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Generalized Linear Models typically use z-scores for inference on parameters ($\beta$s) (see here, for example).

This assumes that parameter estimates ($\hat{\beta}$s) follow a normal distribution? Why is this assumption typically made? The model errors are usually not normally distributed.

Is it just based on the central limit theorem?

Michael Webb
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It is because GLM parameter estimates are maximum likelihood estimates, and those are asypmtotically normal if we assume the observations are independent. See here, for instance. Note that this is only an asymptotic result so for a particular finite sample your test statistics won't be exactly normal.

jld
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  • That makes sense. So why don't we use the t-score since we don't have the true standard deviation of the model? – Michael Webb Aug 18 '17 at 14:16
  • For those who may be interested, I found an answer to my question in the above comment here: https://stats.stackexchange.com/questions/60074/wald-test-for-logistic-regression under "When is a z and when a t value used?" – Michael Webb Aug 18 '17 at 14:20