Assumptions such as linearity of rela... PreviousNext
Mplus Discussion > Structural Equation Modeling >
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 Elina Dale posted on Saturday, October 19, 2013 - 3:16 pm
Dear Dr. Muthen,

I've just realized that unlike with regression models where we have observed predictors and outcomes, in SEM I do not know exactly how to check the assumptions such as linearity of relationship between factors (predictors in this case) and an observed outcome.

I am modeling motivation factors as predictors of intention to stay (measured as observed continuous variable). I am not sure how to check in MPlus after I run my model whether assumptions of the model hold. I can see global fit indices but they don't show how well our assumptions (including linearity) hold, do they?

Thank you very much for your guidance and help!!!!
 Bengt O. Muthen posted on Saturday, October 19, 2013 - 9:35 pm
That's right, global fit indices don't tell you if structural relations are linear or not.

You can estimate factor scores and see if the relationships look linear.
 Elina Dale posted on Saturday, October 19, 2013 - 10:38 pm
Thank you, Dr. Muthen! Do you mean that I'd use those factor scores as observed variables in my regression models and do the usual diagnostics (like looking at residuals)?

So, instead of treating motivation factors as latent variables, I'd treat them as if they were observed.
 Bengt O. Muthen posted on Saturday, October 19, 2013 - 11:00 pm
I would simply plot the factor scores against each other.
 Linda K. Muthen posted on Saturday, October 19, 2013 - 11:26 pm
No. You would use the factors scores as proxies for the factors to check the linear relationships. You would treat the motivation factors as latent variables in your model.
 Elina Dale posted on Sunday, October 20, 2013 - 1:05 am
Thank you so much, Dr. Bengt Muthen and Dr. Linda Muthen! This is very helpful!
 Jinxin ZHU posted on Monday, March 02, 2015 - 2:52 am
Dear Bengt and Linda,

I am going to do a path analysis using 5 sets of plausible value.

I am wondering how I can do the regression diagnostic for the four assumptions of the regression in MPLUS.

Are there any books or online resources on this issue?

Thank you so much!
 Bengt O. Muthen posted on Monday, March 02, 2015 - 4:59 pm
You have to check this using individual residual plots using the Scatterplot option in the plot menu. Because this works with raw data, you have to do it separately for each imputed data set. For individual residuals, see the paper on our website:

Asparouhov, T. & Muthén, B. (2014). Using Mplus individual residual plots for diagnostic and model evaluation in SEM. Web note 20.
 Jinxin ZHU posted on Monday, May 11, 2015 - 7:20 am
Dear Bengt,

Thank you very much for your previous help.

Now I am doing a multilevel path analysis. Random intercepts were modeled for all dependent variables (say A, B, and C).
At level-one, C on A B and other predictors, and B on A and other predictors.
At level-two, only mean and variances were estimated.

1. When I use the individual residual plots, there are some variables begin with B_. What are these variables?

2. Are the residuals differed cross different levels? Say level one residual and level two residual if a path was specified at level two?

3. Only a general variable of residual was estimated for each dependent variable. Would you please kindly suggest the way how to conduct the regression diagnosis for multilevel path analysis using Mplus?

Thank you very much!
 Tihomir Asparouhov posted on Tuesday, May 12, 2015 - 7:01 pm
1. The estimate for the between part of the variable aka random intercept estimate. You can save these with "savedata: file=1.dat; SAVE = FSCORES;"

2. The residual in the Mplus plot is C-E(C|"predictor variables"). The "predictor variables" are the variables that are not dependent variables (are not modeled, i.e. no variance or intercept are reported for those variables). In principle you can construct the residual in different ways depending on what variables you condition on and you can also look at within and between residuals separately but currently Mplus will give you this C-E(C|"predictor variables"). You can use the savedata option to save the estimates and form alternative residuals for example in excel.

3. For every pair of variable you can pick to plot estimated, observed, residual value and check that the plot complies with your model assumptions. See http://www.statmodel.com/examples/webnotes/webnote20.pdf
 Jinxin ZHU posted on Wednesday, May 13, 2015 - 12:49 am
Dear Asparouhov,

Thank you so much for your prompt reply.
May I ask some further questions to see whether I understand you clearly or not?

1. The residuals in Mplus plot for multilevel analysis is the total residuals (within + between), right?

2.In path analysis (C->B->A), if "predictor variables" (say B, A on B) which also serve as dependent variables ( B on C), then plot for B and residual of A is not available in Mplus, right?

Many thanks!
 Tihomir Asparouhov posted on Wednesday, May 13, 2015 - 4:08 pm
1. Yes

2. You can run the model with A on B separately and get E(A|B,other co-variates) OR use the savedata command to obtain the between parts of the variables and construct the residuals yourself.
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