Effect Size interpretation for GLM (Logit)

Question

I am using the following code from effectsize package in R:

glmmodel <- glm(Ydummy ~ X1 + X2 + X3 + X2*X3, data = mydata, family = "binomial")
effectsizes <- standardize_parameters(glmmodel)

The cofficients that I get for the interaction term are .7 from the glmmodel, but it is .07 for when I run the effectsize model. Which one should I interpret? the coefficients from the logit regular model or the coefficents from the effect size model? I get standarsized coefficents along with CI (confidence intervals) from the standardize_parameters function.

Answer 1

Though you can get standardized coefficients for logit binomial (logistic) models, the logistic model comes with it's own standardized effect size: the Odds ratio. So you can look at standardized odds ratios, using effectsize::standardize_parameters(..., exp = TRUE).

For example:

m <- glm(am ~ hp + drat, 
         family = binomial(link = "logit"),
         data = mtcars)

effectsize::standardize_parameters(m, exp = TRUE)
#> # Standardization method: refit
#> 
#> Parameter   | Odds Ratio (std.) |          95% CI
#> -------------------------------------------------
#> (Intercept) |              0.30 | [0.04,    1.08]
#> hp          |              2.10 | [0.65,    9.92]
#> drat        |             49.82 | [5.09, 4488.48]
#> 
#> (Response is unstandardized)

^{Created on 2022-01-13 by the reprex package (v2.0.1)}

So we can say that:

• an increase in 1 SD of $hp$ is associated with an OR of 2.1 (large medium effect size)
• an increase in 1 SD of $drat$ is associated with an OR of 49 (HUGE effect size).

Note that for an interaction term the OR is an Odds ratio-ratio (the change in the Odds ratio).