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Combining Likert Categories and Embracing a Simulation-Based Mindset

Quite often we'll be developing simulations based on models in which the DV is a 6-point Likert-style response scale. (Usually it's somethign like: strongly disagree / disagree / mildly disagree / mildly agree / agree / strongly agree.) For presentation purposes, it's often useful to reduce this down into two categories: any form of agreement / any form of disagreement. In particular, when graphing, it is much easier to show one cut with confidence intervals than to show five cuts with confidence intervals. 

In the past we've done this by converting the DV into a binary variable, then running a logistic regression. But this has numerous drawbacks. First and foremost, it simply throws away all the information about how strongly a person agrees or disagrees. As a result, errors tend to be larger than necessary. Second, and relatedly, the results often aren't as similar to the ologit regressions run against the more information-rich likert DV as one would like. And third, if we want to report both kinds of findings -- binary and likert-style -- this means reporting two separate models that don't always give the same results. In short, it's been a mess, and we've usually just chosen one or the other. But when we've gone with a logit regression, this seems like sad choice to make just to achieve greater simplicity of presentation.

Recently, though, I had coffee with Jeff Lax-- of state-level policy analysis & Gelman Blog fame -- and he suggested something that, in retrospect, reveals that I'm still often trapped in a non-simulation mindset. In essence, he suggested this: "Run simulations on your ologit model & combine the simulations for the agree levels and again for the disagree levels; then take your confidence intervals from those combined simulations." In retrospect, that is so clearly the correct approach that the question is why I didn't see it myself. The answer, I think, is that I was still thinking in terms of the regression model rather than the simulations.  

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