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As mentioned previously, the independent or predictor variables in logistic regression can take any form. That is, logistic regression makes no assumption about the distribution of the independent variables. They do not have to be normally distributed, linearly related or of equal variance within each group.The relationship between the predictor and response variables is not a linear function in logistic regression, instead, the logistic regression function is used, which is the logit transformation of q:

Hey I don't have to worry about violating assumptions (other than MC) with this....I like it

Categorical Data Analysis (Agresti, 2002)

Does anyone know if autocorrelation is as much a violation of logistic regression as it is of OLS?

Thanks all for the comments. It really helps.

I find the binomial assumption a bit puzzling because (according to what I have seen in some text) if your observations are independent this assumption is always met. If you don't have independence you have other, major problems

The problem I'm thinking of is that in the logistic regression case if we're working with actual binomial data then given the levels of the covariates we expect the outcome to follow a binomial distribution with success probability of [math]1/(1 + exp(-X\beta))[/math]. But it's plausible that we might see some overdispersion. It might be overly optimistic to believe that given the covariates that the success probability is exactly the same for any observation we might make with those covariate levels. One way to fix this might be to assume that the outcome follows a beta-binomial distribution where the mean of that beta-binomial is what we do the regression on. This allows added variability. The problem gets a little bit more difficult if you do this but it might do a better job capturing what's going on.

Although in practice one might just fit a mixed GLM instead with some normal random effects...

Another assumption, I imagine, not really discussed so far is that you measure things without error - a common regression assumption that to me is absurd. It is why I like SEM, where you don't make this assumption.

I suspect that commerical software does not even address beta-binomial distributions (which I have never heard of in honesty).

While the binominal assumption may not always be met, in practice there is no way (as far as I know) to test for this.

Another assumption, I imagine, not really discussed so far is that you measure things without error - a common regression assumption that to me is absurd.

Of course (like say William Berry an expert in regression who wrote monographs on the topic) I doubt we can ever known the true paramater. So we agree that this concern is probably overblown in practice.

It does raise the point, like independence, of why you make assumptions you can never test and almost certainly are not correct.

In logistic regression, if you have a continuous predictor the assumption is a liner relationship between logit and the continuous predictor variable. Another assumption is the outcome can in fact be modelled with binomial/multinomial distribution.

(Noetsi I wish I could also refer to ur suggested books for help, I can't find them though =( )

cheers,

Katharina

So for categorical predictors, both in linear and logistic regression, there can not be the assumption of linearity due to the very nature of categorical predictors

Well there can be that assumption. It's just relatively easy to meet since you're only assuming that a line can fit two points (which is always true). So linearity for categorical stuff isn't bad.

Because it doesn't always hold for continuous predictors and it's annoying to have to clarify that you can always do it for dummy variables - instead it's just easier to make it an assumption. And if something always holds then I'd say it is *really* relatively easy to meet that condition.

I should note that I said that the assumption always holds for categorical predictors and that is true and easy to see for a single categorical predictor. If we have multiple categorical predictors that assumption might fail if we don't include an interaction term. But if we do include an interaction then the assumption is definitely met (although other assumptions might not hold).