# Multiple regression with a odd-numbered Likert items

In the questionnaire, individuals were asked to pick from an odd number of options (5 or 7) how much they agree with the statement (from completely agree to completely disagree).

Now, if there where an even number of options, it's be easy to code as 0 or 1. Sadly, here, the median option means "neutral. I'm unsure of how to code this.

As I see it, I could:

• Create two dummies (for and against). Neutral would be if both equal 0.
• Leave it as is (which complicates the interpretation?).

I was wondering if there's a more elegant way to go about it.

• I strongly suspect that question has been asked and answered before. Sadly, my google-fu was insufficient. Apr 18 '19 at 20:04
• Put me down as 'strongly opposed' to a 7-option likert scale. Pre-supposes more finely tuned opinions than may exist. Is it possible that most of the neutral responses are 'polite' somewhat-negatives. Apr 18 '19 at 22:03
• is this an outcome variable or a predictor? Have you looked into treating such items as ordinal variables? Do you just have one or a handful of items, or do you have enough to combine into a Likert scale?
– EdM
Apr 18 '19 at 22:03
• I suggest that you use the independent Likert scale variables as they are. The coefficients $\beta$ would mean something like: if we consider a higher category in the Likert variable, the odds of a higher outcome of the dependent variable would be higher if $\beta > 0$ (lower if $\beta < 0$). Don't forget to check if there is collinearity between the independent variables (it may happen, for instance, if there are similar questions). Apr 18 '19 at 23:51
• @EdM: A predictor, and I only have a few handleful of them. They act as proxy variables for personally traits. Apr 19 '19 at 0:33

## 1 Answer

You don't gain anything by throwing away information, so the most elegant solution is to maintain the ordering inherent in each 7-level Likert item by treating each of them as a 7-level ordinal predictor. In R these are called ordered factors.

Although you don't know that each of the 6 steps between levels for each Likert item has the same magnitude with respect to predicting your outcome variable, you do presumably suspect that each higher step is more strongly related to outcome. Hence each item is appropriately considered a multi-level ordinal variable.

When a factor is specified as an ordered predictor in R it is modeled as a set of orthogonal polynomials. That, however, converts each 7-level Likert item into 6 predictors, so there is a danger of overfitting if you have multiple Likert items and only a moderate-sized data set.

This page discusses other approaches to using ordinal variables as predictors, with links to further discussion. In particular, the ordSmooth() function in the R package ordPens smooths ordinal predictors with penalization to lessen the chance of overfitting while taking advantage of the ordering of the levels,