Message/Author 

Anonymous posted on Tuesday, October 12, 2004  12:35 pm



I am running a CFA and I'm wondering if it is possible to avoid having the path for the first item on each factor equal to 1. I would like to get factor loadings similar to those from an EFA. The MPlus user's guide mentions that there is an option for removing this restriction, but I couldn't find it. Thanks! 

Anonymous posted on Tuesday, October 12, 2004  1:33 pm



I guess if you use the option in the syntax: Output: Standardized. You get standardized loadings not equal but similar to those estimated in an EFA. But i haven't found yet the possibilty for a "Rotation" (Varimax...) in an CFA. With the @option in the syntax it should be possible to equal other factor loadings besides the first one to 1. 


Re: October 12, 12:35pm  see the BY option of the MODEL command in the Mplus User's Guide. There is a description of how to free the factor loadings for the first item and fix the factor variances to one. 


Re: October 12, 1:33 pm  CFA does not do a rotation because the model is already identified. You can do an EFA in a CFA framework. 

Anonymous posted on Wednesday, October 13, 2004  8:45 am



I am estimating a 3factor CFA, any suggestions on how to interpret the factor loadings? Secondly, what goodness of fit statistics should I be looking at? 

bmuthen posted on Wednesday, October 13, 2004  4:57 pm



Those are broad questions that you would have to turn to the literature for  or come to Day 1 of our upcoming short course. The website has several references related to factor analysis that can help with these types of questions. 

Yesi posted on Monday, May 09, 2005  3:12 pm



I am familiar with other SEM stats programs, but I am learning about Mplus in one of my classes this semester. When looking at factor loadings, I have been used to see them as being less than 1.0, similar to an R2, but in mplus I am getting factor loadings greater than 1.0 (e.g., 2.569), but also some that are definitely less than 1.0 (e.g., .844). How do I interpret these numbers? Thanks for your help. 


A factor loading is a regression coefficient. If factor loadings are continuous, they are simple linear regression coefficients and are interpreted as such. They can be greater than one. There is a discussion of this on the LISREL website under Karl's Corner. If the factor indicators are categorical, then the factor loadings are probit or logistic regression coefficients depending on the estimator used in Mplus. 


I measured a factor at two points in time with four indicators, respectively. The factors loadings (but not the indicator intercepts) are invariant over time. Now I want to construct a standardized test for that factor based on that findings. How can I use the factor loadings to construct a regression formula to compute the factor loadings from the indicators (in later studies)? Specifically, how do I account for the different indicator intercepts when building that formula? Or can I ignore them? 


Sorry, there's a mistake in my previous posting. Here's th correct version: I measured a factor at two points in time with four indicators, respectively. The factors loadings (but not the indicator intercepts) are invariant over time. Now I want to construct a standardized test for that factor based on that findings. How can I use the factor loadings to construct a regression formula to compute the factor VALUES from the indicators (in later studies)? Specifically, how do I account for the different indicator intercepts when building that formula? Or can I ignore them? 

Boliang Guo posted on Thursday, October 06, 2005  3:52 am



hello Michael Schneider, if you wanan compute factor score, why not use the MPlus to get it?fscoefficient in outpust 


Hi Boliang, I need the factor scores in studies were SEM is not appropriate (experiments with small samples). 

bmuthen posted on Saturday, October 08, 2005  11:59 am



The formulas for the regression method of computing factor scores are given in Appendix 11 of the Version 2 Technical Appendices. If you want to compare factor scores across time with respect to their level, I would work from a model with invariant intercepts as well. 

Tom Hardie posted on Wednesday, October 12, 2005  2:37 pm



I am doing a EFA in a CFA have examined the fscore file. Is there a way to export the subject ID to this file. It appears that several cased were dropped but I can not identify were to insert missing for a factor score for futher analysis. Thanks in advance 


See the IDVARIABLE option of the VARIABLE command. 

joe posted on Friday, October 14, 2005  6:07 pm



I would like to Validate a Questionnaire, I have the data collected from 300 patients, so i want some suggets on statistical analysis i can do, i know i can use factor analysis, but what other test can i do to validate the questionnaire. 


In Mplus, you could use factor analysis or regression analysis for predictive validity. There is a large literature related to various types of validity that you can see for further information. 

SH posted on Thursday, December 15, 2005  8:53 am



I am running a CFA (1 latent variable with 5 continuous indictors). I’d like to report all the significant level of the factor loadings so I freed the first indictor in the model: TYPE IS missing H1; MODEL: f1 BY x1* x2 x3 x4 x5 ; f1@0; But I got an error message: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 6. FACTOR SCORES WILL NOT BE COMPUTED DUE TO NONCONVERGENCE OR NONIDENTIFIED MODEL. Would you please tell me what’s problem? I also noticed the EST./SE for x2, x3, x4, x5 are different when x1 is fixed and x1 is freed. Which one should I use? Thank you very much! 


If you want all of the factor loadings to be free, then you need to set the metric of the factor by fixing the factor variance to one. f1@1; If this does not solve your problem, send your input, data, output, and license number to support@statmodel.com. 

SH posted on Thursday, December 15, 2005  9:26 am



Thank you very much for your help. BTW, would you please answer my second question? 


If the factor is in a different metric, the factor loadings will be different. 

SH posted on Thursday, December 15, 2005  10:56 am



Thanks, Linda. 

mcole posted on Saturday, January 28, 2006  7:52 am



In answer to the first question posted above: "I am running a CFA and I'm wondering if it is possible to avoid having the path for the first item on each factor equal to 1. I would like to get factor loadings similar to those from an EFA" add this output statement to your input OUTPUT: STAND; You will then report the StdYX values in the Model results as your factor loadings. 


Yes, this is described in the user's guide under the BY statement. You free the first loading by placing an * behind the factor indicator. 

JPower posted on Monday, May 08, 2006  3:41 pm



Hello, I am measuring 4 factors (five indicators each) at four time points in the same group of people. How do I evaluate whether there is measurement invariance over time? I assume that measurement invariance means that the factor loadings are invariant over time. Is this correct? Thank you. 


Whether you are assessing measurement invariance across time or groups, the steps are the same. See pages 345347 of the Mplus User's Guide that is on the website for a brief description of the steps to use for testing measurement invariance. 


When I fit a CFA model to my data, some of the standardized factor loadings were less than 1.0. I was told that standardized factor loadings greater that 1.0 might be indicative of a misspecified model. Is the negative (standardized) factor loading problematic too? 


Standardized factor loadings can be greater than one. There is a discussion of this on the LISREL website under Karl's Corner. If a raw coefficient is negative, it's standardized coefficient will also be negative. 


Thank you very much for your answer! 


Going back to Linda's posting on May 9, 2005 , quoted here "If factor loadings are continuous, they are simple linear regression coefficients and are interpreted as such....If the factor indicators are categorical, then the factor loadings are probit or logistic regression coefficients depending on the estimator used in Mplus." Just to clarify  if factor indicators are both categorical and continuous in the same CFA model, does this mean that the obtained loadings are linear regression coefficients for the continuous indicators and probit regression coefficients for ordinal (13 scale) indicators using the WLSMV estimator? 


Yes. 


Hello! I am running a CFA with 20274 observations and 5 factors, and getting acceptable model fit according to CFI and TLI, but RMSEA is little above acceptable 0.10 and WRMR is far from <0.90. Can this be explained? It's my first time I have to do CFA and I'm not sure if this result can be accepted or I have to try another model. Her is par of the output: TESTS OF MODEL FIT ChiSquare Test of Model Fit Value 19748.320* Degrees of Freedom 79** PValue 0.0000 ChiSquare Test of Model Fit for the Baseline Model Value 271312.327 Degrees of Freedom 10 PValue 0.0000 CFI 0.928 TLI 0.991 Number of Free Parameters 33 RMSEA 0.111 SRMR 0.041 WRMR 8.871 


I would be concerned about model fit with these contradictory fit statistics. I would start with an EFA to see if the items you have are behaving as you expect them to. 


Thank you for your answer. I now did EFA, wich shows, that there are probably no more than 2 factors, but if I run CFA on these 2 factors the fit statistics are even more contradictory. The same happens if I choose 1, 3 or 4 factors. I'm confused... 


I suspect that you have large crossloadings for some of your factor indicators so that when you go from EFA to CFA, this causes the misfit. If the factor indicators were developed to load on only one factor and they load on both, you might want to think about why this is happening. 


I'm a bit confused...is there a difference between factor loadings and factor scores? I understand that the obtained loadings in a CFA are regression coefficients (probit or logit) in the case of categorical indicators. But is there a difference between scores and loadings? If not, then I should just add the following to the output statement (OUTPUT: STAND;) to get loadings similar to what is obtained with an EFA? And use the loadings from the StdYX column? 


Factor scores are the estimated values on the factor variables for the individuals, so yes they are different than loadings. To get estimated factor loadings in the metric of EFA you should use StdYX. 


I have three ordinallevel indicators for a single factor at two levels. At the between level, the stdYX for all three indicators is 1.000. The std and the unstandardized estimates are not all the same. Does this make sense? TYPE=TWOLEVEL; ESTIMATOR=MLR; %Within% fw BY u1u3; %Between% fb BY u1u3; Thanks 


For categorical outcomes, the default is to set the residual variances to zero on the between level because each one represents a dimension of integration. You can free them if you want. 


Just to be certain that I understand: I thought that the setting of the residual variances to zero lead to rsquares of 1.0 for the factor indicators, but you're saying that this leads to the stdYX values being 1.0 also? Thanks. 


StdYX for a factor loading is equal to (factor loading * s.d. factor) divided by the square root of (factor loading squared times the factor variance plus the residual variance). See below for a factor loading of .5, a factor variance of 4, and a residual variance of 0: .5 * 2/ sqrt (.25*4 + 0) = 1 

Tracy Witte posted on Thursday, June 05, 2008  12:30 pm



Going back to the question about factor loadings being greater than 1, I thought that they were only regression coefficients in models that are NOT congeneric. Otherwise, I thought that they should be less than 1. I have a CFA with 2 factors (some variables are categorical and some are continuous) in which in indicator only loads onto one factor (i.e., it is congeneric). Some of my factor loadings are greater than 1  is this a heywood case? Are the factor loadings given in the mplus output standardized or unstandardized? Thanks! 


Factor loadings are always coefficients in linear regressions of each y on f's. With more than one factor that are correlated there is no need for loadings to be less than 1 even when the y variance is 1 (as when analyzing correlations); the residual variance can still be positive as required. With CFA, the y variance is typically not 1 and loadings can be big, certainly bigger than 1. Mplus reports unstandardized loadings unless you also request standardized ones. Heywood cases occur when residual variances are negative. 

Michael M posted on Friday, January 27, 2012  8:25 am



First  thanks for having such a great resource available to us modelers. I've run a CFA with categorical responses (dichotmomous) using the WLSMV estimator. I've got a standardized factor loading greater than 1 (and from what I understand, this is an indication of a negative residual variance). Is it possible to fix the residual variance to zero for this item? For some reason, I have it in my head that I can not do this with the WLSMV estimation. Thanks. 


You may have too many factors. Check your factor correlations in TECH4. Some may be very high. The residual variance is not a parameter in the model so you can't fix it. You could do this with the Theta parametrization but I'm betting the problem is with your model. 

Michael M posted on Wednesday, February 01, 2012  2:25 pm



Thanks Linda  again this is a great resource you provide to all of us. 

Lin Gu posted on Wednesday, February 08, 2012  9:15 pm



Does the product of two factor loadings in the same column of Lambda provides an estimate of the correlation between the two observed measures involved? 


Only of the corresponding variables don't load on other factors and the factor variance is one. 


Dear Dr. Muthen, In my CFA model with two latent variables (parent's and children's religiosity) measured by 4 items each, the (unstandardized) loadings of these items are 1.5 to 2.5 times higher in the full model (including moderations of the effect of one latent variable on the other), compared to the model in which only the CFA is specified. Is this problematic? If so, what can I do about it? All items are binary and the loadings are constrained to be the same for parents and children. The specification of the CFA is as follows: MODEL: relig BY cr1 (1) cr2 (2) cr3 (3) cr4 (4); parrelig BY pr1 (1) pr2 (2) pr3 (3) pr4 (4); Thank you very much for your help! 


The factor variances are probably different in your full model than in the CFA. This would make the loadings different. The standardized loadings should be more similar. 


hello if factor loading in CFA is less than 0.3 we must omitted that factor? thanks 


The size of a factor loadings depends on the scale of the factor and the variable. You should consider its significance. You don't omit a factor when a loading is small  you may want to omit the variable. 

Linh Nguyen posted on Friday, August 01, 2014  12:02 am



Acceptable loadings in a secondorder CFA model? Hi I am running CFA for a secondorder construct with 4 firstorder factors (measured by 14 observed variables). I am wondering what is an acceptable loading for firstorder factors in a secondorder CFA model? The loadings of 4 firstorder factors on the secondorder factor are: .70, .34, .46, .82 ( all significant at p<.001). Model fit: CMIN/df = 2.31, CFI =.93,RMSEA =.08, SRMR =.08. Should I keep the .34 loading? This firstorder factor is measured by 3 observed variables, so I cannot delete any observed variable. Thank you Kind regards Linh 


This question is better suited for a general discussion forum like SEMNET. 

M T posted on Monday, March 21, 2016  8:19 am



Hi, Is it possible to constrain the standardized factor loading of two items to be equal? I have used @(1) after the items but it gives me equal factor loading before not after standardization. 


No. Standardized loadings are computed after model estimation using standard deviations from each group. Unless all groups have the same standard deviations, the standardized loadings will not be the same. 


Dear MPLUS support, I performed a CFA with 6 indicators to measure one latent variable. I obtained 4 positive loadings, and 2 negative loadings. A good chisquare and good RMSEA. Do you think it's a problem to present a CFA with 2 negative loadings? should I reverse the 2 variables with the negative loadings to have positive loadings in the model? Because I knew that with some negative loadings we have a reliability analysis with terrible indexes. Is it true? I can not understand why negative loadings should be a problem. Many thanks Marco 


Negative loadings is not a problem unless you want to use them for reliability estimation. If you like you can reverse the variables. 


I am running structural equation models with a measurement model that contains categorical indicators. I have noticed that when I change which item is the reference variable with the loading set to 1 for each factor, the value of other estimated parameters changes. For example, there are differences in the values for structural path coefficients between the factors and outcome variable, factor variances, and factor correlations when I use different items as the reference variable. Why would this be the case? I would expect the other estimates besides the factor loadings to remain the same regardless of which item is used to scale the factor. If not, is there a recommendation on which item should be fixed to 1? For instance, is using the item that loads highest on the factor as the reference an appropriate choice? The model fit statistics do not differ. Because I plan to do multigroup analysis, I do not intend to use standardized values since the group variances may differ, so I'm trying to determine which output I should be relying on. 


Different choices of loadings to fix give different metrics for the factor. This is the reason that structural parameters change. I would choose the largest loading. 


Thank you. Would you also say the same applies for choosing the path to fix in multiple group comparisons? 


It is better that you ask this general modeling strategy question on SEMNET.b 

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