# interpretation of ordered logit regression with categorical independent variate

I would like to predict the quality of plants in certain area. I divided the quality of the plants in 5 groups; 0 to 5. And we've measured 5 different areas; control, 1, 2, 3, and 4.

I ran a logit regression using the polr function in R. I get the following output.

Call:
polr(formula = factor(quality) ~ factor(area), data = data,
Hess = T, method = "logistic")

Coefficients:
Value    Std. Error  t value
factor(area)1 -0.01047     0.2998 -0.03492
factor(area)2  0.91798     0.2832  3.24139
factor(area)3  0.49045     0.2837  1.72905
factor(area)4 -0.75037     0.2833 -2.64905

Intercepts:
Value   Std. Error t value
Quality0|Quality1  -2.9874   0.2881   -10.3684
Quality1|Quality2  -1.1031   0.2093    -5.2693
Quality2|Quality3   1.2909   0.2142     6.0274
Quality3|Quality4   2.9733   0.2744    10.8362

Residual Deviance: 1083.045
AIC: 1099.045


Now I would like to interpret my results. Where I would like to know the change (in %) of having a plant with quality 4 in area 4. I'm using the following equation

exp(2.97-0.75)/(1+exp(2.97-0.75))


the result of this equation is 0.90. This means that when my plant grows in area 4. I've got a 10% change of having a plant with quality 4. However, in my data the plants growing in area 4 have almost no plants with a quality of 4. While the most plants with quality 4 grows in area 2 and 3.

While I predict the amount of quality 4 plants in area 2 and 3 I got a number of respectively of 0.02 (2%) and 0.03 (3%). This is counterintuitive. I think my interpration or equation is wrong.

Can somebody explain me how to interpret and predict these values?

• You could try the ggeffects-package: ggpredict(model, "area") should show you the predicted values. – Daniel Mar 11 at 18:46
• I used this predict function and it works. However, I don't know what underlying math is in this function. I would like to know how this exactly works. For others who encounter the same problem I used predict(model, new, type = "p"). – Soml Mar 12 at 11:25