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I get the following coefficients from a logistic glm but need to convert it into a formula, i.e. Y= b0 + bx1 + bx2...

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My challenge is that the variables are discrete and each missing a category: OSHIGH, highcHIGH, highpHIGH, altregionDK. How do I get the coefficients for these variables or create a formula including all?

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  • $\begingroup$ I think indicator variables can be used. $\endgroup$
    – Shanks
    Commented May 20, 2018 at 13:47
  • $\begingroup$ The equatiomatic package should make this easy. $\endgroup$
    – COOLSerdash
    Commented Sep 3 at 13:52

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Your problem is that R is using one level of each categorical predictor as a reference level. You can actually derive your values from your current output, but I believe you can also get explicit output by forcing regression through the origin with formula = Y ~ X1 - 1 (of course adapt this to fit your use case).

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    $\begingroup$ This solution works when there's only one categorical variable. The most reliable, explicit solution is to review the model matrix that R uses, which can be found by calling stats::model.matrix. $\endgroup$
    – whuber ♦
    Commented Sep 3 at 15:06
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Your formula would be

y = inv_logit(.9 + .5 * (OS = low) + .2 * (OS = medium) + ...)

when OS is high your prediction would be inv_logit(.9 + ...) where all others can be set to 0 or their mean.

In a Bayesian model (or neural network) you could have effects/coefficients for all three OS levels.

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In order to model effects for categorical factors in a regression model, you have to contrast code your factors. The degrees of freedom for your categorical factor will always be k - 1, where k is the number of levels in the factor which is why you see only 1 coefficient for a 2-level categorical factor.

Dummy coding is the factory default in R and presumably what you are using here if you didn’t change anything and it compares group B, C, D etc to group A, where group A is the reference group to which all other levels of the factor are compared.

TL;DR: nothing is wrong here or missing, this is as to be expected. To read more about contrast coding, you can read here at this excellent resource: https://stats.oarc.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/

If you want to 'recover' the estimates for each group, there are a variety of options. I think this function from emmeans package should work:

emm1 = emmeans(fit1, specs = pairwise ~ OS)

You could also do the following function from ggeffects package:

ggpredict(fit1, c("OS"))

For more reading on marginal effects, this excellent digital textbook is available: https://marginaleffects.com/vignettes/predictions.html

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