homoscedasticity assumption in logistic models?

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adeldaoud
Posts: 63
Joined: Sat Aug 15, 2015 4:00 pm

homoscedasticity assumption in logistic models?

Post by adeldaoud »

Hi

1)
It is usually suggested that it is not meaningful to check the homoscedasticity assumption in single level logistic models because the outcome is binary, but is it meaningful to check homoscedasticity on the log-odds scale? Probably the answer is still no, since one does not assume homoscedasticity at all, right?

2) Is homoscedasticity assumed for the second level variance?

I plotted “the standardised residual x fixed part prediction” for the second level, and wonder if it shows anything meaningful for you?
Image

3) in terms of model assumptions, is the 95% residual-rank plot used for anything specific? That is, more than checking some clusters are deviating from the mean estimate and warranting the need for a multilevel model.


Thanks in advance
Attachments
standard normal vs fixed part pred.png
standard normal vs fixed part pred.png (1.6 KiB) Viewed 3499 times
GeorgeLeckie
Site Admin
Posts: 432
Joined: Fri Apr 01, 2011 2:14 pm

Re: homoscedasticity assumption in logistic models?

Post by GeorgeLeckie »

Dear adeldaoud,

Yes there is no level-1 residual in the linear predictor of a two-level random-intercept logistic regression and so we only assess the distributional assumption of the level-2 random effect, namely that it is normally distributed and homoskedastic. You can assess the plausibility of the normality assumption by inspecting a histogram or quantile-quantile plot of the predicted random effects. You can assess the homoskedasticity assumption by plotting the predicted random effects against the covariates.

Best wishes

George
adeldaoud
Posts: 63
Joined: Sat Aug 15, 2015 4:00 pm

Re: homoscedasticity assumption in logistic models?

Post by adeldaoud »

Thanks George for the reply. So the “the standardised residual x fixed part prediction” in the Mlwin enviroment should show me this, right?

Best,
Adel
cippi2021
Posts: 3
Joined: Thu Jan 14, 2021 4:04 pm

Re: homoscedasticity assumption in logistic models?

Post by cippi2021 »

Hi, I am finding this post interesting as i am looking for testing for homoschedasticity for my 2 level model. I have a question concerning the plot indicated here, hope you can help:

"You can assess the homoskedasticity assumption by plotting the predicted random effects against the covariates."

When you say "against the covariates", do you mean I should take the average value by level 2 group, and plot those against predicted random effect? What should i take in case of a categorical covariate? Or, should i take some sort of predicted value?

thanks in advance.
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