# Effect Size interpretation for GLM (Logit)

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.

• What is the goal of this analysis? Your thought process should be, "how can I use this model to estimate the quantity I want to estimate?" rather than "which output from this model should I interpret?" If your goal was to estimate and interpret standardized coefficients, then interpret them. If your goal was to estimate and interpret the original coefficients, then interpret those. Without any context there is no way to answer this question in a helpful way.
– Noah
Dec 8, 2021 at 1:45
• So, my goal is theory testing. I wanted to see if my interactions are supported by empirical evidence. Since the sample size is huge I was asked to check effect size instead of p-values. Dec 9, 2021 at 16:33

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,
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).