If the residuals are non-normal, you can't trust your GLM results. Playing with a post hoc test will not fix it. Try a data transform like the Box-Cox package in R. Best wishes, David Booth

I have used TweedieGLM. In my case data has zero values. Zeroes make dataset skewed.

Hello, in my opinion when the normality and homogeneity of variance assumptions for applying ANOVA are violated, a Kruskal–Wallis nonparametric

test followed by a Dunn’s multiple range test should be used to identify

significance.

thanks Alexandros Mavrommatis and Eugene Booth

There isn't much information in your question, so this will be a bit vague.

If your residuals are not normal that is an indication of poor model fit and GLM inference is questionable at best. But it sounds like you have a mixed or censored data distribution so you are not using a true GLM, then right?

You are using some sort of specialized extension. Most of these functions will give you the distribution-based p-values (usually from a t-distribution), or at least standard errors, that can be converted to p-values. Every fitting method should give you uncertainty estimates for each parameter. In case of factors, that means for each level of a factor (i'm assuming you care about factors b/c you ask about post-hock tests). By default, those p-values are usually tests for differences in levels vs the intercept (or treatment contrasts), which is what i would assume you want from post-hock tests. If you want different comparisons, you can, of cause, change the contrast matrix.

There is a lot to be said abound error propagation. The parameter uncertainty is often calculated as a quadratic approximation to the objective function at the parameter estimate (see your specific function). If you think that the objective function is poorly behaved, you can use some re-sampling techniques or uncertainty profiling to assess parameter uncertainty. If the fitting method is Bayesian, you should get the whole posterior for uncertainty assessment.

Thanks (@Fjodor Melnikov). I have exact zeroes in my data and have used Tweedie GLM. I am much less informed in stats and hence cannot give more detailed suggestion for your comments. But yes I have tried releveling the factors.