I have three different scales in my analyses. Two are on a 6-point Likert scale (Independent variables), and one on a 5-point Likert scale (Dependent variable). For non-nested data, readings suggest standardizing the scale scores before analysis for comparison and interpretation.
For multilevel modelling, given group and/or grand mean centring the variables is recommended, do I still need to standardize prior to centring? Or will centring essentially equate to standardization of the variables?
Article The Effect of Different Forms of Centering in Hierarchical L...
is an early discussion of this.
To handle an ordinal response, I would use multinomial ordinal regression, this relatively parsimonious, but to estimate a model you may have to combine categories, eg 1&2, 3, 4&5 see
Ordinal responses: multiple categories ordered
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#discrete
To handle an ordinal predictor I would use an orthogonal polynomial coding, this has a natural centering of zero, and is both flexible and parsimonious; indeed in its simplest form it is a linear trend, in its most complex there is a separate parameter for each ordered category, see this site in general
https://stats.idre.ucla.edu/stata/webbooks/reg/chapter5/regression-with-statachapter-5-additional-coding-systems-for-categorical-variables-in-regressionanalysis/
and this publication for a mixed model example
Data Manual supplement for MLwiN Version 2.14
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