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I have two logistic mixed-effects models, nested within each other and differing in only one fixed variable:

mod1<- glmer(y ~ x1 + x2 + (x1 + x2| subject_ID), data = dat, family = binomial)
mod2<- glmer(y ~ x1 + (x1 + x2| subject_ID), data = dat, family = binomial)

I use the R function anova to compare the two with test="Chisq", which gives me a likelihood ratio test of whether the fixed effect missing from mod2 significantly improves mod1. I would like to calculate the effect size (specifically, Cohen's w) for this test.

How can I accomplish this?

Relatedly, it seems that to calculate Cramer's V or Cohen's w I need to know the sample size, number of rows, and number of columns of my test. What do rows and columns refer to in this case?

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I have found out here that Cohen's w is also known as phi. Rows and columns refer to contingency tables. Instead, here we care about (one-dimensional) goodness of fit. The correct way to get phi/w is:

w = sqrt(chisq/N)

Where chisq is the statistic obtained with the anova function and N is the sample size.

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