Nelder & Wedderburn 1972 - GLM - MLE - Equivalence to Weighted LS - Normal Distribution Example

[@HamiltonHammy-g6w]

Brilliant! Thank you so much for the playlist so far. This video really helps link the prior more general theory to a more concrete example. However, I was wondering if you would also be showing how the variances of the betas are estimated for this model in this framework, and also whether a similar video would be possible where you focus on illustrating this framework for a GLM where the link isn't the identity and the weights aren't 1, so it's clearer how those more flexible parts work when "actually needed"?

[@Stats4Everyone]

Thanks so much for this comment!! The holidays are slowing me down a bit with adding more to this playlist, though my next few videos will be a Bernoulli distribution (Yes/No, or 0,1, outcomes) example, where the weights will not be 1. I will also use R to provide an example for how to calculate the estimates of beta. Regarding estimating the variance for the beta estimates - this is a very good point - I have not read ahead yet on the Nelder paper to know if they cover this topic (I would hope that they do…) However, if they don’t, I will definitely add a video at some point on this - estimating beta is not very useful, unless we also have an idea about its variance.

[@Stats4Everyone]

Here are the links to the bernoulli example: Step 1 (Show Bernoulli is from Exponential family): kzbin.info/www/bejne/bnyte5WboJh8bMk Step 2 (find the link function and the weights and y for weighted Least Squares): kzbin.info/www/bejne/l5zCZJd5ZdV9m9U Step 3 (wrap up and program everything in R to show that you get the same thing as their GLM function): kzbin.info/www/bejne/onmsfKKCiq2td80

[@HamiltonHammy-g6w]

@@Stats4Everyone I hope you had a lovely holiday and happy New Year! The new videos are fantastic. You're a stats star. Especially showing how you can implement it in R. If it's possible to eventually add a video/videos on estimating the variances that would be amazing. You could obviously use bootstrapping to estimate confidence intervals (or permutation methods to estimate p-values, if you really care about them), but it would be great to see where the analytical SEs come from.

[@Stats4Everyone]

@@HamiltonHammy-g6w yup. That is definitely on my radar for another topic to cover in this glm playlist :)