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I'm currently testing a (binary) logistic regression model, which seems to have at least some issues with multicollinearity. Now I don't really trust the data anymore and would like to also test it on heteroscedasticity. I found some information on Breusch-Pagan Test on the internet, but I could not find an answer to the question if this test also applys on Maximum-Likelihood-Methods, as it is usually mentioned in the context of OLS. So, can I apply the Breusch-Pagan Test on my model?

Related to this question: How could I plot for heteroscedasticity-detection? I found this thread, but due to the binary nature of my dependent variable, the plot does not really work and unfortunately I'm pretty novice on plotting with R.

Thanks in advance!

Community
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Leo.SurveyMeth
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2 Answers2

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The variance of binomial data is determined by the mean. One number rules them all. Logistic regression is designed around this and therefore there is no assumption of equal variance. The assumptions are:

  1. linearity in log odds space
  2. independent errors
  3. multicollinearity among predictors isn't too high
John
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  • There's no assumption of non-multicollinearity (unless perhaps you mean perfect multicollinearity). Also worth explaining that linearity means the log-odds are a linear function of the parameters, so various types of non-linear relationships between log-odds & predictors are possible (using e.g. polynomials or splines). And that overdispersion is some circumstances what you ought to be looking for rather than the (expected) heteroskedasticity. – Scortchi - Reinstate Monica Apr 07 '14 at 13:03
  • Thanks @ John for clarification. @Scortchi Would I compare fitted vs. predicted values (maybe in a plot) to look out for non-linear relationships? – Leo.SurveyMeth Apr 07 '14 at 13:07
  • What's the difference between "fitted" & "predicted"? – Scortchi - Reinstate Monica Apr 07 '14 at 13:07
  • Oh, replace "predicted" with "residuals". I've seen a plot like this while scanning for information about the topic. – Leo.SurveyMeth Apr 07 '14 at 13:10
  • Yes, & vs individual predictors. Use loess to smooth if necessary. – Scortchi - Reinstate Monica Apr 07 '14 at 13:14
  • Scortchi, it was a quick answer... I edited. I didn't mean perfect collinearity but I did mean very high collinearity could not be allowed. How high is too high needs to be taken on a case by case basis but the correlation doesn't need to b 1 to compromise the model. Regardless, homoscedasticity isn't one of the assumptions. – John Apr 07 '14 at 14:11
  • Agreed (+1) - IMO it was just worth qualifying a couple of the subsidiary points. – Scortchi - Reinstate Monica Apr 07 '14 at 14:32
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Unlike what other responses claim, heteroskedasticity can cause serious inconsistency in logit and probit models. For example, see http://davegiles.blogspot.com.au/2015/06/logit-probit-heteroskedasticity.html

BP test cannot be used to test heteroskedasticity after logit or probit. You can use "hetprob" command of Stata which accounts for heteroskedasticity and will also conduct a formal heteroskedasticity test on your data. "clogithet" command of Stata does the same for conditional logit models, I assume: https://ideas.repec.org/c/boc/bocode/s456737.html.

Majid
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