MLM Regression of latent vars within...
Message/Author
 Amber Watts posted on Thursday, August 06, 2009 - 2:04 pm
I am building a multi-level model that contains latent factors indicated by multiple observed variables on both levels. This part of the model runs fine.

I would like to use regression to predict a latent factor in the within part of the model using several latent factors in the between part of the model.

Where would I write this statement in the MODEL code? It doesn't seem to fit in either the within or between part of the model. Should the variables in the regression be omitted from the VARIABLE statement specifying the within and between variables?
 Linda K. Muthen posted on Thursday, August 06, 2009 - 3:51 pm
See Example 9.9. If there were one factor on within, for example, fw BY u1-u6 instead of fw1 and fw2 with equality of factor loadings across between and within, this would be how you would do it.
 Amber Watts posted on Friday, August 07, 2009 - 9:47 am
Thanks for your helpful suggestion. This allowed the model to run but gave the warning that Latent Variable Covariance Matrix is not positive definite. The TECH4 OUTPUT gives correlation estimates of 999.000 for all of the latent variables with one another on the within level and for all variables with the Y variable on the between level. Can you suggest where the problem might be?

Thank you
 Linda K. Muthen posted on Friday, August 07, 2009 - 9:55 am
 Amber Watts posted on Friday, August 07, 2009 - 9:55 am
Please disregard that last post. My syntax for constraining the factor loadings was not done correctly and this appears to be the source of the problem. Thanks
 Student 09 posted on Thursday, August 13, 2009 - 9:49 am
Hi

in my twolevel regression, an observed level two covariate exerts a significant effect on a latent level 2 factor. Despite the significant effect, the test statistic associated with hh level 2 R-between says that the amount of variacne explained in the latent factor is not significant. How can that be? Could you please point out where I find information how Mplus calculates the s.e. of the R-squares?

Many thanks!
 Linda K. Muthen posted on Thursday, August 13, 2009 - 11:14 am
Although a predictor may be significantly from zero, this does not mean that it explains a significant amount of the variance of a variable.

The Delta method is used to compute the standard error of R-square.
 Student 09 posted on Thursday, August 13, 2009 - 4:10 pm
Hi Linda

could you please add a reference for your explanation - even though my request apparently does not relate directly to the way Mplus handles the data. In fact, I consulted a number of regression text books before posting my request but could not find any source dealing with the apparent finding that a significant predictor does not explain a significant amount of variance.

Thank you
 Linda K. Muthen posted on Friday, August 14, 2009 - 12:32 pm
What you see can happen. I believe the explanation may be the same as for raw versus standardized coefficients where in rare cases one may be significant and one may not be. If you send your output and license number to support@statmodel.com, we can see the full picture and give you a more thorough explanation.