Page: Multiple Ordered Logistic Regression

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Multivariate ordered logistic regression shares a lot of the same principles as binary logistic regression. The major difference is that it is suited to situations where the dependent variable is an ordinal variable that has more than two outcomes (e.g., self-rated health -- where respondents may choose excellent, very good, good, fair, or poor). 

Findings from ordered logistic regression are reported in proportional odds ratios, which indicate the estimated change in odds at each categorical break in the dependent variable. The estimated odds ratio applies equally to each break. Thus, the odds ratios refer to the likelihood of being "above" each of the breaks for every one unit change in an independent variable. Another way of thinking about it, the odds ratio reported in ordered logistic regression summarizes the average change in odds for moving across any of the thresholds of the dependent variable for every one unit change in the value of an independent variable. 

As with binary logistic regression, predicted probabilities (or margins) can also be calculated and reported using the margins command in Stata. 

In the following hypothetical case, the dependent variable (dv) is an ordinal variable comprised of 3 categories (0 - low, 1 - medium, and 2 - high). In this case, I include margins commands to calculate the predicted probabilities for different categories of iv3 for each of the different outcomes, while holding iv1 and iv2 constant at their means. 

. ologit dv iv1 iv2 i.iv3

. margins i.iv3, predict(outcome(0)) atmeans

. margins i.iv3, predict(outcome(1)) atmeans

. margins i.iv3, predict(outcome(2)) atmeans

You may also graph the predicted probabilities (for a particular outcome of the dv) using the following two commands:

. margins iv3, atmeans predict(outcome(2))

. marginsplot, xdimension(iv3) recast(bar)