# Analysing a grouped 0 to 10 scale using ordinal logistic regression

I read in an article that the logit link is considered suitable for analyzing ordered categorical data evenly distributed among all categories.

I want to do ordinal logistic regression and I have an ordinal variable on the scale of 0-10 and have to make three groups, 0-6, 7-8 and 9-10. Does this mean that the data is not evenly distributed and I shouldn't use ordinal regression or do they mean that there has to be approximately the same number of observations in each category?

-
forgot to add that the variable that i want to group is the response variable. – stat3 Feb 24 '13 at 23:10
I don't see what benefit you get from grouping adjacent response categories unless you have categories w/ few or no observations in them. In general, the ordinal logistic regression model does not assume that there will be equal numbers of observations in each category. – gung Feb 24 '13 at 23:26
My response variable is NPS(Net promoter score), which is a measure of customer satisfaction. It is considered that people who answered 0-6 are unsatisfied customers, 7-8 neutral and 9-10 satisfied customers, that is why I want to group the response categories.Ok, if the model does not assume that there will be equal numbers of observations in each category, what do they mean by saying "logit link is considered suitable for analyzing ordered categorical data evenly distributed among all categories"? – stat3 Feb 25 '13 at 0:46
I'm not sure who "they" are, or what they mean. The ordinal logistic regression model estimates a single set of betas, and then a set of l-1 thresholds or cutpoints (where you have l levels). If you have 0, or sufficiently few observations in a level, the cutpoint cannot be calculated. That would be my best guess at what they meant, but I don't really know. – gung Feb 25 '13 at 1:00
What article said this? (a link would be nice). As @gung just said, the usual ordinal logistic model assumes that the same $\beta$s apply between any two levels of the dependent variable, and only the cutpoints (or intercepts) vary. One thing to do is to try both ordinal and multinomial logistic and see if the predicted values differ by much. – Peter Flom Feb 25 '13 at 11:07

The specific values on your scale (i.e., 0 through 10 values) are irrelevant; only their order matters. The various ordered models with their myriad of names only focus on the order and discard the specific scale values. (The specific values are only really relevant when data has been rounded or categorized, neither of which has occurred in your case.)

Other than ensuring that you have a few observations in each of your groups I would not worry too much about the proportion of observations in each group (I can't think of any statistical justification and pretty much no real-world data set would meet such a requirement anyway).

One other thing to keep in mind is that you will get a bit more statistical power if you estimate the model using all 11 data points and apply the Net Promoter Score coding only at the time of prediction (however, if doing this, you would want to check that the parameter estimates for the independent variables are approximately the same either way).

-