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In a multiple group problem that is a CFA of a set of dichotomous items, I would like to constrain the residual variances to invariance over groups. The manual discusses equality constraints in the multiple group context on pp.7980. I do not want to constrain the residual variances to equality within the groups; only crossgroup constraints are desired. Unfortunately, it is not clear from the manual how this would be done in the multigrp case. My idea is that, for y1, y2, y3 (say), you would specify in the general model command: MODEL f1 by y1y3; y1 (1) y2 (2) y3 (3); This would, I thought, introduce invariance without also producing withingroup equality. But it doesn't work; the program gives an error. So how is it done? 


There are two issues here. First, with categorical outcomes, residual variances (Theta diagonal elements) do not enter into the model. Their values are computed as "remainders", see Appendix, page 271. This is because correlation matrices are analyzed, so that the diagonal does not enter into the computations (does not carry information). So, these residual variances cannot be held equal over groups as in the continuous case. There are scale factor parameters than can be worked with, but they refer to the inverted y* s.d.'s and are therefore functions of several parameters. The second issue has to do with between and within group equalities. One note here is that only one equality () can be specified per line. MODEL: f1 BY y1y4; y1y4 (1); specifies that the residual variances of continuous outcomes y1y4 will be held equal both within and between groups. MODEL: f1 BY y1y4; y1 (1); y2 (2); y3 (3); y4 (4); specifies that the residual variances of continuous outcomes y1y4 are equal across groups but not within groups. 

Feng Tian posted on Thursday, April 10, 2008  9:18 am



I have a question also related to constraining the residual variances. I tried the following approach to constrain the residual to be equal across both groups, MODEL: f1 BY y1y4; y1 (1); y2 (2); y3 (3); y4 (4); but when I checked the output I found that the residual variances are not equal across groups. For the first group, they are all 1s (one)s but for the second, they seem like free estimates. Why does this happen? 


It sounds like you have categorical outcomes and are using the Theta parameterization in which case residual variances must be fixed to one in one group. If this is not the case, please send your input, data, output, and license number to support@statmodel.com. 

anonymous posted on Thursday, April 10, 2008  9:52 am



Yes, I have categorical data and use Theta parameterization. How do I constrain the residual variances to be equal in this case? 


The comparison is of a model with residual variance one in one group and free in the other groups to a model with the residual variances fixed to one in all groups. 

anonymous posted on Thursday, April 10, 2008  12:01 pm



so how to fix residual variances to one for all groups? I followed e.g 12.10 (equalities in a multiple group analysis) with model: y1y4 (1); which should hold residual variances of y1 to y4 equal to each other and equal across groups. but still the output shows the residual variances fixed to one only for one group not the other. Is this because that example is for continuous variables? and how to fix residual variances to one for all groups or constrain them to be equal across groups? 


y1y4@1; 


I am trying to test invariance of uniqueness across two groups in multiplegroup EFA. My indicators are continuous. When I tried to model, say: f1f3 BY y1y12 (*1); y1y12@1; I got a message saying the residuals cannot be fixed. What is the correct way to test invariance of residuals in EFA models? 


The correct way is to compare a model with the residual variances free across groups to a model with them held equal across groups. f1f3 BY y1y12 (*1); y1y12: versus f1f3 BY y1y12 (*1); y1 (2) y2 (3) y4 (4) y4 (5); 


I was hoping to confirm the syntax for longitudinal invariance with categorical indicators. Following the user guide (p.485) I constrained factor loadings and thresholds in tandem. I am using the theta parameterization and the chi square diff test. So as I understand it the factor mean of the first factor needs to be fixed to zero and the variances of all factors fixed to 1. I believe the syntax below reflects this. Also, I have seen examples where people have added syntax to the configural model, though this was for multiple group approaches so I am not sure if it applies. Configural: sport3 by oshwsw3 ostcsw3 oseesw3; sport5 by oshwsw5 ostcsw5 oseesw5; sport6 by oshwsw6 ostcsw6 oseesw6; sport7 by oshwsw7 ostcsw7 oseesw7; sport8 by oshwsw8 ostcsw8 oseesw8; (cont. below) 


Constrained model: sport3 by oshwsw3 ostcsw3 oseesw3 (12); sport5 by oshwsw5 ostcsw5 oseesw5 (12); sport6 by oshwsw6 ostcsw6 oseesw6 (12); sport7 by oshwsw7 ostcsw7 oseesw7 (12); sport8 by oshwsw8 ostcsw8 oseesw8 (12); [ oshwsw3$1 oshwsw5$1 oshwsw6$1 oshwsw7$1 oshwsw8$1] (3); { oshwsw3@1 oshwsw5@1 oshwsw6@1 oshwsw7@1 oshwsw8@1} (4); [ ostcsw3$1 ostcsw5$1 ostcsw6$1 ostcsw7$1 ostcsw8$1 ] (5); { ostcsw3@1 ostcsw5@1 ostcsw6@1 ostcsw7@1 ostcsw8@1} (6); [ oseesw3$1 oseesw5$1 oseesw6$1 oseesw7$1 oseesw8$1 ] (7); { oseesw3@1 oseesw5@1 oseesw6@1 oseesw7@1 oseesw8@1 } (8); [sport3@0 sport5 sport6 sport7 sport8]; sport3@1 sport5@1 sport6@1 sport7@1 sport8@1; 


Hi Linda, I am trying to run a Multiplegroup CFA with categorical variables (one latent variable and 15 items) using the Model=config metric scalar. However, although I think I follow all the necessary steps, I continuously get the following message: Measurement invariance testing with MODEL=METRIC is not available when categorical outcomes are binary using the WLSMV estimator because the model is not identified. Use MODEL=CONFIGURAL or MODEL=SCALAR, or use PRAMETERIZATION=THETA and constrain the residual variances to be equal across groups by fixing them at one for all outcomes in all groups. My syntax is: data: file is Response Time_PGAT AN scale.dat; variable: names are ID Gender an1 an2 an3 an4 an5 an6 an7 an8 an9 an10 an11 an12 an13 an14 an15 an_rt1 an_rt2 an_rt3 an_rt4 an_rt5 an_rt6 an_rt7 an_rt8 an_rt9 an_rt10 an_rt11 an_rt12 an_rt13 an_rt14 an_rt15 an_rttot; USEVARIABLES ARE an1 an2 an3 an4 an5 an6 an7 an8 an9 an10 an11 an12 an13 an14 an15; CATEGORICAL ARE an1 an2 an3 an4 an5 an6 an7 an8 an9 an10 an11 an12 an13 an14 an15; GROUPING IS Gender (1=Males 2=Females); analysis: TYPE is general; PARAMETERIZATION=THETA; MODEL=CONFIG METRIC SCALAR; model: f1 by an1* an2 an3 an4 an5 an6 an7 an8 an9 an10 an11 an12 an13 an14 an15; f1@1; an1an15@1; output: sampstat residual ; 


The message portrays the situation correctly. 


So, what I do wrong? Why I do not get any results? Best, Ioannis 


Because Model=Metric is not available here, just say Model=config scalar; 


Ok. Thanks a lot. 

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