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I am running a CFA with ordered categorical data using Mplus 5.1 and trying to test threefactor and fourfactor solutions. I am finding generally acceptable (but not great) fit for the CFI, TLI, and RMSEA but poor fit for the WRMR  one of my colleagues tells me I can also obtain the SRMR  but I cannot figure out how to request the SRMR. It does not show up in my output  here is a sample: CFI/TLI CFI 0.900 TLI 0.939 Number of Free Parameters 42 RMSEA (Root Mean Square Error Of Approximation)Estimate 0.084 WRMR (Weighted Root Mean Square Residual) Value 1.571 Is there any way to request that the SRMR also be calculated? Dave Kosson 


When SRMR is available it will be given automatically. 


What I do not understand is why SRMR was available in the older version of Mplus but is not available in the current version  that is, i am using Mplus 5.1 and I do not get the SRMR  One of my colleagues has Mplus 4.21, and he gets it: here is his output for the 3factor model: CFI 0.922 TLI 0.955 Number of Free Parameters 16 RMSEA (Root Mean Square Error Of Approximation) Estimate .078 SRMR (Standardized Root Mean Square Residual) Value 0.060 WRMR (Weighted Root Mean Square Residual) Value 1.553 Here is my output with version 5.1: CFI 0.922 TLI 0.955 Number of Free Parameters 42 RMSEA (Root Mean Square Error Of Approximation) Estimate 0.078 WRMR (Weighted Root Mean Square Residual) Value 1.345 Has the program changed in some way so that the SRMR is no longer appropriate but used to be considered appropriate? I also noticed that the number of free parameters seems to be different  it appears that now Mplus counts the number of items as part of the number of parameters? Dave Kosson 


Between the two versions you mention, TYPE=MEANSTRUCTURE became the default. SRMR is not available in this situation. Add MODEL=NOMEANSTRUCTURE to the ANALYSIS command to run the model without means. 


Linda, Thanks. That may be what I need to do. However, it is not currently working  here is the syntax i tried to use: VARIABLES: NAMES ARE r1pcl1 r1pcl2 r1pcl3 r1pcl4 r1pcl5 r1pcl6 r1pcl7 r1pcl8 r1pcl9 r1pcl10 r1pcl12 r1pcl13 r1pcl14 r1pcl15 r1pcl16 r1pcl18 r1pcl19 r1pcl20 misgrp; MISSING = *; USEOBSERVATIONS ARE (misgrp eq 0); MODEL: f1 BY r1pcl1 r1pcl2 r1pcl4 r1pcl5; f2 BY r1pcl6 r1pcl7 r1pcl8 r1pcl16; f3 BY r1pcl3 r1pcl9 r1pcl13 r1pcl14 r1pcl15; ANALYSIS: TYPE = GENERAL; MODEL = NOMEANSTRUCTURE; I was using this so that i could use the same dataset for my primary analyses that do not include cases with missing data and for supplementary analyses that include estimation of missing data. However, it did not work  here is the message I got: *** WARNING in ANALYSIS command MODEL=NOMEANSTRUCTURE is not allowed in conjuction with TYPE=MISSING. Request for MODEL=NOMEANSTRUCTURE will be ignored. 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS Is there a way to do this without MEANSTRUCTURE? Dave 


I think you need to also add LISTWISE=ON; to the DATA command. 


That was a big help. I was able to complete all my analyses that did not include missing values using this approach. Now, I am wondering if there is a way to run an analysis without using mean structures that does include missing values  that is, my colleague has been able to run such an analysis in Mplus 4.21, but the following warning makes me think it may not be possible in Mplus 5.1  *** WARNING in ANALYSIS command MODEL=NOMEANSTRUCTURE is not allowed in conjuction with TYPE=MISSING. Request for MODEL=NOMEANSTRUCTURE will be ignored. Dave 


I don't think your colleague was able to to this in Version 4.21. TYPE=MISSING has always included meanstructure. Having unstructured means is the same as having no means. 


Linda, I think you are correct. My colleague now realizes that he was mistaken about this issue. I am guessing that this means that there is no way in Mplus to estimate missing values without using mean structures. I have one additional question. The final step of my project is to conduct multigroup CFAs to compare the fit of the models across groups  e.g., for one of these, we are comparing equivalence of the models in North American versus European samples. Once again, i would prefer to do these analyses without using mean structures, if possible. My reading suggests that it is possible to conduct multigroup CFAs that do not use mean structures, but I am having trouble getting Mplus to allow this  even though I am limiting my multigroup analyses to cases with full data. Is there a way to do this in Mplus? Dave 


You cannot exclude means from the analysis with TYPEMISSING. However, if the means are unstructured, the fit will be the same as for a model without means. With multiple group analysis, to obtain an unstructured mean model, relax the default equality of the intercepts across groups and fix the factor means to zero in all groups. This is the same as not having means in the model. 


With respect to the multiple group analysis, my impression is that with ordered categorical data, thresholds are modeled rather than intercepts  so instead of relaxing the equality of the intercepts across groups, should i allow the thresholds to vary freely across groups? (For my dataset, each indicator has three possible scores (0, 1, and 2), so I think I do this by mentioning the thresholds in a 2nd MODEL paragraph that is specific to the 2nd group  e.g., if Europe is my 2nd group, I have a 2nd paragraph that says: MODEL Europe (after my general model paragraph) and then specify: [u1$1]; [u1$2]; for each indicator for which i want to let the thresholds vary  Does that sound right? 


Correct. If you have ordered categorical variables, you need to free all of the thresholds as you show. You should check the results or TECH1 to be sure you have successfully achieved your goal. 


And if I fix the factor means to 0 in each group (as I did), does that mean that the multigroup CFA will not examine whether there are differences between the two groups in the average levels of the latent factors? If so, then I think that means that the only difference between the model in which I allow the groups to differ on parameters (i.e., loadings and thresholds but not factor means) and the model in which i constrain the parameters to be the same is that, in the more constrained model, I require that the loadings be the same in the two groups  but i still allow the thresholds to differ. Does that sound right? 


Yes. Yes. 

David Kosson posted on Wednesday, September 01, 2010  8:21 am



Thanks again. I have now run all the multiple group CFAs and the results suggest a lack of invariance. I am sorry to say that I still have two questions for you. 1) Is there any evidence that the software is overly sensitive to failures of invariance so that people should not worry too much about a small degree of variance  e.g., in one case, the result of the chisquare difference test is fairly close to .05  ChiSquare Test for Difference Testing Value 19. Degrees of Freedom 9** PValue 0.0249 2) Given that I expect the mean levels of the latent factors to differ between the two groups, I am now wondering if it is possible to run the analysis without setting the means of the latent factors to 0 in both groups but allowing the program to estimate the means? And if I do that, would any differences between the groups in the levels of the factor means lead to a lack of invariance? 


1. I don't of any formal study of this. You might do a literature search to see if you can find anything or ask on SEMNET. 2. To estimate factor means, thresholds must be held equal across classes. This is the Mplus default for multiple group modeling. Comparing means across groups requires threshold invariance. 


Hello Linda and Bengt, Can you point me to the technical details behind why there is an incompatibility between missing data methods and no mean structure (e.g. NOMEANSTRUCTURE is not possible with TYPE=MISSING). Thanks, Leslie 


See Muthén, B., Kaplan, D. & Hollis, M. (1987). On structural equation modeling with data that are not missing completely at random. Psychometrika, 42, 431462. which you find on my UCLA web site. This article shows that ML estimation under MAR involves a mean structure which cannot be ignored if you want ML estimates. 

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