# Interpreting ordinal regression with categorical predictors in SPSS

I am running an ordinal regression in SPSS, with a categorical predictor (9 neighbourhoods) and an ordinal dependent (satisfaction, with three levels: 1 '(very) satisfied' 2 'not satisfied, not unsatisfied' 3 '(very) unsatisfied'). I want to test whether living in a certain neighbourhood affects a person's satisfaction-score. My Parameter Estimates table in my SPSS Output looks like this

                              Estimate      Sig
Threshold  satisfaction = 1   -,275         ,011
satisfaction = 2   ,355          ,001
Location   neighbourhood1     -,822         ,000
neighbourhood2     ,418          ,024
neighbourhood3     -,047         ,795
neighbourhood4     -,622         ,001
neighbourhood5     -,636         ,001
neighbourhood6     -,285         ,123
neighbourhood7     -,595         ,000
neighbourhood8     -1,033        ,000
neighbourhood9     0


I am struggling with interpreting the estimates here. I have seen on several websites that the estimates are supposed to be interpreted the same way they would in 'normal' linear regression, in that "if a subject were to increase its neighbourhood1 score by one point, its ordered log-odds of being in a higher satisfaction category would decrease by 0,822 while the other variables in the model are held constant" (https://stats.idre.ucla.edu/spss/output/ordered-logistic-regression/). However, increasing the score on neighbourhood1 doesn't make sense, since a subject either lives there or does not. So how do I deduce the direction of the effect from this output? Am I even running the appropriate analysis? Help!

Furthermore, would it be necessary to maybe rescore the satisfaction-variable so that 1 denotes (very) unsatisfied and 3 means (very) satisfied?

Thanks a lot in advance!

## 1 Answer

The interpretation you presented based on the references you referred to is right.

Regarding increasing "neighbourhood1 score by one point", here is what it means. When categorical variables with several levels are used in regression (ordinal or other), each level of the categorical variable (other than the one left out as a reference category) is dummy coded (i.e., coded 1 if the observation falls in that category and 0 otherwise). Hence, an increase of one unit in neighborhood1 score means a change from 0 to 1. That is equivalent to saying living in neighborhood1 and you could (preferably) interpret it as such.

Concerning the coding of the dependent variable, interpretation of results would be easier if it is done in increasing order of intensity (i.e., 1 = (Very) unsatisfied, 2 = not satisfied, not unsatisfied and 3 = (very) satisfied). That means, higher numbers should indicate a higher intensity of the dependent variable (i.e., higher satisfaction). Thus, the interpretation you presented above doesn't apply to your case, because higher numbers indicate lower intensities of the dependent variable. Therefore, as you said, you need to recode your dependent variable so that the interpretation you presented would be meaningful for your case.

Besides, exponentiating the coefficients would help you to interpret the results in terms of odds ratios.