# Interpreting coefficients of ordinal independent variables in logistic regression in R

I have conducted a logistic regression in R

> Model <- glm(A ~ B + C, family = "binomial", data = Data)
> summary(Model)

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)          -1.6138   678.6939  -0.002   0.9981
BPu                   1.0003     0.5539   1.806   0.0709 .
C.L                  21.2450  2146.2181   0.010   0.9921
C.Q                   1.2210  1813.8853   0.001   0.9995
C.C                   9.8965  1073.1091   0.009   0.9926
C^4                  -0.3275   405.5973  -0.001   0.9994

exp(coef(Model))

(Intercept)           BPu               C.L                 C.Q
1.991295e-01       2.719031e+00       1.684921e+09       3.390646e+00
C.C             C^4
1.986151e+04       7.207529e-01



As I understand it when the independent variable, B, (a binary variable) changes to Pu this is associated with an increase in the log odds of a "success" in the dependent by 1.0003, or that odds of increasing the dependent variable are multiplied by 3.22 relative to the intercept, and this change is near significant.

Can I say a similar statement for the variable CR, a 5 level ordinal variable? I've found online that L, Q, C, ^4 represent linear quadratic, cubic ... but I haven't found an answer outlining what I can practically say about these coefficients or how to interpret them.

I understand that the influence is likely to be insignificant, but which P value do I use? What can I say about the other coefficients?

I think a lot of your answers can be found in the answer to a similar question. The one caveat is that the linear, quadratic, cubic, and quartic terms do not directly correspond to numeric effects as though you used the factor levels as a raw number. You can see this by typing contr.poly(5) in $$R$$ to see how the various levels are coded (beyond the intercept = constant = all 1's).
• contr.poly(n) tells you the encoding for a factor with n levels (omitting the encoding for the base = constant which is just all ones. The weights create orthogonal polynomials; however, that also lets you figure out the effect of a given factor level: take the product of encoding values for that factor and coefficient estimates. If C.L has a significant $p$-value, that is evidence that there is a significant linear relationship with respect to your ordinal factor. (For the above: increases in the factor lead to significant increases in the log-odds for the dependent variable.) – kurtosis Jul 26 '20 at 23:58