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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?

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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).

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  • $\begingroup$ Thanks for this answer. Would you mind expanding on what contr.poly(5) tells me. Additionally, suppose C.L (in the example above) had a significant p value here, what statement can be made about that ordinal variable? By statement, I mean something similar to the first paragraph after my example. $\endgroup$ – Harry Jul 25 at 16:09
  • $\begingroup$ 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.) $\endgroup$ – kurtosis Jul 26 at 23:58

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