worry too much about the size of the correlations. 


BArd: That's correct  WLS is not the same estimator as WLSM in terms of point estimates and thus there is no direct relation between these chisquare statistics (beyond the same asymptotic properties). The scaling parameter for WLSM is calculated according to formula (106) in the Technical Appendices http://statmodel.com/download/techappen.pdf The output gives you the scaling correction factor to use in the difference testing. Are you not getting this? There are no adjusted degrees of freedom for WLSM. You can either use the difference in the degrees of freedom or the difference in the number of free parameters. 

David Bard posted on Friday, August 03, 2007  10:21 pm



Thank you. I do get the scaling parameter in the individual output files with WLSM. I was hoping to use the Mplus Montecarlo output, though, for speed considerations. I do not get the scaling parameter in that output, right? If true, is there a way to add these scaling parameters to the results file in Monte Carlo? 


The scaling factor is not saved for Monte Carlo simulations. 


Is there any known reason why Mplus does not produce exactly the same ML chisquare as do other SEM programs such as EQS? I read exactly the same covariance matrix in Mplus 4.2 and EQS 6.1 and obtained slightly different chisquares. The issue is that the editor of a journal wants me to reproduce exactly the same findings (in the revision of a paper) he gets with obviously a different program than Mplus. I get the same chisquare he gets in EQS but not in Mplus. So I am just wondering what the reason might be... Thanks. 


The reason is likely that we use n and the other program uses n1. 


I am running a CFA with ordinal variables. The CFI is greater than 0.95, suggesting good model fit  but the RMSEA is high (0.3) and the chisquare is high also (likely due to sample size  n=9,000). I have not found a paper that has suggested cutoffs for ordinal data. Is it appropriate to rely solely on the CFI/TLI criteria? Also  I used a * after the first variable in my model statement to free it for estimation  but it appears that doing that creates a situation in which the standard errors are not able to be calculated (identification problem). Is there a way to get around this in MPLUS so that I can report factor loadings for all of the variables? Thank you. 


If you free the first factor loading, you need to either fix another one or fix the factor variance to one. This is described in Chapter 16 of the user's guide under the BY option. See the Yu dissertation on the website for cutoffs for categorical outcomes. 


I ran simple CFA model via Mplus and LISREl but got substantially different model fit indices. Chisquare statistics were similar, but CFI was .732 in Mplus (.895 in LISREL), TLI=.708 in Mplus (.886 in LISREL), and RMSEA=.099 in Mplus (.107 in LISREL). Any suggestions? Thanks, 


The difference you see in Chisquare and RMSEA is likely due to the fact that Mplus uses n and LISREL uses n1. The differences in CFI and TLI are due to the baseline models that are used to compute CFI and TLI being different. LISREL uses a baseline model that includes covariates with zero covariances among the covariates. This causes the baseline model to fit poorly and makes the H0 model fit look better. We do not believe in this baseline model. 


Greetings Linda, Following up on this one, I saw this in the Tech appendices (p. 23): "the baseline model has uncorrelated outcomes with unrestricted variances unrestricted means and/or thresholds. With twolevels models, the baseline model sets both the between and within covariances to zero. With categorical outcomes, the baseline model does not set to zero the covariances among the covariates of X because the x variables are not part of the model". From what you replied to the previous question, I am now led to believe that the baseline models for any kind of outcomes includes covariances among covariates ? Is that it ? 


We never fix the covariances of covariates to zero. 


I am doing multiple group factor analysis to test the invariance of parameters. There are more than 13000 cases in my dataset. In doing difference test,I found that the chisquare value (108) is highly significant with 10 degrees of freedom, but the other fit indices (TLI, CFI, and RMSEA) are satisfactory in both models, H1 and Ho, although the more relaxed model is a little bit better. I guess this is because of the huge sample size. Maybe I can just ignore the chisquare test for now? However, when the model gets more restricted, the other fit indices might fall just a little bit below the acceptable criteria, and I will not be able to use chisquare to test if this is really serious. So, my question is: is there any way to test the invariance other than the chisquare test when the sample size is very large? Thank you. 


Even though chisquare may be sensitive to large samples, I think this sensitivity is less when chisquare is used for difference testing. I don't know of any other option for difference testing. 


Thank you, Linda. But then, do you think I should stick to chisquare test result or refer to the other fit indices when chisquare says highly significantly different but the other fit indices say both acceptable? Thank you again. 


I have not seen other fit statistics used for difference testing. Another option is randomly splitting your sample to reduce the sample size. 


Hello, Linda, it's me again. The indicators in my dataset are categorical variables (4 levels). n>=13000. Three questions: 1.I found from watching instruction movie on web that chisquare test for categorical indicators is not good. But is it still ok to do the difference test by comparing chisquare values using the difftest? 2. Yu's dissertation seemed to suggest that WRMR is a good fit index, while SRMR is not recommended. However, as similar to the experience with my dataset and the example shown in the movie, WRMR seems large when the other indices seem reasonably good. Should I care about WRMR with my case? 3. I found that the fit indices look better when I constrained loadings and thresholds across groups (model: f1 by y15y23; f2 by y24y28; y22 with y23; y17 with y18; model female: [f1f2];) than when I set them free ( model: f1 by y15y23; f2 by y24y28; y22 with y23; y17 with y18; [f1f2@0]; {y15y28@1}; model female: f1 by y16y23; f2 by y25y28; y22 with y23; y17 with y18;). Is this possible? As we usually want to free more parameters when the model does not fit well. Thank you. 


1. I think what you mean is that for WLSMV, the chisquare value and degrees of freedom cannot be interpreted in the regular way. The proper way to do difference testing with WLSMV is to use the DIFFTEST option. 2. I think Yu conlcuded CFI does well. I would pay more attention to CFI than to WRMR. 3. I'm not sure what you mean. The MODEL commands you show are for the unrestricted not the restricted model. If you have further questions on this, please send your input, data, output, and license number to support@statmodel.com. 


I use WLSMV for categorical data. I read in the user's guide that when doing chisquare tests for nested models with WLSMV as the estimator, DIFFTEST should be used. However, in the appendices on the web, it seems to me that DIFFTEST is suitable for continuous but nonnormal data, not for categorical data. So I cannot use DIFFTEST for my categorical data? Am I correct? Thank you. 


DIFFTEST is used with WLSMV and MLMV for chisquare difference testing. It is appropriate for categorical data. 


Linda, One more question: when doing the DIFFTEST: The chisquare turned out several hundred and significant, but the CFI dropped only slightly, still within the acceptable range, like from CFI=.968 to CFI=.955. In this case, should I make the model selection decision based on the difftest or on CFI? That is, should I accept that there is a group difference in some parameter (factor mean) based on the difftest? Or, since the CFI looks OK, should I say they are acceptably invariant? Thank you. 


The chisquare difference test answers the question of whether the model restrictions significantly worsen the fit of the model. You can't answer that question with CFI. With CFI, you are answering the question about the fit of two different models. I think a CFI of .955 is marginal. The chisquare difference test is a more stringent test. 


Dear Linda, Regarding the contradictory suggestions by DIFFTEST value and CFI value in categorical outcome variables with continuous latent variables, I got an even more extreme case: The DIFFTEST result: chisquare= 42.01, df=1 whereas CFI jumps from .974 to .983. This happens when I am testing if the factor variances are the same across groups. The sample size is about 13000. Should I accept the advice of difftest and say that the two variances are different? or take the advice of CFI and regard them as equal ? Thank you for your help. 


I would use the DIFFTEST results. CFI does not answer the question about the variances being different. 


Thank you, Linda. I have four more questions regarding multipe group confirmatory factor analysis: 1. The suggestions in the Mplus short course handout suggests freeing factor loadings (and other things) and fixing factor means as the second group. The third step does most of the reverse. The two models from these two steps do not seem to be nested. So do we use only the model fit index as the criteria for them? 2. Is residual covariance also part of the measurement model? 3. Do I have to do DIFFTEST for it? 4. If the model fit is not better (or DIFFTEST looks bad) when I constrain the residual covariance to be equal across groups, do I stop here and do not test for population heterogeneity? 


The models shown are nested. Note that Topic 1 covers continuous variables. For the models to test with categorical outcomes so the section on measurement invariance in Chapter 13. With WLSMV, all nested model comparisons must be done using DIFFTEST. Although residual variances and covariances are measurement parameters, many disciplines do not require measurement invariance of these parameters. Once you establish measurement invariance, it is appropriate to test the structural parameters. 


Dear Linda, Thanks for the information regarding the covariance of residuals. However, I am still confused about testing measurement invariance: On page 399 of Users' Guide version 5, there are 2 steps under the title of 'WEIGHTED LEAST SQUARES ESTIMATOR USING THE DELTA PARAMETERIZATION.' The first one frees thresholds and factor loadings, and fixes scale factors and factor means. The second step constrains thresholds and factor loadings, and frees scale factors and factor means for one group. These do not seem to be nested models to me. When I request DIFFTEST, the model says that they are not nested models either. So, how do I make them become nested? Thank you. 


The models are nested. You must not be setting up the model correctly. Please send the relevant files and your license number to support@statmodel.com. 


Dear Linda, Thank you for the confirmation. I got the difftest done with your assurance of the models being nested. I have one more question. It is about CFA rather than multiple group CFA. When I test whether a parameter should be included, do I also have to check with DIFFTEST or do I just look at the CFI or the size of the parameter? In my case, one item's cross loading on a second factor has a small value, such as .3 or .4. Dropping it lowers the CFI. But when I include another parameter (residual covariance of still another two items), the CFI jumps higher than before the crossloading is dropped. Obviously, including the latter is more useful than including the former. But, Should I keep the former? Is there any criteria for this? Thank you. 


DIFFTEST is used to compare nested models. Whether a cross loading should be included should be driven by whether it is significant both in the statistical and practical sense and whether it is substantively supported. Residual covariances should also be substantively driven. Parameters should not be added and removed solely to affect model fit. 


Dear Linda, If I request residuals [i.e. difference between observed and modelimplied values] using the "RESIDUALS" option in the output command, does Mplus then print standardized or unstandardized residuals? Thank you Sophie 


Sorry, and related question: can I write these residuals to a file to plot them? [eyeballing all residuals for all my groups doesnt seem an trustworthy option...] thanks! sophie 


The RESIDUAL option in the OUTPUT command provides raw, normalized, and standardized residuals for continuous outcomes. Residuals cannot be saved. These are not individual residuals but residuals of the sample statistics. 


Dear Linda, You seem to suggest that I get (or can choose between?) three types of residuals (raw, normalized, standardized), but I only seem to get 1 type of residuals and I can't infer from the output what kind of residuals are printed. My output statement equals: Output: standardized residual; and then I get the following output [like in the manual, page 506]: ESTIMATED MODEL AND RESIDUALS (OBSERVED  ESTIMATED) FOR GROUP1 Model Estimated Covariances/Correlations/Residual Correlations ZPCR ZSIR ________ ________ ZPCR 1.211 ZSIR 0.895 1.294 Residuals for Covariances/Correlations/Residual Correlations ZPCR ZSIR ________ ________ ZPCR 0.029 ZSIR 0.047 0.115 Are these residuals standardized, raw, normalized? [NB the residuals do not change when I delete the 'standardized' option from the Output command line]. If I can choose between different kinds of residuals, how do I do that? I don't see that option described in the manual. Thanks Sophie 


It sounds like you are not using Version 5 or 5.1. The residuals you are getting are raw. 


Hi Linda, You're right: I updated to version 5 and get all the residuals; great improvement! Thanks again Sophie 


Hi Linda, I now get the standardized residuals in Mplus version 5, but sometimes the standardized residuals for (co) variances and intercepts are printed as 999.000 while the raw and normalized residuals [which may be positive or negative] seem ok [see below for example]. do you maybe have an explanation? Best Sophie Residuals for Covariances/Correlatio ZRESPC 0.017 ZRESBD 0.009 0.036 Standardized Residuals (zscores) ZRESPC 0.441 ZRESBD 999.000 999.000 Normalized Residuals for Covariances/ ZRESPC 0.217 ZRESBD 0.207 0.679 


We have a technical appendix on standardized residuals on the website. If the variance in formula 16 is negative, 999 is printed. 


Hello, It has occurred to me that the BIC can be computed using the chisquare value. (BIC = chisquare  df (ln (N)). However, I believe that one assumption is that the chisquare value has to be based on the likelihood values of the null model and the model of interest. 1)What is the formula for the chisquare test of model fit when using the WLSMV estimator? (I cannot find this in the technical appendix). 2)If the chisquare value is not a function of the likelihood, is it defensible to compute the BIC from it? 


1. Technical Appendix 4, formula 108. 2. No. 

Erika Wolf posted on Friday, July 11, 2008  4:47 pm



I'm using the MLR estimator for clustered categorical data (a CFA with 8 categorical indicators) for a nested and comparison model. My ouput gives me: 1. The loglikelihood and scaling correction factor 2. AIC 3. BIC 4. Chisquare test of model fit for the binary and ordered categorical outcomes (for which a large number of cells with presumably low frequencies were deleted) 5. The likelihood ratio chi square 6. Pearson Chi square for MCAR 7. Likelihood ratio Chi Square for MCAR I've computed the chisquare difference test using the 2 log likelihood formula on the website, but my question is, are there any stats here that can help me interpret absolute (not relative) model fit? I read that 4 and 5 (above) are not approporiate to evaluate with 8 or more variables in the model. Thanks for your help. 


I would use 5 and 6 if they agree. Ignore them if they don't. I would also look at the standardized bivariate residuals from TECH10. 

Erika Wolf posted on Tuesday, July 15, 2008  1:36 pm



Thanks for your help. Are 5 and 6 (above) interpreted in the same way as the traditional model chi square? In my case, both values are large (likelihood ratio chi square = 1483, DF = 6511; Pearson chi square = 1407, DF = 13038, and the pvalue is 1.0 for both stats). How is this interpreted? Thanks again. 


The chisquare in 5 and 6 are not testing the full model. They test the observed versus the estimated entries in the multiway contingency table for the categorical latent class indicators. When they both have probabilities of one they should be ignored. 


Prof. Muthen, 1. What should be the exact citation for your 1997 paper (WLSMV estimator)? 2. Apart from citing Yu’s dissertation, is there any other way of citing Yu and Muthen’s (2001) work on cutoff criteria? I mean journal article. 3. Did (ChingYun) Yu publish her work any where? I constantly refer back to her dissertation while working on latent variable models. But for some journals, dissertation could not be cited in the reference. They just don’t accept. I don’t know why though. Thanks and regards 


1. Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Accepted for publication in Psychometrika. Or you could call it a technical report. It was accepted but never revised and at this point won't be. 2. No. 3. No. 


Thank you Madam. Reagrads 


Dear Prof./s, it seems to me, that I don't understand well, what do You mean under "residual correlations" in Section "Residuals for Covariances/Correlations/Residual Correlations" of residualsoutput (I have a multigroup CFA with categorical data and use PARAMeterisation=theta and estim=WLSMV). You say, "residuals for <...>" = (estimatedobserved) value, but I'm interesting, how can I get the Residual Correlations? Is it the parameter, that is adressed to with WITHoperator? If I see the term "residual correlation matrix", should I understand it as the matrix of residuals for correlations or as the matrix of correlations of residuals? Thank You. ! I hope, I could explain all this clearly, I'm not very good in english. 


In the residual output, the residual is the difference between the observed correlation and the model estimated correlation. This is a way of assessing model fit. If you want to include a residual correlation in your model, you do this using the WITH option. 


Dear Linda & Bengt, I am fitting CFA where country is the grouping variable. I notice that the chisquare is broken down by group contribution, but that there are no other group specific fit statistics. Is there a way to request this? Or is is necessary to fit separate models for each country? Thanks for your response and happy New Year! 


There is no way to request this. It is always a good idea to fit each group separately as a first step to be sure that the model is correct for each group. I would do an EFA in each country as a first step to be sure that each country has at a minimum the same number of factors. 

ehsan malek posted on Wednesday, January 14, 2009  8:37 am



Dear Dr. Muthen, I am running a CFA model with 4 latent variables (I have around 130 cases). the chisquare of the model is around 200 with 49 degrees of freedom using pearson correlation (a poor fit). I used kendall correlation and there was a strange result. the chisquare was around 30 (a very good fit) and cfi=1 and rmsr=0.0. what is your interpretation? can I use kendall correlation and say that I have a very good fit? thank you in advance. 


The program does not know that you are using Kendall's correlations rather than Pearson. I would say the results using the Kendall's correlations are not meaningful. 

ehsan malek posted on Thursday, January 15, 2009  3:37 pm



What about Spearman's correlation? As spearman or kendall's correlation can show relations other than linear, can't we take this (much better fit with Kendall's or Spearman's correlation) as an evidence of nonlinear relations among variables? 


Whatever type of correlations you use will be interpreted as though they are Pearson correlations. It would be incorrect to use other types of correlations. 

Derek Kosty posted on Wednesday, February 04, 2009  11:17 pm



Dear Mplus Team, This is a followup to a previous post I made on July 7th, 2008. I asked, “If the chisquare value is not a function of the likelihood, is it defensible to compute the BIC from it?” Linda simply responded, “No”. Now, after further consideration of our current research, it has been decided that the AIC would be more appropriate (I don’t expect this to change Linda’s response). Is this application of AIC/BIC not defensible because the computation of chisquare under WLSMV “essentially involves the usual chisquare statistic multiplied by an adjustment akin to the Satorra and Bentler (1986, 1988) robust chisquare test statistic…” (Flora & Curran, 2004, p. 470)? Or is the reason more fundamental than this? Any feedback would truly be appreciated as we have been wrestling with the issue of comparing the fit of nonnested models when using the WLSMV estimator. Thank you for your support, Derek 


Hi, I ran a CFA on data obtained from a questionnaire with 3 latent variables and 28 observed (likert scale) variables. I used WLSMV as the estimator and did not get a very good fit. I therefore went back to doing an EFA 14 factors. I did this borth with WLSM and then got very high chisquare values. I then used estimator0 WLSMV, and the chisquare values went down. the other indicators stayed more or less the same. Now I am wondering if there is a way to do chi square difference testing when WLSMV is used as estimator. if not, how would one go about to assess if one modell fits the data better than the other? Best regards, Elisabet 


Derek: The chisquare for weighted least squares estimation is not based on a loglikelihood. It is a Wald chisquare. See Muthen (1984). Both AIC and BIC are based on the loglikelihood. If you want further information about this, see Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461464. 


Elisabet: With WLSMV, only the pvalue should be interpreted not the chisquare value or the degrees of freedom. You can test nested models with WLSMV using the DIFFTEST option. 


Thank you very much for your answer! Elisabet 


Is the SRMR index available for CFA with ordinal data (WLSMV estimator) in Mplus version 5? 


Hello, I am having some trouble on how to interpet this. I know this means that the model I specificed is different from the baseline. Is this something I can report as signficant? Can I report the chisquare for the baseline model? ChiSquare Test of Model Fit Value 0.000 Degrees of Freedom 0 PValue 0.0000 ChiSquare Test of Model Fit for the Baseline Model Value 5.314 Degrees of Freedom 5 PValue 0.3784 CFI/TLI CFI 1.000 TLI 1.000 Loglikelihood H0 Value 1017.132 H1 Value 1017.132 Information CriteriaNumber of Free Parameters 6 Akaike (AIC) 2046.264 Bayesian (BIC) 2066.289 SampleSize Adjusted BIC 2047.279 (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate 0.000 90 Percent C.I. 0.000 0.000 Probability RMSEA <= .05 0.000 SRMR (Standardized Root Mean Square Residual) Value 0.000 


Craig: SRMR has been available for categorical outcomes since Version 1 when all outcomes are categorical and there are no thresholds or covariates in the model. With Version 5, thresholds are included in the model as the default. To remove them from the modeling request MODEL=NOMEANSTRUCTURE in the ANALYSIS command. 


Sheretta: Model fit cannot be assessed for a model with zero degrees of freedom. 


Dear Linda, Am i correct that the bayes factor can be calculated in Mplus by the following formula: bayes factor = exp((BIC_model1  BIC_model2)/2)? Thank you in advance, Bjorn Roelstraete 


I am not sure but you should be able to find the answer in: Kass and Raftery (1995). Bayes Factors. Journal of the American Statistical Association, 90, 430, 773795. 


Sorry for not being clear. My actual question was how the BIC in Mplus is calculated? Is it based on the loglikelihood or 2 * loglikelihood? If its the former, BF = exp(BIC_model1  BIC_model2), but if its the latter, I should devide the difference by 2 first. Thank you, Bjorn 


Mplus BIC = 2*LL + #par.'s*log(n), so just like in the Kass & Raftery article. 


Thank you very much. 

Eric Chen posted on Tuesday, March 10, 2009  7:26 am



Dear professor: I run an 2PL IRT analysis like example5.5 mentioned in manual chapter5. And I have a problem about the test of model fit. The output fit indices of Mplus were H0 Value, AIC, BIC and adjusted BIC. These indices seem to use to compare 2 or more models. But I only specify 1 model. How do I explain these indices and assess my modle fit? Thank you! Eric Chen 


The values given for the fit statistics are for the H0 model that is estimated in the analysis. These values do not compare two models. 


Dear Prof., I am new to use the Mplus. I am trying to conduct MCFA with simulated complex data. Data were generated in SAS. The following attached program gave me errors. Could you please look at my Mplus syntex if there is any error? If no, what could be the errors? Thanks a lot in advance. Program :Configural Invariance title: MCFA with complex survey data DATA: FILE = data_MCreplist.dat; type=montecarlo; VARIABLE: NAMES = y1y6 strata cluster weight_f; USEVARIABLES = y1y6; CLUSTER = cluster; weight=weight_f; grouping is strata (1=g1 2=g2); ANALYSIS: TYPE = COMPLEX; model: f1 by y1y3; f2 by y4y6; model g1: f1 by y2y3; f2 by y5y6; model g1: [y1y6]; output: tech9; Errors: THE MODEL ESTIMATION TERMINATED NORMALLY THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 36. THE CONDITION NUMBER IS 0.510D08. THE ROBUST CHISQUARE COULD NOT BE COMPUTED. 


Dear Prof., Again I am posting another program for scalar invariance. I ran the following syntex in Mplus demo version currently available. Would you think there is an error in syntex? Your help is appreciated. The same data sets were used for configural invariance but that program gave different errors that I posted in my previous posting. Program: Scalar Invariance title: Scalar Invariance MCFA with complex survey data DATA: FILE = data_MCreplist.dat; TYPE = MONTECARLO; VARIABLE: NAMES = y1y6 strata cluster weight_f; USEVARIABLES = y1y6; CLUSTER = cluster; weight=weight_f; grouping is strata (1=g1 2=g2); ANALYSIS: TYPE = COMPLEX; model: f1 by y1y3; f2 by y4y6; output: tech9; Program gives: Errors for replication with data files data_MCrep_1.dat to data_MCrep_10.dat, as there are 10 data files in data_MCreplist.dat : 


For your first question, when you free the factor loadings and intercepts, the factor means must be fixed to zero in all groups. For the second question, please send your output and license number to support@statmodel.com. 


Dear Dr. Muthen, Thanks for your quick reply. Could you please tell me how can I fix the factor means to zero in all groups, when I free the factor loadings and intercepts? Another question: Is it possible to generate complex sample data with strata, cluster, and weight in Mplus ? 


If a factor is named f, you say, [f@0]; See Chapter 16 of the user's guide for a full description of the MODEL command. You can generate clustered data but not weighted data. See Example 11.4 and 11.6 Step 1. See also Chapter 18 of the user's guide for related options. 


Dear Dr. Muthen, I took your Mplus short course in 2008 at Johns Hopkins University. In the classes and in your handouts, you stated that RMSR and RMSEA less 0.05 were recommended. I constantly have people ask me about the rationle or reference about the 0.05 value. Do you have a reference that I can cite for the recommended 0.05 value? Thanks. WenHung Chen 


See the following: Yu, C.Y. (2002). Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes. Doctoral dissertation, University of California, Los Angeles. On the website. Hu, L. & Bentler, P.M. (1999). Cutoff criterion for fit indices in covariance structure analysis: conventional criteria versus new alternatives. Structural Equation Modeling, 6, 155. 


Dear Mplus Team, I ran a confirmatory factor analysis (four highly correlated items loading on one factor, N = 420). While CFI = .99, TLI = .96, SRMR = .02, the RMSEA = .129 (Chi2 = 12.39, df = 2). I am not sure how to interprete these results  is the model fit acceptable? I have the same problem with another CFA using this data (six highly correlated items loading on one factor): Chi2 = 157.27, df = 20, CFI = .92, TLI = .89, RMSEA = .147, SRMR = .04. I would appreciate your help very much. Christine 


I think with highly correlated data CFI and TLI fit measures may be too high. 


Dear Mplus Team, Can TLI value over 1.00 ? thank you so much tam 


When the value is larger than 1, just round it off as 1. 


I have 10 items that fit well on a single factor, based on CFI or TLI greater then or equal to 0.95 and RMSEA less than 0.06. I now have three alternate versions of another item and I want to know which version fits best with the other 10 items. When I do a single factor EFA using ESEM, version 3 of the item shows the largest CFI (0.973), TLI (0.977) and the lowest RMSEA (0.035) of all three versions and a singlefactor model is supported. But when I do an IRT analysis with the MLR estimator, the AIC/BIC/SSBIC model fit indices are lowest for version 1 of the item, indicating that version 1 fits best with the other 10 items. Why would this happen, that one version of the item appears to fit better based on factor analysis and a different version based on IRT? Which set of model fit indices are more reliable? 


I think when you say you do IRT you mean that you treat the factor indicators as categorical. Is this the case? 


Yes, I should have mentioned that all the items are categorical, actually dichotomous. 


You cannot compare BIC when the observed variables are not the same. I think this is the problem. 


Dear Linda and Bengt, I am running a CFA with MPlus 2.0 (type is complex), on a matrix of 2448 observations : each line of the matrix corresponds to several ratings of 1 stimulus by 1 subject (in total, 56 stimuli are rated by 351 subjects, but there are several missing lines, ie 2248 instead of 2457 expected). There are some missing data (blanks) within the 2248 lines. We set CLUSTER IS subject. My problem is that the output indicates that the analyses are performed on 2358 observations, and I don't understand why it doesn't use the initial 2448 (I tried to remove all lines with missing data in the matrix, just in case MPlus automatically removes these lines, but the number of remaining observations does not correspond). Can you please help me with this? Thanks a lot! 


It sounds like you are reading the data in free format. Blanks are not allowed in free format. You either need to change the blanks to a different missing value flag or read the data using a FORMAT statement. 

Zoe Chan posted on Sunday, April 25, 2010  8:23 pm



Hello, I am new to CFA. I am trying to test if my data fit the model and the analyses showed that it doesn't. I try to modify the model so that it fits and I can proceed to the next level to test for measurement invariance. However, regardless of how i try to modify it, the data still doesn't fit. What can I do? Thanks! 


Hello, I’m testing measurement invariance for 33 countries using groupcfa, based on imputated data (so, I’m using the imp option). I’m wonder if it is possible to obtain the fit statistics for the separated countries besides the overall fit statistics, as possible in Lisrel. Thank you for your reaction. 


Zoe: I would do an EFA to see what is happening with the data. 


Hidde: With IMPUTATION Mplus does not give the chisquare for each group. However, you should run each country separately as a first step before doing multiple group analysis to determine whether the same factor model fits in each country. If it does not, multiple group analysis should not be done. 

ehsan malek posted on Tuesday, April 27, 2010  6:20 pm



Hello Is there a way to calculate RMSEA, NFI, GFI, CR and AVE value for a CFA model using MPlus? 


Of those fit statistics, Mplus gives RMSEA. 

ehsan malek posted on Wednesday, April 28, 2010  3:26 am



could I calculate the other statistics myself using Mplus output? if yes, please introduce a reference. 


You would need to obtain the formulas for the other fit statistics and see if the information is available in the Mplus output. 


Hi, Hopefully a quick question. I'm fitting a twolevel CFA with continuous indicators. I want to compare two models. In the first, the indicators load on their respective traits and also on a method factor; in the second, I constrain the loadings on the method factor to zero using Model Constraint. The difference in df between the models is 6. When I use a Wald test (Model test) in the first model to test whether the factor loadings are collectively zero, it is clearly rejected (p < .000). This suggests the method factor is meaningful. When I use a chisquare difference test (following the procedure for MLR), the difference is 9.87 with 6 df, which is not significant (p = .13). This tells me the method factor is not meaningful. Any advice on reconciling or interpreting this difference is appreciated. Thanks, Al 


Hello, I was running a very simple CFA with 4 indicators and 1 factor. Chisquare and other indices indicated a very good fit! However, one item had a very low loading on the factor what was expected due to preceding EFAanalyses. When I exclude this item from the model I get the following fit statistics: ChiSquare Test of Model Fit Value 0.000 Degrees of Freedom 0 PValue 0.0000 ChiSquare Test of Model Fit for the Baseline Model Value 136.263 Degrees of Freedom 3 PValue 0.0000 CFI/TLI CFI 1.000 TLI 1.000 RMSEA (Root Mean Square Error Of Approximation) Estimate 0.000 90 Percent C.I. 0.000 0.000 Probability RMSEA <= .05 0.000 SRMR (Standardized Root Mean Square Residual) Value 0.000 Does that mean to be a very good model? It looks a bit weird... 


Albert: The two tests are asymptotically equivalent. If you have a small sample, this could cause the discrepancy. Or perhaps one test was not done correctly. If you want further help on this, send the information along with your license number to support@statmodel.com. 


Mario: With three factor indicators, the model is justidentified so model fit cannot be assessed. 


I seem to be a little confused as to the significance of the chi square test of model fit. I was wondering, what does it tell you about your data and what is the difference between the test of model fit and the test of model fit for the baseline model? Thank you 


The baseline model is the model used along with the H0 model in the computation of CFI and TLI. Chisquare tests the fit of H0 model against the unrestricted H1 model. 


Dr. Muthen, Thank you. So are there standards to what the number should be (ie cutoffs or standards, as with the CLI or RMSEA)? What do the values/ degrees of freedom of the chi square test indicate? 


See an SEM book like the Bollen book where you can find a full discussion of various fit statistics. Or listen to our Topic 1 course video where fit statistics and cutoffs are discussed along with difference testing. 


Thank you very much. I will look for that information. 


Hello Linda and Bengt, I'm having trouble finding what the default unrestricted model is in Mplus. That is, what is the model that generates the H1 log likelihood value? Thanks, Leslie 


This is the model of means, variances, and covariances. 

Abdel posted on Thursday, April 28, 2011  8:06 am



Dear Linda and Bengt, I am running a multigroup CFA on categorical data (10 items underlying 1 latent factor) with the WLSMV estimator and PARAMETERIZATION = THETA (because I put constraints on the residual item variances), and the COMPLEX option. I would like to get a BIC value out of this analysis, and I was wondering whether it is possible to calculate that with the available output? I know that the chisquare is not based on the log likelihood, so that can't be used. If I try to get the BIC out by using MLR instead of WLSMV, I get the warnings: *** WARNING in ANALYSIS command PARAMETERIZATION=THETA is not allowed for TYPE=MIXTURE or ALGORITHM=INTEGRATION. Setting is ignored. *** ERROR in ANALYSIS command ALGORITHM=INTEGRATION is not available for multiple group analysis. Try using the KNOWNCLASS option for TYPE=MIXTURE. And I'm not even using TYPE=MIXTURE of ALGORITHM=INTEGRATION. My analysis command looks like this: ANALYSIS: TYPE = mgroup COMPLEX MISSING h1 ; ESTIMATOR = MLR ; !MLR used to be WLSMV PARAMETERIZATION = THETA ; ITERATIONS = 1000 ; Is there any way to get the BIC out in this model? Many thanks in advance! 


BIC is not available with weighted least squares estimation only with maximum likelihood estimation. Remove PARAMETERIZATION=THETA; That is only for weighted least squares estimation. 

Abdel posted on Thursday, April 28, 2011  2:36 pm



Thanks! Is it possible to calculate the BIC manually using the output from a weighted least squares estimation? Or do you perhaps have other recommendations for a fit statistic that can be used to compare different models and can be calculated from the output of a weighted least squares estimation? 


I know of no way to calculate BIC for weighted least squares estimation. With WLSMV, you obtain chisquare and other related fit statistics. 


Dear Linda, To my understanding, Mplus does not provide other fit statistics than the standard report obtained from the analysis. I normally get RMSEA, CFI, TLI and SRMR from the analysis but please could you let me know how to obtain IFI. Many thanks. Pat 


Dear Linda, Regarding the question about IFI that I posted earlier, I already got the formula from a book. Thanks. Pat 

Ellinor Owe posted on Monday, November 07, 2011  1:15 pm



Hi, I want to compare three nonnested multilevel CFA models and was thinking of using the AIC for this. I know that a smaller AIC indicate better fit, but is there a way of knowing which magnitude of difference can be considered meaningful and which can be considered trivial? Thank you very much Ellinor 


I am not aware that a way to do this exists. See the following FAQ on the website which discusses this issue for BIC: # BIC citations of interest  how big a difference 

WenHsu Lin posted on Friday, November 25, 2011  1:47 am



Hi, I have 5 imputated datasets. I ran CFA in each set using same model and each individual analysis showed acceptable fit (CFI = .94~.96; TLI = .95~.96; RMSEA .053~.61). However, when I use type = imputation, the result was strange (CFI = 0; TLI = 4.3; RMSEA = .53). Any suggestion? Thank you 


If you are not using Version 6.12, please do so. If you are, please send the relevant files and your license number to support@statmodel.com. 

Jiyeon So posted on Tuesday, December 06, 2011  3:06 am



Hi Prof. Muthen, I was wondering if Mplus gives out "Gamma hat" and "McDonald's NCI" as fit indices in the CFA output. I can't find them in my output. Is there syntax that asks Mplus to give these out? Thank you in advance! 


There is no option to request additional fit indices. All that are available are given. 


Linda, Given that it is impossible to request additional fit indices (bummer!), what would you suggest when using categorical (ordinal) data? We would prefer two absolute and two incremental fit indices. We would have preferred to have GFI estimated, as it is said to be analogous to Rsquared and we would like some "variance explained" index. We would also have wanted an index akin to PCFI (to compare similar models) or AIC (which includes a "penalty" for increasing parameters in comparing similar models). We would appreciate any advice you could give, including a way to make the best use of the existing mplus output. Thanks very much, Becky 


If you want variance explained, ask for STANDARDIZED in the OUTPUT command and you will get Rsquare. For maximum likelihood, AIC and BIC are given. These indices are not appropriate for weighted least squares which is the default for categorical outcomes. If you want other fit indices, you should be able to find the information to compute them. 


Thank you! One followup question: Rsquare seems only to account for variance explained by each item. Is there a way to find variance explained by the model as a whole? 


We provide Rsquare for each dependent variable not for the model. 


I am running a CFA on a nineitem measure. Each item is orderedcategorical in nature. I have 3% missing cases. I used multiple imputation in MPlus to generate 25 datasets. However when I ran the CFA with WLSMV estimator on the imputed datasets, I do not get a pooled chisquare, I only get pooled parameter estimates and SE's. I've had a quick look at the literature am I correct in saying that pooled chisquare is only given in MPlus for the ML estimator? If that's the case, is there any other way to calculate the pooled chi square when WLSMV estimator has been used? I have read somewhere that once you obtain parameter estimates from the WLSMV run you can change the estimator to ML to get the pooled chi square in a second run but this doesn't seem right given the ordinal nature of the variables. Any suggestions on how else I am able to correctly analyse my data? Thanks! 


It is true that the pooled chisquare is given for only the ML estimator with multiple imputation. Research on how to correctly pool in other cases does not exist. It sounds like you have one factor. In this case, you can use maximum likelihood with the CATEGORICAL option. The default is logistic regression. You can use PARAMETERIZATION=PROBIT if you want probit regression. 


Thanks for the prompt reply Linda. There are two factors actually. Will this change the suggestions you have made? 


No. 


Hi again, I have run the analysis as per your suggestions but my chi square p value is coming up as 1.00 and i get the following message underneath "of the 82944 cells in the latent class indicator table, 51 were deleted in the calculation of chi square due to extreme values" I also don't get any of the usual fit indices. I am a little confused. 


With maximum likelihood and categorical outcomes, means, variances, and covariances are not sufficient statistics for model estimation. As a result, a chisquare comparing sample and model estimated covariance matrices and related fit statistics are not available. The chisquare values you are looking at compare observed versus estimated multiway frequency tables of the categorical items. With more than eight categorical items these tables become vary large and empty cells are a problem. They should not be used with more than about eight items or if they do not agree. 


Thanks Linda. 

Julia Lee posted on Saturday, March 24, 2012  9:59 pm



I am conducting: 1) CFA to determine whether 5 indicators in the fall & spring of first grade, respectively, form a unitary factor (literacy). (n = 521) Question: a)If there are floor effects and outliers, is MLR robust enough to handle the issue? Should the floor effects and outliers be deleted? I am retaining the floor effects & outliers; I used MLR because in my main research question I am interested in the latent profiles & latent transitions of this sample. My CFA fit indices are mixed: I have p < .001, high RMSEA, great fits for SRMR and CFI/TLI. I do not know why this is happening because these indicators are theoretically driven. However, nobody has tested these constructs in tandem. b)Would ill scaled covariance matrices result in this kind of fit indices? My covariance matrix has a combination of variance as high as 1074.168 and as low as 16. 


a) Theoreticallydriven indicators very often give poor model fit when the indicators have not also been subjected to a previous series of pilot studies using EFA to refine them. MLR is not enough if you have strong floor effects because in that case the linear model is wrong. You can instead for instance treat the indicators as censorednormal. b) No, the scales of the variances don't affect fit. But you do want to make the variances more similar for purposes of easier convergence. 

Julia Lee posted on Sunday, March 25, 2012  12:28 am



Thank you for your reply, Dr. Muthen! 1) I found something on the CENSORED option on UG p. 487. Do you have any recommendations of good articles on censorednormal? What other alternatives would you recommend for floor effects apart from censorednormal? I was thinking of transformation, which would affect the interpretation of the results.... 3) Are the suggested cutpoints of skewness and univariate kurtosis values of 2 and 7 (Finney & Distefano, 2006), respectively, conservative enough for MLR? One spring indicator has a skewness of .471 and kurtosis of .250; another with skewness = .026 and kurtosis = .823; one with skewness = .316 and kurtosis = .280). I think the challenge is not being able to visualise what the multivariate abnormality looks like based on the bivariate plots. The fall indicators are more nonnormal. I have indicators with skewness = 1.625 and kurtosis = 3.026, skewness = .948 and kurtosis = 3.157, and skewness = 1.010 and kurtosis = .267. 


1) Google "tobit regression". You can also categorize (discretize) the variable and put them on the Categorical=list. This may be the simplest approach. A more advanced approach is "twopart (semicontinuous)" modeling as in Kim, Y.K. & Muthén, B. (2009). Twopart factor mixture modeling: Application to an aggressive behavior measurement instrument. Structural Equation Modeling, 16, 602624. I would not transform variables. It would not avoid the main problem of the floor effect. 3) Skewness and kurtosis are not a problem  that's what the "R" in MLR takes care of. The problem is the floor effect. But perhaps the most likely reason for the poor fit by chisquare is that the model needs adjustment, such as using crossloadings or more factors. 


Hi Anyone would have an exlication. The pvalue of my ChiSquare are 1,000 Seem too nice to be true. Thanks 


The degrees of freedom are probably zero in which case model fit cannot be assessed. 

Lisa Aschan posted on Saturday, June 30, 2012  4:00 pm



Hi, I have a question about the fit indices of a CFA which I am planning to use in a larger SEM model. I am using version 6. I have 5 observed variables and 1 factor. The observed variables are categorical or binary, and the analysis is complex with clusters and weights. My sample size is 1700 but I have some missing data. My model is: F1 by y1* y2 y3 y4 y5 ; F1@1 ; My fit indices are: Chisquare(5) = 51.67 (p<.001) RMSEA: 0.074 (90% CI: 0.057  0.093) CFI: 0.972 TLI: 0.943 So my model fit is not great. However, all of my factor loadings are highly significant. Why might my model fit be inadequate? How can I improve my model fit? I have thought maybe I am violating assumptions of independent error. How can I test this assumption? Many thanks for your help. 


Significance is not fit. It tests whether a parameter is significantly different from zero. Fit compares the model estimated and sample covariance matrices. Ask for MODINDICES (ALL) in the OUTPUT command to see if you are violating assumptions of independent error. 


Dear Dr Multhen, I have tested the factor structure of Maslach Burnout Inventory. I made a correlated three factor model (with emotional exhaustion, depersonalization and personal accomplishment), and a second order factor model (burnout on EE, DP, PA). The fit indices are: correlated three factor model: chisquare = 844, df = 206, p < 0.001, RMSEA = 0.069 (0.064 0.074), CFI = 0.85, TLI = 0.84, SRMR = 0.07 second order factor model: chisquare = 878, df = 206, p < 0.001, RMSEA = 0.072 (0.067 0.077), CFI = 0.84, TLI = 0.82, SRMR = 0.07 My question is, how is it possible, that the two model's degree of freedom are the same, but the other modification indices are different? Thank you for your answer: Veronika 


You should get the same fit because the secondorder factor is just identified. Try using STARTS = 10; in the ANALYSIS command for the secondorder model. You must be hitting a local solution. 

Hass posted on Thursday, November 29, 2012  8:49 pm



Hello, I tried to RUN this model, but I got the following error: Unexpected end of file reached in data file. I know the file is big (10 variables, 41 items), but it shouldn't be a problem? Your advice is much appreciated. G 


It sounds like you either have blanks in your data set which is not allowed with free format data or the number of names in the NAMES statement is not the same as the number of columns in the data set. 

Kofan Lee posted on Thursday, December 06, 2012  1:24 pm



Hi, I was running a 5 factor CFA using MLM estimation. The final model takes one factor removed because the items fails to support this factor. Also, several measurement errors are added. To assess the improvement of the new model, I try to use stickly positive approach, but how should I use the start values obtained from Model 0 to Model 10 since that particular factor is removed? Should I delete those values or just set as 0? Another question is when Mplus use ML estimation even if I input as MLM. This happens when I try to calculate Nodel 10. Thanks for your time k 


Are you trying to compare a 4factor to a 5factor CFA? Regarding getting ML when requesting MLM, please send output and license number to Support. 


Dear Dr. Muthén! Do you know any references regarding the perfomance of the MLRestimator under nonnormal data conditions? I only found studies investigating the performance of the SBCorrection (MLM). Thanks Christoph Weber 


See Web Note 2 on the website. 


Thanks a lot for the hint! At the end of the web note it is noted: "To study the generalizability of these findings, it may be of interest to study variations on the Monte Carlo setup, varying the sample size and the degree of missingness." Are you aware of such extensions? Thanks Christoph Weber 


No, I am not. You could do this your self. 


Thanks, it's on my to do list! 

Jenny L. posted on Tuesday, June 11, 2013  2:29 pm



Dear Drs. Muthen, I was doing a path analysis with imputed data. One dependent variable was count and thus Poisson regression and MLR were used, but I'm not familiar with interpreting the output. Under Model Fit Information, I saw mean scores of Log Likelihood, AIC, BIC, and samplesize adjusted BIC. I thought AIC and BIC were most useful when comparing different models. Could you tell me how I can assess model fitness of this particular model by looking at these indices? Thank you in advance for your help. 


Unfortunately, there doesn't seem to be statistics developed for this conbination. You can analyze each imputed data set separately and use what's available in that case  comparing competing models by BIC and by likelihoodratio chisquare testing (and I think also Tech10). 

Jenny L. posted on Tuesday, June 11, 2013  7:35 pm



I see. Thank you for your advice! 

Tracy Witte posted on Wednesday, August 28, 2013  2:15 pm



I am attempting to replicate an article that, among other methods, compared two nonnested models by subtracting the modelimplied correlation matrices from one another to identify differences in predictions across the models. The authors state that they used Mplus v. 6.1 for their analyses. However, I'm unsure how to get model implied correlation (not covariance) matrices with Mplus. (Note  the authors used the ML estimator with continuous indicators). Can this information be obtained with the TECH1 and TECH3 output? Specifically, if I look at the TECH1 output to get the parameter numbers for the NU matrix, and then look at the estimated correlation matrix in TECH3 for the corresponding parameter numbers, do those values represent the model implied correlation matrix? 


TECH4 gives this for latent variables and RESIDUAL gives it for observed variables. 

Tracy Witte posted on Wednesday, August 28, 2013  3:32 pm



It looks like the residual output gives only the standardized and normalized values (i.e., z scores) and the covariance matrix. Perhaps I'm missing something? 


Please send the output and your license number to support@statmodel.com. 

Nancy Lewis posted on Tuesday, September 17, 2013  5:17 pm



I have run a 4factor CFA on four independent samples of respondents to a 31 item Likert scale measure (1 to 7 range of answer choices). I ran the models using the MLM estimator. The N for each model was around 300. In all of the models, the CFI indicates marginal fit (.90.92) but the RMSEA indicates good fit (.06.07) and the SRMR also indicates good fit (.06.08). I am struggling to understand why the CFI doesn't agree with the RMSEA and SRMR. The factor loadings for the items are all moderate or better (.60 and above with most .70 and above). 


I think it sounds like the model can be improved, even in terms of RMSEA. Check the modification indices. You can also try multiplegroup ESEM (see our website for ESEM papers), which is less restrictive than multiplegroup CFA. 

Nancy Lewis posted on Tuesday, September 17, 2013  6:53 pm



Dr. Muthen, Thank you for responding to my question. I should have added that the mod indices don't indicate any means of improving the model. The values are all quite low. I have tried several of the highest ones and they make no difference in the fit. 


A low CFI is sometimes seen with variables that have low correlations so that the independence model doesn't fit too badly. Otherwise, many small misspecifications can be the cause; that would suggest that it's worth trying ESEM. 

Nancy Lewis posted on Tuesday, September 17, 2013  7:13 pm



Also, I should add that the model structure was built based on EFA results. 

Nancy Lewis posted on Tuesday, September 17, 2013  7:17 pm



Yes, I considered that the problem could be low correlations. This doesn't seem to be the case. Within each factor, the item intercorrelations are medium to large. The factors are moderately correlated with each other. I have also run a 3factor model on the data using a factor structure proposed by the scale's authors. It had poor fit on the CFI, SRMR and RMSEA. Is there anything else that could cause CFI to be low? Thank you. 


Some of the small EFA crossloadings may be significant and can produce CFA misfit. 


We are conducting CFA (estimator=ML). All indicators are continuous. The following are the fit indices (part): RMSEA = 0.064 (CI = 0.062, 0.066) CFI = 0.743 TLI = 0.710 SRMR = 0.066 Since CFI and TLI are low, we turn to use Hu and Benther's two index presentation strategy, focusing on RMSEA and SRMR: RMSEA < 0.06 and SRMR < 0.09. Our question is that our RMSEA = 0.064, slightly larger than the cutpoint 0.06. Is it still possible to say that our model and data have sufficient fit?  Further, we dichotomized two indictors (to one factor), so, two categorical variables are in CFA. The following are fit indices (part): (Estimator=WLSMV) RMSEA = 0.061 (CI = 0.059, 0.064) CFI = 0.685 TLI = 0.643 WRMR = 2.780 We found that SRMR does not provided in this case, but replaced by WRMR. How to evaluate the fit now? Many thanks, Xuecheng 


I would not dichotomize the two indicators. Try using ESTIMATOR = MLR which is robust to nonnormality. Perhaps that is one problems. You may also want to start with an EFA to see if your CFA is viable for the data. 

RuoShui posted on Friday, February 07, 2014  7:22 pm



Dear Dr. Muthen, I am using SatorraBentler chisquare test (using MLR as estimator) to test the difference between my SEM mediation model and the direct path model without mediators. I know that chisquare test is sensitive to sample size. But is the chisquare difference test also sensitive to sample size? Do I need to consult other fit indices such as delta CFI as suggested by cheung & Rensvold (2002) and chen (2007)? Thank you very much! 


This is a good question for a general discussion forum like SEMNET. 


were changes made between version 6.1 and 7.11 to how fit statistics were being calculated? We have a model that was originally run in 6.1, having updated to 7.11 I ran the model again. The coefficients and SE change a very small amount (.001  .003 on average), but the values for model fit have changed substantially. Chi square is 69.67, df = 25 in version 6.1 and 144.56, df = 41 in 7.11. Relatedly, version 6.1 output CFI, TLI, RMSEA, and SRMR are .94, .83, .10, and .04 respectively. In version 7.11 they are .87, .76, .12 and .09. Yet I have confirmed that it is the same exact model. I also had a friend who still has 6.1 rerun the model with consistent findings. 


Please send the two outputs and your license number to support@statmodel.com so I can see your model and estimator. 


Dr. Muthen, I've read through the forum and manual and can't find a reason for my issue. Using the MLR estimator, MPLUS doesn't provide an RMSEA. Using the MLM estimator on the same model, it does. Any possible reason for this that I can look into would be much appreciated. Thank you! 


Please send the output and your license number to support@statmodel.com. 


Good Evening Dr.s Muthen, I'm a newbie at Mplus and structural/simultaneous equation modeling and I am currently trying to run a CFA with count variables as my indicators however I am not receiving my CFI, TLI, and RMSEA. Obviously I am doing something wrong. Could you provide your insight? below is my code: Data: File is !LISTWISE=ON; Variable: NAMES ARE male crimeser hispanic black white curoffm curoffs curoffr curoffov curoffb curoffp curoffd curoffw curoffo prprison prsupvio reconv1 reconv2 reconv3 ageberec timeserv reimpr1 reimpr2 reimpr3 reimpr1n reimpr2n reimpr3n married emplstud female poliforc recon123 housserv educserv emplserv healserv housreco educreco emplreco STUDENT2 employ1 emplstat povrate unemploy unemrate passrate; USEVARIABLES ARE housreco educreco emplreco; COUNT IS housreco educreco emplreco; Missing are all .; Analysis: Type = GENERAL; Model: reenserv BY housreco educreco emplreco; OUTPUT: TECH1 TECH8; !standardized sampstat; 


Chisquare and related fit statistics are not available when means, variances, and covariances are not sufficient statistics for model estimation. This is the case with count variables. Nested models can be compared because 2 times the loglikelihood difference is distributed as chisquare. 

SY Khan posted on Tuesday, April 22, 2014  4:42 pm



Hi Dr. Muthen, I am running a CFA of my Independent variables with binary indicators using WLSMV estimator in Mplus version 7.11. Theory supports four correlated factors. All indicators load heavily onto their respective constructs (0.600.9). Their respective Rsqaured values are also above 0.38 and all cosnstructs have high discriminant validity (AVE); meaning that all constructs are different from eachother. However, the overall fit for the CFA remains low: Chisq= 4710.814 with df=318 RMSEA=0.072 CFI=0.878 TLI=0.865 One of the fators have low correlation (0.142, 0.109, 0.005) with other 3 factors, while the other three factors have interconstruct correlations of 0.668, 0.694 and 0.797. I have done an EFA also and as a large part of theory says the practices do not load in meaningful way as such based on theory. Hence, I have grouped practices based on theory. I have done individual CFA of the four constructs out of which three factors give good model fit of above 0.915 CFI/TLI based on the items grouped based on theory. Can you guide me on why the overall CFA model fit may be low when each construct has high factor loadings and AVEs and how to improve it? Could the low correlation of one factor may be the reason of not so good overall model fit? Is it appropriate to proceed with SEM based on these fit statistics? Many thanks for your help and guidance. 


The model fit is not good. The EFA results tell you that perhaps the items are not valid measures of the construct they were developed to measure. See the Topic 1 course handout and video where we go through an EFA in detail. 

j guo posted on Tuesday, May 27, 2014  11:56 pm



Hi Dr. Muthen, I ran a CFA model using robust maximum likelihood (MLR)as estimator in MPLUS. I was wondering if I can calculate RMSEA by hand based on ChiSquare, df and scaling correction factor. Thank you very much. 


Don't you have RMSEA in the output? Which version are you using? 

j guo posted on Wednesday, May 28, 2014  2:57 am



I do have RMSEA. I just wonder how to calculate it by hand based on MLR. Thank you. 


Dear Dr. Muthen, I was running a very simple CFA with 3 indicators and 1 factor. Is it right, that the model is justidentified so global model fit cannot be assessed? Or is it possible to modify one indicator, so that I get global model fit indices? And how do I have to act, if I use only 2 indicators – I know, that’s not possible normally, but I read, that it is possible to use it for a CFA with more than one factor? So is it right, that in this case I only report the global fit indices of the CFA with more factors? Thank you so much, K. Dehmel 


A model with three indicators is justidentified so model fit cannot be assessed. A model with two indicators is not identified. If it is in a model with another factor, it can be identified by borrowing information from other parts of the model. I would recommend having at least four indicators. 


J Guo The RMSEA with estimator=MLR is already adjusted. What you get in the output is based on the MLR chisquare value. 


Hi, I am running a multiple group analysis using latent variable A predicting an observed continuous variable b. I have 3 continuous control variables (all observed) included in the model as well. First, I ran the CFA with these model testing for measurement invariance, and the model fit was pretty good (CFI=.94, RMSEA = .045, etc) at each step. The chi square testing also confirmed each step of measurement invariance. The general input I used for CFA was: A BY v1 v2 v3 v4; A@1.0; v1 WITH v3; v3 WITH v4; b WITH A; However, when I moved into the SEM model(I swiched WITH to ON), where latent construct A is predicting manifest variable b, the model fit suddenly became poor, and chi square also became significantly larger. Here are my questions: 1) Why is this happening? 2) I've learned to compare my SEM model to strong invariance model to find out if my models are fitting well  given the significant change in the model fit/chi square, does this mean I cannot do this anymore? 3) Is there a way to fix this? 3) Is chi square testing still appropriate using model fit chi square? If not, what is the step for comparing models now? Thank you again for all your assistance! 


Please send the two outputs and your license number to support@statmodel.com. 


Dear Dr. Muthen, thank you so much for your fast answer. Now I specified a model, the model fit is good  could you please check, if it is right, I am not sure if such a model fit is possible cause of my small size of the sample. Could I send you my output? Thank you again! 


If you are a registered user with a current upgrade and support contract, send the output to support@statmodel.com. Although interpretation of results is not part of Mplus support, I can see if I see any glaring errors. 

Eulalia Puig posted on Thursday, February 12, 2015  2:50 pm



Hello, I am trying to run a secondorder CFA with continuous variables (scale is 05 for all variables). The model is: ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; MODEL: A by a1* a2 a3 a4; B by b1* b1 b3 b4;; C by c1* c2 c3 c4 c5 c6 c7 c8 c9; D by A* B C; A@1 B@1 C@1 D@1; And the output I get for model fit, which I what I am interested in is: MODEL FIT INFORMATION Number of Free Parameters 60 Loglikelihood H0 Value 4993.516 Information Criteria Akaike (AIC) 10107.032 Bayesian (BIC) 10271.204 SampleSize Adjusted BIC 10081.564 (n* = (n + 2) / 24) Degrees of Freedom 149 Where are the model fit indices? I thought that X2 & RMSEA would be given. I understand CFI & TLI have to be calculated, but where are the X2 and RMSEA? Thanks! 


Did you declare your variables as categorical? Did the H1 model not converge? If that doesn't explain it, please send your output to support along with your license number. 


Dear Linda, I have run a CFA using WLSMV on a small model  4 categorial indicators, one latent variable that was developed through an EFA. The fit statistics are good, but I"m wondering if they are too good. I've never had a model with these results: Chisquare 1.967 df = 2 p. = .374 RMSEA = 0.000 CFI = 1.000 The factor loadings are strong (.78.99) and error terms are small (.40.01). Could the model fit the data this well? Or could this indicate the model may be better represented as a composite model? Thanks, 


This can happen with small sample size and low correlations, so that you have low power to reject the model. 


Thank you. The sample size was 307, correlations .45.71. Should I keep this model or add in indicators that had previously worked in the model, but made the model fit less perfect. I have just run the model in the full sample of 614, but the outcome was the same. 


Getting rid of misfitting indicators can certainly cause such a good fit. I wouldn't do this kind of item trimming unless items have a truly bad fit. 


I have a question regarding model fit with different estimators. My question is to explain model fit discrepancy when I use ML vs. MLR. I ran an LGM with time invariant covariates. Model 1 was my basic model, and Model 2 added one additional (and theoretically relevant) time invariant covariate. With an ML estimator, my difference in ChiSquare test showed that Model 2 had significantly worse fit than Model 1. However, with a MLR estimator, my 2LL test showed that Model 2 had significantly better fit than Model 1. Question: Is the difference in these findings a reflection of skewed variables in my model? I'm just curious how different estimators can yield opposite results. Thank you for your help! 


If you did the MLRspecific 2LL difference test shown on our website, then the difference between the ML and MLR testing is due to the skewness. 


Hello, I am fitting a CFA model using the WLMSV estimator, using version 7.11. For some reason, when I use the command OUTPUT: Residual; I only get raw residual correlations; standardized and normalized values are not printed in the output. Can you think why this is happening? My MODEL command is: positive by clpersa3 clpersb3 clpersc3 clpersd3 clpersg3 clpersh3 clpersm3 clperso3; lacksupp by clperse3 clpersi3 clpersj3 clpersn3; And the factor items clpersa3  clpers03, are categorical (4 categories). Thanks, Dharmi 


Those are available only with continuous outcomes. 


Good night, I am working on a CFA for a scale. The data comes from 14 different schools, so I decided to use type=complex. When I treat the data as cluster, the RMSEA improves substantially but the CFI and TLI worsen substantially as well. So, my questions are if there is something related to clustering that helps RMSEA but harms the CFI/TLI? Should I look at other indexes? Last question is if apart from the modification indices, what else can I do to improve the model? Thanks! Laura Here you have the results: Nonclustered: RMSEA (Root Mean Square Error Of Approximation) Estimate 0.066 90 Percent C.I. 0.065 0.068 Probability RMSEA <= .05 0.000 CFI/TLI CFI 0.940 TLI 0.930 Clustered: RMSEA (Root Mean Square Error Of Approximation) Estimate 0.029 90 Percent C.I. 0.027 0.031 Probability RMSEA <= .05 1.000 CFI/TLI CFI 0.871 TLI 0.845 


There is no reason clustering would affect one fit statistic. With only 14 clusters, I would recommend using 13 dummy variables as covariates in the model to control for nonindependence of observations. The recommendation for clustered data is a minimum of 3050 clusters. 


Hi there, I am looking at the dimensionality of an attitude construct in two data sets, both of which contain ordinal measures. In the first data set I ran an EFA and found considerable evidence that there are two factors and after rotation it was clear that the items coalesced in a meaningful and substantively predictable way. I then attempted to confirm this two factor structure in a separate data set using CFA. The CFI (.975) and TLI (.968) all indicate good fit. But the chisquare is significant (p < .001, n  1,700) and the RMSEA also suggests poor fit (= .105). It is worth noting that when I run a one factor model the fit is substantially worse (CFI = .891; TLI = .91; RMSEA = .184). Because of this I followed some of your previous suggestions of going back and running an EFA on this data set and, again, there is a clear indication that there are two factors and that the items come together in a similar way to the first data set. What could explain why the models are fitting the data poorly in the CFA? Do you have any suggestions on how to proceed? 


I would go the route of the paper on our website: Muthén, B. & Asparouhov, T. (2012). Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17, 313335. See also Asparouhov, T., Muthén, B. & Morin, A. J. S. (2015). Bayesian structural equation modeling with crossloadings and residual covariances: Comments on Stromeyer et al. Accepted for publication in Journal of Management. 


Dear Bengt and Linda, I am doing a CFA with 10 categorical (Likerttype) indicators (WLSMV estimator), 4 firstorder factors and 2 secondorder factors in a sample of N=13,500, as shown below: f1 BY u1 u2; f2 BY u3 u4; f3 BY u5 u6; f4 BY u7u10; ff1 BY f1 f2; ff2 BY f3 f4; The overall model is identified and the estimation terminates normally. The model has 55 free parameters (chisquare = 587.55, df=30, p<.001). In contrast, the model with only 4 firstorder factors and no second order factors has 56 free parameters (chisquare = 593.960, df=29, p<.001). RMSEA, CFI and TLI indicate close fit for both models. 1. Do I understand correctly, that the secondorder factors are locally underidentified because I'd need >2 firstorder factors loading on each? 2. Elsewhere in this forum I read that such models are only identified since they "use information from other parts of the model". I wonder what that piece of information is and whether you have a reference for this? I fitted an alternative solution with only 2 firstorder factors that seems to do the trick without these problems, but I need to explain why the secondorder model is problematic because it has been reported in the literature before as the correct measurement model for this particular scale. Best wishes, Seb 


All first and secondorder factors with two indicators are identified only because they borrow from other parts of the model. They have negative degrees of freedom and are not identified when they are alone. See an SEM book like the Bolen book for a discussion of identification. 

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