I have a dataset of several hundred respondents who each answered 100 or so questions having Likert-type responses (e.g., 0 for "not at all" to 7 for "always"). The problem is, as we all know, some respondents tend to answer most questions on the extreme end, for example mostly 5s, 6s and 7s. Or some will never give responses outside a narrow middle range.
My question is, how would one "normalize" these scores?. I've though of converting each subject's scores to a Z-score, not based on the entire group but based only on their scores for the roughly 100 questions that each subject responded to. That way, one subject's z-score would be comparable to another subject's z-score, comparing apples to apples, so to speak. Is this the proper way to do this?
Dear Jerry,
I would not recommend doing what you are proposing as it amounts to a reinterpretation of each subject's responses. Very often individual items are combined together into scales. If the regression model is used it will partly take care of your concern.
I would recommend you to check out polytomous item response theory models that treat such Likert-type items as ordinal categories and estimate both item parameters as well as person scores on the same scale. A big advantage of this process is that you would not treat the labels for those response categories (i.e., 0 for not at all to 7 for always) as if they are continuous values (because they are, in fact, just ordinal values). Scores obtained from IRT models are a logistic scale typically ranging from -4 to +4. The distribution of scores may or may not be necessarily normal but at least the problem of observing particular response categories more often than others would not be a big problem anymore. I am attaching a few good sources on the topic.
Chapter Item Response Theory (IRT) Models for Rating Scale Data
Article An NCME Instructional Module on Polytomous Item Response Theory Models
Dear Jerry,
I would not recommend doing what you are proposing as it amounts to a reinterpretation of each subject's responses. Very often individual items are combined together into scales. If the regression model is used it will partly take care of your concern.
I also don't recommend doing that.
Depending on the analysis, one option to address your concern is to treat each subject in the model as a block or a random block. This way, for example, when comparing between groups of questions, the tendency of a respondent to always answer e.g. high is taken into account statistically.
Hi, Dear Jerry Miller
Thanks, for raising an interesting question, I agree with Claudia Abreu Lopes and Peter Samuels,
Regdards
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