Latent Variable Decomposition with MLR
Message/Author
 Sarah Victor posted on Friday, October 05, 2018 - 12:55 pm
I am trying to run a 2-level, random effects model with a random slope at the within level (a ON b) and using that slope to predict a categorical outcome (c) at the between level. I would like to use latent variable decomposition for a and b.

Starting with this code:
ANALYSIS:
TYPE IS TWOLEVEL RANDOM;
ESTIMATOR = MLR;

MODEL:
%WITHIN%
slope | a ON b;

%BETWEEN%
c ON a b slope;
a WITH b slope;
b WITH slope;

Caused an error: latent variable decomposition of an x variable (b) is not available unless it is treated as a y variable by mentioning its variance.

However, I get the same error with this code:

%WITHIN%
slope | a ON b;
b;

I also tried your strategy noted here: https://tinyurl.com/y8mytnx8 with this code:

%WITHIN%
fw_b BY b; b@0;
fw_a BY a; a@0;
slope | fw_a ON fw_b;

%BETWEEN%
fb_b BY b; b@0;
fb_a BY a; a@0;
c ON slope fb_a fb_b;
slope WITH fb_a fb_b;
fb_a WITH fb_b;

The model "runs" but says the estimated within covariance matrix cannot be inverted and so computation could not be completed.

Suggestions (other than moving to ESTIMATOR=BAYES)?
 Bengt O. Muthen posted on Friday, October 05, 2018 - 2:30 pm
The best approach is to move to Bayes; ML is not natural for this.
 Sarah Victor posted on Saturday, October 06, 2018 - 10:49 am
Thank you for the prompt reply! That was my fear, unfortunately - we are interested in looking at an interaction between the within-person slope (latent variable) and an observed binary variable using the XWITH command, and then using that interaction term as a predictor, but it seems like that is not possible with Bayes
 Bengt O. Muthen posted on Saturday, October 06, 2018 - 1:45 pm
If your binary is exogenous, you can use a 2-group analysis to capture the interaction.
 Sarah Victor posted on Sunday, October 07, 2018 - 5:49 pm
I'm sorry, I mis-wrote - I would actually like to create an interaction between the within-person slope (latent variable) and an observed *interval* variable using XWITH, and then that interaction term would be used as a predictor of the *binary* outcome. So the interaction itself is two dimensional/interval variables, one latent and one observed.
 Bengt O. Muthen posted on Monday, October 08, 2018 - 10:49 am
Then you are in luck if you can wait a bit. The forthcoming Mplus Version 8.2 will have XWITH for Bayes.