After reading a lot of different papers and a lot of different posts on the internet I still don't have a clue how to test on heteroskedasticity with my logistic regression (binary). The White test works only for OLS regression right?
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4$\begingroup$ A binary response must be heteroscedastic given the predictors. Think of the extremes. A mean of 0 or a mean of 1 can only be 0 or 1 if all values are 0 or 1 respectively, so the variance will be 0 at the extremes but positive in between. What authoritative texts tell you to test for heteroscedasticity? $\endgroup$– Nick CoxDec 1, 2014 at 10:02
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1$\begingroup$ stats.stackexchange.com/questions/124818/… and its links may help. $\endgroup$– Nick CoxDec 1, 2014 at 10:06
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$\begingroup$ You can test for a particular type of heteroskedasticity in a probit model. Stata's hetprobit is one implementation. $\endgroup$– dimitriyDec 2, 2014 at 20:41
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$\begingroup$ In logistic regression, the variance depends on the mean. So it must be heteroskedastic. $\endgroup$– Liu JimApr 2, 2015 at 2:51
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Heteroscedasticity as such is not the main worry in logistic regression. For count data, the concern is overdispersion. The logistic model assumes that the probability of "success" is given by the model ... but what if the probability of success is, say, a Beta random variable whose mean is your model mean? The expected counts would no longer be what the logistic predicts.
You could check for this possibility by fitting a beta-binomial model to see if the fit was substantially better --- See R package bbmle.
To me, I would only go that route if I had subject matter grounds for modeling the success probability that way.
Overdispersion can also happen with Poisson counts.
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2$\begingroup$ If the distribution of the error term is misspecified or heteroskedastic, then the maximum likelihood estimator is generally inconsistent. See Yatchew and Griliches 1985 paper in RESAT for a proof. $\endgroup$– dimitriyDec 2, 2014 at 20:46
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1$\begingroup$ Logistic regression has no error term. $\endgroup$ Jan 2, 2015 at 13:50