# Choosing between Ordinal logistic Regression and Multiple linear regression

I have data in which the response variable (attitudes towards tourism) is scaled in nature ranging from -10 to +10 (calculated from the summation of scores of a few questions related to tourism). The independent variables are continuous, categorical (3-4 categories), and binary (Yes/NO) in nature. I can categorize the response (attitude) into Negative, Neutral, and Positive and run an ordinal logistic regression (not very sure even this is the correct way). But I have come across some literature relevant to my study where they have used multiple linear regression even when their independent variable was Categorical (Negative, Neutral and Positive) and some cases when the independent variable was scaled like mine. Can I use multiple linear regression in this case?? IF not, what about ordinal logistic regression?

With a response variable on an ordinal scale of -10 to +10 this is a valid reason for treating it as numeric and running a standard multivariable regression. You will need to inspect residual plots in order to assess whether they are plausibly normally distributed if you are going to make certain inferences.

This will likely be much better than categorizing into 3 levels as this will result in a lot of information loss.

• Thank you for the prompt response to my query. So, now I should test the normality to ensure that I can use standard multivariate regression. Can you help to get access to reading materials related to my query so that I reference that in my method section? Jul 17 '20 at 14:33
• Don't test normality. Just assess it with residual plots. You can use multivariable regression, not multivariate regression. Jul 17 '20 at 14:38
• Yes, it answers my query. Jul 21 '20 at 15:31
• Done. Sorry, I was unaware of this. Jul 21 '20 at 23:12
• After checked the residuals plots what I found is that the lower-left points are not along the line (are below the line). I also did the shapiro.test (I am not sure if this is the right way of seeing normality in this case) and found value less than .05. So, I guess I have to opt for ordinal logistic regression now. Jul 23 '20 at 17:03

First off, +1 to Robert's answer.

In particular, he makes a great point that you should not bin your data into "negative"/"neutral"/"positive" categories, because that just needlessly loses too much information. For instance, if you bin $$[-10,-4]$$ as "negative", $$[-3,3]$$ as "neutral" and $$[4,10]$$ as "positive", then this binning treats someone with a score of $$-10$$ exactly the same as someone with a score of $$-4$$ - but presumably the first respondent was quite a bit more negative than the second one. So we have lost information. Don't do it.

As Robert writes, with 21 ordered categories, you can likely enough use Ordinary Least Squares (OLS) rather than ordered logistic regression, because the difference between the two approaches will be very small for such a large number of categories. And in any case, this difference in models will be completely dominated by the fact that your measurements only imperfectly measure the underlying construct you are really interested in.

I would not put too much emphasis on the normality of residuals, whether assessed graphically or by formal tests. This is nice to have, but regression parameters are quite robust to departures from normality. I would rather run diagnostic plots of residuals against your predictors: if there is a pattern in such plots, it suggests some unmodeled nonlinearities. (Note that such diagnostics will bias your p-values, so if these are what you are interested in, then don't overdo it.)

If you are really interested in deciding between OLS and ordered logistic regression, and if you have enough data, then consider cross-validating both approaches and seeing which one yields lower out-of-bag mean squared errors. If they are within one standard error, then go with the simpler model, which here is the OLS one.