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In my working paper, I have some questions about whether I should add some control variables in SEM. Some persons suggest that my paper has lack of control varialbes such as age, education background act as. However I found when I add these variblae (7 variables) in SEM the model fit reduces largely. According to many stuides published in top journal, maybe there are many advantages withouht adding control variables. But I do not know how to say the advantage. Can you help me to explain how to express the advantage without adding control variables in SEM? 


If you add covariates and the fit of your model becomes worse, this suggests a need for direct effects from the covariates to the factor indicators. If they are significant, this indicates measurement noninvariance due to differential item functioning (DIF). 

Haiqing Bai posted on Sunday, March 14, 2010  11:36 pm



Thank you Muthen. my mean is that I don't want to add these control variables in the SEM. How to explain the advantage? 


I cannot think of an argument to support not including the observed covariates. By not including them, you are assuming that the latent variables in the model have measurement invariance with respect to those covariates. The fact that direct effects are needed means that you don't have measurement invariance. 

Hewa G posted on Tuesday, August 09, 2016  6:04 pm



Dear Dr Muthen, My question is regarding the control variables. When I include a control variable (gender) with ON command both IV and DV, the control variable has a significant effect with IVs and DV. I tested model without control then the R2 (Rsquared) reduced in the model. What does this mean? Control variable is dummy coded. 


It sounds like you are comparing the 2 models: 1. DV ON IV; 2.a DV ON IV C; 2.b IV ON C; Are you comparing Rsquare for 1 with 2a? 

Hewa G posted on Tuesday, August 09, 2016  6:40 pm



Thank you for the reply. yes I'm comparing the model with and without control as indicated by 1 with 2a. l need to explain the significant effect of the control variable. What further analysis should I do? 

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