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I am trying to fit a bifactor model of intelligence for the WISCIV using the following model specifications: VIQ by sim vocab comp; PIQ by bd pc matreas; WM by ds lns; PS by dsc ss; g by sim vocab comp bd pc matreas ds lns dsc ss; g with viqps@0; viq with piqps@0; piq with wmps@0; wm with ps@0; However, the model gives the following error: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 28. THE CONDITION NUMBER IS 0.986D17. Any suggestions on what is going wrong? 


When specific factors have only 2 indicators you cannot identify the loading for the second of those indicators. Think of the specific factor as absorbing a residual correlation between those 2 indicators  there is only 1 such correlation and therefore you can only identify 1 parameter, in this case the specific factor variance. 

Li Lin posted on Tuesday, March 02, 2010  12:35 pm



Hi, Can bifactor model be used in EFA? If it can, could you provide an example with Mplus code? Thanks! 


The bifactor model is a CFA model, not an EFA model  it imposes more than m^2 restrictions. There is a general factor and uncorrelated specific factors. Or am I misunderstanding your question? 

Li Lin posted on Tuesday, March 02, 2010  1:19 pm



Thanks, Dr. Muthen. You have got my question correctly. I saw bifactor model was included in "Results of different exploratory factor models" Table in this paper "The role of the bifactor model in resolving dimensionality issues in health outcomes measures" (http://www.springerlink.com/content/jh561175967n4503/), and wondered. 

Kätlin Peets posted on Wednesday, February 23, 2011  8:25 am



We are interested in testing the degree of subjectspecificity versus subjectgeneralizability of motivational constructs. We are comparing secondorder factor models with bifactor models. We are not sure about the interpretation though. What can we say about subjectspecificity of a construct if the secondorder factor model does not worsen the fit compared to the bifactor solution? We also have another question. If we find that a bifactor model fits the data best but subjectspecific factors do not have significant variance, should we still prefer this model over the others? In addition, as our sample size is not very high (less than 200), can the low variance estimates be influenced by sample size? 


I don't know how much power there is to reject a secondorder model in favor of a bifactor model under various circumstances. For one thing, it depends on how many items you have per specific factor  at some point the models are not distinguishable. You want to read the literature on this, such as the Yung, Thissen, McLoad (1999) Psychometrika article. Or do a simulation study. You would want the specific factor variances to be substantial relative to their SEs, but you are right that a small sample may not produce that in which case you can still argue for the model. Again, a simulation study might shed more light. 


Hello, I am running a bifactor CFA with categorical indicators; this is to examine whether PTSD items load onto both a general factor and specific symptom factors. I have fixed the correlations of the general factor with the symptom factors at zero. Do I need to fix the correlations of the symptom factors with eachother at zero? Conceptually, it makes sense that they would be correlated. However, in all the examples the lowerorder factors are fixed to be uncorrelated. MODEL: f1 BY u1u5; f2 BY u6u7; f3 BY u8u12; f4 BY u13u17; f5 BY u1u17; f5 WITH f1f4@0; Could you shed some light on this? Thank you very much for your continued help! Sheila 


In general, I don't think the correlations among the specific factors are identified. If you ask for Modindices when they are fixed at zero, you can see if any MIs are nonzero which would indicate that they could be identified. 


We are working on a bifactor CFA we received a warning that the model may not be identified and the parameter involved is the in the PSI matrix between anger and psych. Is there an issue with the input syntax? Thanks in advance. ANALYSIS: ESTIMATOR=WLSMV; processors = 8(starts); MODEL: FEAR by P_023 P_022 P_019 P_020 P_018 P_008 P_015 P_017 S_067 S_065 S_068 P_101 P_102 S_066 S_015; ANGER by P_054 P_052 P_051 P_056 P_047 P_055 P_049 P_046 P_045 P_048 P_050 P_059 P_057 P_058; OVER by P_007 P_004 P_061 P_012 P_011 P_064 P_118 P_067 P_063 P_112; COG by P_105 P_090 P_084 P_106 P_095 P_085; PSYCH by P_023 P_022 P_019 P_020 P_018 P_008 P_015 P_017 S_067 S_065 S_068 P_101 P_102 S_066 S_015 P_054 P_052 P_051 P_056 P_047 P_055 P_049 P_046 P_045 P_048 P_050 P_059 P_057 P_058 P_007 P_004 P_061 P_012 P_011 P_064 P_118 P_067 P_063 P_112 P_105 P_090 P_084 P_106 P_095 P_085; OUTPUT: standardized res TECH1 TECH2 modindices; 


In general, the correlations between the specific factors need to be fixed at zero. Also, the correlations between the specific factors and the general factor need to be fixed at zero. In a model where therefore all factor correlations are fixed at zero, you can specify this conveniently by saying Model=nocovariances; See the V6 UG pages 540541 


This worked. Thank you very much. 

Joshua Isen posted on Thursday, October 25, 2012  5:39 pm



I'm implementing a bifactor model where the correlations amongst all factors are fixed at zero. (There are no other variables/covariates in the model besides the factor indicators.) The Mplus output indeed confirms that all factor correlations are zero. However, when I save the data as Fscores, and then simply use these factor scores in a followup analysis, the correlations amongst factor scores are nonzero. This seems puzzling to me. Why is this happening? 


Estimated factor scores do not behave like true factors unless they are very well measured. See for example: Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563575. 


The correlations among the factors in the model and the correlations using factor scores are not the same unless factor determinacy is one. 

Joshua Isen posted on Saturday, October 27, 2012  1:03 pm



Thank you for the reference. I assume the "quality" of my estimated factor scores is based on the factor determinacies. Since there seems to be a rule of thumb that determinacies < .80 are unreliable, this suggests that I shouldn't use my estimated factor scores for further analysis. 


Drs. Muthen, We ran a bifactor analysis to specify a new measurement model. The bifactor model fits better than any other plausible model we have compared it to, but we get an error that the residual covariance matrix is not positive definite. When I check the residual variances for the estimated R^2, there is one small negative residual variance (.09 for a 17item model and .14 for a 15item model). Also, the item with this problem has a loading on its content factor of .94 and .96 respectively, which seem questionably high. Should we be concerned with this? If so, what are some possible solutions? Some other models we have tried that eliminate this message include: 1) Using THETA parametrization, which gets rid of this error message, and also reduces the factor loading on the content factor to .87. However, we are unsure about the implications of this switch and whether it is a legitimate "fix." 2) Freeing the item factor loadings and fixing the factor variances to 1 and factor means to 0, as well as allowing the content factors to correlate. This reduces the standardized content factor loading for the item in question to .76. This, however, complicates multiple group analyses. Also, we did run the model as continuous data and got the same warning. In this model, the same item's residual variance was not estimated, and again the residual variance for the estimated R^2 was negative and small. 


Perhaps you want to try bifactor EFA to see if there should be modifications to your bifactor CFA model. 

Li Lin posted on Wednesday, January 23, 2013  12:17 pm



I am trying to fit a bifactor model using the following model specifications: model: VULD by SFVULb SFVULj SFVULc SFVULk SFVULd SFVULl SFVULh SFVULm SFVULi SFVULn SFVULe SFVULo SFVULf SFVULp SFVULg SFVULq; LABD by SFVULb SFVULj SFVULc SFVULk SFVULd SFVULl SFVULh SFVULm SFVULi SFVULn; CLID by SFVULe SFVULo SFVULf SFVULp SFVULg SFVULq; VULD with LABDCLID @0; LABD with CLID @0; However, error message appeared in output  "NO CONVERGENCE. NUMBER OF ITERATIONS EXCEEDED." Any suggestion to fix this? 


Please send output to support@statmodel.com 


I have more like a couple of questions about the bifactor model than a problem per se. I am using the factors in my bifactor model as predictors in a survival analysis. Given that the factors are all constrained to be orthogonal to me, it seems to me that there is no need to run a model with all of them entered simultaneously as predictors given that the results shouldn't be different for a set of orthogonal predictors than the zeroorder results for each predictor entered by itself. Does that make sense? I hope so as given that there are several factors (13 actually) in my bifactor model there are too many integration points for memory capacity when I do try to enter all the factors simultaneously as predictors to try to confirm my intuition. When I use Monte Carlo integration with 5000 integration points to run the full model, the results do differ from the zeroorder results for each predictor entered by itself. Is the Monte Carlo integration accounting for this pattern going contrary to my intuition? Or is my intuition just wrong in the first place? Thanks! 


Try it out for a model with only 2 orthogonal factors. With 13 factors the Monte Carlo integration may not be very precise. 


I have a similar question as Richard E. Zinbarg. I have a bifactor model with uncorrelated three specific personality factors and a general personality factor. I want to know the unique predictive value of each of the variables on Y. The results do not make sense when I examine the three specific and the general factors simultaneously as predictors of Y (i.e., the sign of the specific factors become reversed but remain significant compared to the model without the general factor). Is it redundant to examine them simultaneously as predictors of they are technically supposed to be orthogonal? Why might my results be changing in this odd way? 


This should work given that all 4 factors are uncorrelated. You may be interested in the article by Gustafsson & Balke in MBR 1993 where they discuss such prediction. 


I am trying to fit a bifactor model in which one of the specific factors has only two indicator variables. I note this advice from Dr Muthen (May 11 2008): When specific factors have only 2 indicators you cannot identify the loading for the second of those indicators. Think of the specific factor as absorbing a residual correlation between those 2 indicators  there is only 1 such correlation and therefore you can only identify 1 parameter, in this case the specific factor variance. I have been trying various strategies, such as constraining the loadings on the specific factor to be equal or both one, but without success. Is there a sensible way to proceed in this case? Thanks. 


Equality of loadings should work. Please send input, output, data, and license number to support. 


I estimated a bifactor model with categorical indicators. There are two specific factors and one general factor, and all factors are uncorrelated. This model fit the data well. I am using the latent factors as outcome variables and I have found significant interactions in predicting the latent factors. However since the latent factors have categorical indicators, I read that I won't get an intercept for the analysis nor will specifying [factor] produce the intercept coefficient. I would like to obtain the intercept so I can interpret the interaction effect. I tried a "trick" specified in a previous post of putting a factor behind each observed variable (e.g. f1 by item1@1; item1@0;) and then used these factors as the indicators. I used the theta parameterization. However, the model would not run and I get this error message: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. Any suggestions or ideas of what I may be failing to do in order to get the model to run? Or why the model won't run? I have 34 indicators. All 34 load onto the general factor and 8 and 24 items on the specific factors, respectively. 


You don't need to estimate an intercept to interpret an interaction effect. The factor intercept is zero. 

wong hua posted on Friday, September 13, 2013  6:37 am



I'm trying to fit a bifactor model. I was trying this command: TITLE: bifactor analysis DATA: FILE IS listening.dat; VARIABLE: NAMES ARE y1y5; ANALYSIS: ESTIMATOR = MLM; MODEL: g BY y1y5; f1 BY y1y3; f2 BY y4y5; g with f1 f2@0; f1 with f2@0; Mplus gives the follwong error: THE DEGREES OF FREEDOM FOR THIS MODEL ARE NEGATIVE. THE MODEL IS NOT IDENTIFIED. NO CHISQUARE TEST IS AVAILABLE. CHECK YOUR MODEL. THE MODEL ESTIMATION TERMINATED NORMALLY WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE G. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. I've seen that you answered a same question, suggesting that equality of loading should work. But I don't know how to set equality of loading. Can you give an example? Thank you. 


The problem is that g with f1 f2@0; does not fix the covariance of g with f1 at 0. Try g with f1@0 f2@0; 

wong hua posted on Sunday, September 15, 2013  7:15 pm



I tried the following command, as you suggested, TITLE: bifactor analysis DATA: FILE IS listening.dat; VARIABLE: NAMES ARE y1y5; ANALYSIS: ESTIMATOR = ML; MODEL: g BY y1y5; f1 BY y1y3; f2 BY y4y5; g with f1@0 f2@0; f1 with f2@0; but it still didn't work,Mplus gives the follwong error: 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 19. 


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

Tyler Moore posted on Friday, November 22, 2013  9:58 am



I have a bifactor measurement model within an SEM, in which a single predictor is "causing" all of the latent factors. Because the measurement model changes when I change predictors, I've fixed all paths within the measurement model (based on the coefficients estimated with no predictor at all). So, I believe the only things being estimated in my SEM are the paths from the predictor to the latent variables (and the residual variances of said latent variables). This model runs fine, and the path coefficients are reasonable. However, I noticed that when I remove one of the paths from the predictor to a latent variable, the remaining paths change (sometimes substantially). Do you know why this is happening? Thanks! 


I would not fix the measurement parameters because they change when adding predictors. That is a sign that you have direct effects from some predictors to some indicators, that is, measurement noninvariance. Instead, explore the need for direct effects. With a bifactor model I can imagine that paths change as you describe because the factors are defined relative to each other  for instance if the general factor changes due to changing which predictors point to it, the specific factors change meaning and therefore their their relationships to predictors change. 

jml posted on Wednesday, January 29, 2014  10:40 am



Dear Drs. Muthen, I am attempting to fit a bifactor model with two specific factors, but where some items only load on the general factor (as opposed to the general factor and one specific factor). I hadn't heard of this being done before, but saw it recently in Cai, Yang, and Hansen (2011) Generalized fullinformation item bifactor analysis, and I think it would make theoretical sense in my case. However, I can't get the model to converge. My (abbreviated) model and analysis statements are: MODEL: G BY Quant1 Quant2 Quant3 Quant5 Qual1 Qual2 Qual3 Qual4 Ctrl1 Ctrl5 Ctrl6 Dis2 Dis3; DISTRESS BY Ctrl1 Ctrl5 Ctrl6 Dis2 Dis3; ENGAGED BY Quant3 Quant5 Qual1 Qual2; G WITH DISTRESS@0 ENGAGED@0; DISTRESS WITH ENGAGED@0; ANALYSIS: TYPE IS GENERAL; ESTIMATOR IS ML; ALGORITHM IS EM; ITERATIONS = 1000; CONVERGENCE = 0.00005; Can you see any obvious mistakes? The items that should not load on any specific factor are Quant1, Quant2, Qual3, and Qual4. I use Mplus 6.12. Thank you! 


That should work fine and is generally speaking a good idea given that it more clearly defines what the general factor is. Please send output and data to Support. 


Hello Dear Prof. Muthen I'm trying to fit a bifactor model. How I can to obtain, percentage of variance accounted for by general and group factors. Thanks! 


You can divide the sum of the squared factor loadings by the sum of the variances of the factor indicators. This works because all factors are uncorrelated. 


You can do this using MODEL CONSTRAINT. 


Dear Prof. Muthen, I'm trying to run a bifactor model with dichotomous indicators, which, unfortunately, does not converge. However, a second order (hierarchical) factor model (with the generic factor of the bifactor model as second order factor) runs without problems. Could you please help me? Thanks in advance. Marloes 


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

Ted Fong posted on Tuesday, April 01, 2014  3:10 am



Dear Dr. Muthén, For bifactor modeling, Mplus 7.11 allows bifactor EFA (ESEM), CFA, and BSEM. I would like to ask if one can perform a Bayes bifactor EFA? I have tried running a bifactor EFA using Bayes estimator but the output file is blank despite running for nearly 20,000 iterations. Is Bayes estimator available for bifactor EFA yet? If not, is WLSMV currently the only feasible choice for 20 categorical indicators with 4 latent factors? Thanks a lot, Ted 


Please send the data, input and license number to Support@statmodel.com. 

jtw posted on Thursday, May 01, 2014  8:32 am



Hi there, I have estimated a bifactor structural equation model predicting an external variable (Y) with the general (g) and specific factors (f1  f6) obtained through the bifactor specification. Can one use all seven factors (g and f1f6) to predict an external variable? While I have seen this done in examples, my reservations about using all of the factors at the same time comes from the literature. Specifically, Chen et al. (2006, MBR) note that "only a limited set of domain specific factors may be included with the general factor in the prediction of an external criterion. Otherwise, exact linear dependence of the predictors will result and the model cannot be properly estimated. Most current structural equation modeling software does not include adequate checks to reliably detect this problem." Any insights into what the problem actually is? Also, does Mplus detect this problem if it exists? Thank you in advance for your time. 


Typically, g, f1f6 are all uncorrelated so I don't see the problem. See the Gustafsson and Balke (1993) article in MBR for applications. 


Hi I have been running some bifactor models and have a question about the identification of the correlations between the specific factors. One model has three specific factors (each has about 10 indicators) and a general factor on which all items load. The model seems to run fine when the specific factors are specified to be uncorrelated (and uncorrelated with the general factor) and also when specified to be correlated (and uncorrelated with the general factor). Also, when the correlations are fixed to zero Mplus produces modification indices for the factor correlations. I’m still concerned about identification as most of the literature I’ve read suggests that these correlations may not be identified. I’d be interested in your views on this. All models are estimated using WLSMV. Regards, Mark 


You can identify correlations among your specific factors if they are uncorrelated with the general factor. Correlations between specific and the general factor are not in general identified. You can find applicationoriented writings on this when searching for GustafssonBalke (in MBR?) Bifactor EFA is a special case where you can read more about identification; see the JennrichBentler 2011 and 2012 Psychometrika articles referred to in our UG. 

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