My survey data includes a battery of 36 Likert-scale questions, which are the IVs of interest in my analysis. Respondents rank how "alike" they are to an individual being described in each item. However, each trait being described is generally desirable, so responses mostly fall on the upper end of the scale. I always knew this was an issue, but I'm starting to think it is more important than I realized. Today I was circling back to an earlier part of the analysis and ran a Spearman correlation matrix that also included all of these variables--all of them have significant positive correlations with each other. I take this to mean that people who gave higher responses tended to always give high responses to every item.
So...what to do? Some quick Googling found some papers on measuring extreme response style (that's what this is, right?), but it wasn't clear to me what one should do about it. Does this require creating a model of the underlying tendency to give extreme responses, or are there simpler solutions like e.g. using each respondent's mean response to adjust their responses?
Is IRT (something I know approximately nothing about at this point) some help here?
Are all the logit models (DV is a hypothetical decision respondents have to make) I ran using these IVs junk now?