Have you thought about ridge regression or lasso in this capacity. Here is a link that discusses your models. Ridge and lasso both are effective in dealing with multicollinearity. Link:

https://www.bing.com/search?FORM=U528DF&PC=U528&q=lasso+in+linear+mixed+models

In answer to your second question, lasso is effective with hierarchical models as well. Here's a link: https://www.bing.com/search?q=lasso+in+hierarchical+linear+models&qs=n&form=QBRE&sp=-1&pq=lasso+in+hierarchical+linear+models&sc=1-35&sk=&cvid=9AB0A943CE9C438CAA52CDD2744B23BB

HTH Good luck, David Booth

Hi! If the scale is pre tested before using for the actual survey can help to control multicollinearity issues. Thanks.

Rather than suggest ways to deal with multicollinearity, I'll raise a few issues you might want to think about before you do anything.

1. Principal components regression can cause problems. E.g.,

• https://www.jstor.org/stable/2685559?seq=1#metadata_info_tab_contents

2. Sometimes, multicollinearity may not matter.

• https://statisticalhorizons.com/multicollinearity
• https://davegiles.blogspot.com/2011/09/micronumerosity.html

3. Simple correlations are not very good for detecting problematic multicollinearity. There can be no alarming correlations among the predictor variables despite the presence of complete linear dependence (e.g., try estimating a model with 3 X-variables and their sum). And correlations can look quite alarming when there is no untoward multicollinearity (e.g., when X and X2 are both included in a model).

HTH.