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Thoughts on ordinal regression

1 message · Dixon, Philip M [STAT]

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Mahnaz,

You only need to send one request.  Many folks do not check the list daily and I usually wait to see if others respond before I respond.

Likert scale responses are among the most difficult types of data to analyze well.  Many folks use approximate analyses.

A good textbook treatment of ordinal data analysis is the relevant chapters in Frank Harrell's book on Regression modeling strategies.

My go-to reference for categorical predictors is Shah and Madden, who deal with plant disease ratings on an ordinal 0-10 scale.
Title: Nonparametric analysis of ordinal data in designed factorial experiments
Author(s): Shah, DA (Shah, DA); Madden, LV (Madden, LV)
Source: PHYTOPATHOLOGY  Volume: 94  Issue: 1  Pages: 33-43  DOI: 10.1094/PHYTO.2004.94.1.33  Published: JAN 2004

Since your response is the average of 5 Likert scores, you may be able to use standard methods for Gaussian data.  The important issues are:
1) the analysis assumes the scale is linear.  I.e. the average of 2 and 4 is the same (in a subject matter sense) as the average of 1 and 5.  Also, the change between 2 and 3 is the same (in a biological sense) as the change between 4 and 5.  As you can tell, the assumption of linearity has consequences both for averaging 5 responses to get one summary score and for the form of the regression model.
2)  that the variance of the response is smaller when the mean is close to 1 or close to 5.  This may not be a problem if most of the average responses are between 2 and 3.  You may decide to do an approximate analysis and ignore the unequal variances.

Best wishes and good luck!
Philip Dixon