I am attempting a BSEM for categorical data with crossloadings for the first time. How do I set priors for this data which is largely skewed?12 items ordinal 0-5 scoring(psych outcome complex items). A CFA fit well with two crossloading items. I attempted to put this in a Bifactor CFA but saw I should not have crossloaders in bifactor CFA so I would like to use BSEM. I followed your examples using '~ N(0.1, 0.01)' for priors but I'm not sure if this is appropriate here.
Yes, that prior is an ok choice. Large cross-loadings will show up as significant estimates and you can then free them if you want. But try some other variance values as well (smaller and larger) and see how it affects results.
wayne smith posted on Wednesday, May 11, 2016 - 9:05 am
I am trying to estimate a BSEM (Small cross-loadings and covariances) having categorical variables as indicators (5 or 6 point - likert scale), but I am having some questions:
1. From the codes available, it seems that we need to standardize the categorical variables that are indicators of the latent variables and not to declare these categorical variables as categorical. Could you clarify on the effects of the standardization for the model? Should we interpret the parameters results the same way we do when we do not standardize the variables?
2. About the choice of informative priors for residual variances, how is it done when we have categorical variables? The formula to find Sigma (prior for variance) is still valid in this case (Sigma = v*(2p+3)) or Sigma must be 1? If the formula is valid, how do you get the residual variance matrix items (v) for the indicators having categorical data in the ML estimation? Is this why we need to standardize the variables?
I would like to thank you in advance, because these clarifications will help me a lot.
I wouldn't recommend standardizing. Here is an example of doing BSEM with categorical data
VARIABLE: NAMES ARE u1-u6; CATEGORICAL ARE u1-u6; analysis: estimator=bayes; MODEL: f1 BY u1-u3; f2 BY u4-u6; u1-u6 with u1-u6 (p1-p15); f2 by u1-u3 (c1-c3); f1 by u4-u6 (c4-c6); model prior: p1-p15~IW(0,10000); c1-c6~N(0,0.0001);
Start with values 10000 and 0.0001 and then gradually widen the priors until you get good PPP (so the next values to try would be 0.001 and 1000).
Thank you for clarifying about the standardization and for the example.
In the example, you include priors for covariances (u1-u6 with u1-u6), but how should I proceed to define priors for the variances (u1-u6)? The examples that I have seen of applied BSEM approach include the definition of specific priors for the variances.
No. The variances of U are always fixed to one. You are essentially giving a correlation matrix prior. That correlation matrix prior is the marginal distribution of the IW prior specified above complemented by v1-v6~IW(10000,10000); Thus what Mplus does is uses the variance covariance IW prior marginalized to the correlation matrix and essentially Mplus takes care of the variances here automatically.