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What are parameters start, etastart, mustart in the glm() function? I have been looking in the docs and the internet but I have found no clear explanation what this means.

It resembles bayesian "initial values" for the chains, but I doubt this is related, as glm() function in R is frequentist statistics...

Tomas
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2 Answers2

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It just has to do with the estimation technique - how a set of estimates for the parameters in the model are arrived at. A generalized linear model is fit by iteratively reweighted least squares. An arbitrary set of weights is chosen to start with (often all equal to start with), then estimates of the parameters in the linear predictor are chosen that minimise the weighted sum of the squares of residuals. Those estimated parameters in the linear predictor are used to estimate a new vector of means. From this a new set of weights is derived - for example, depending on what family and link function is being used, the variance of the response might be proportional to the mean of the response - so weights will be inversely proportional to the mean. This new set of weights is used in a new iteration of the whole procedure. This process is repeated until it converges.

So the three arguments to glm() you have asked about are just ways for the user to start the procedure at some arbitrary point instead of allowing it to choose its own default starting point. From the help file you linked to:

  • start - starting values for the parameters in the linear predictor.
  • etastart - starting values for the linear predictor.
  • mustart - starting values for the vector of means.
gung - Reinstate Monica
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Peter Ellis
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  • Thanks Peter! It completely resembles the bayesian MCMC procedure! I thought frequentist packages are more clever and doesn't work that way :-) This is what I was confused about... *why* on earth is there something like initial values in the frequentist package :-) – Tomas Jul 23 '13 at 10:00
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    Sometimes without initial values you can fail to converge, or converge on a local maximum that is not a globally optimal solution. So it's good to have the option to try different starting values. – Peter Ellis Jul 23 '13 at 11:33
  • I start to have a feeling that even `glm()` is bayesian :-) – Tomas Jul 23 '13 at 11:34
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    @Curious It's not particularly bayesian. All your asking is for the software package to find a particular point via a search technique. The starting values just tell it where to start - it gives no particular weight to that answer, but it can help if it's wandering over a complicated space. There's nothing particularly bayesian about "I'd start from, say, 0.05 and work from there..." – Fomite Jul 17 '15 at 20:04
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multiple random starting points can be used to avoid being stuck in a local maximum

"frequentist packages"... lol (as if it was a thing): I always find "dichotomous thinking" very interesting

thank god there is a Likehood school along with the Bayesian and the Frequentist.

One can be a Likehoodist without going through the frequentist checkpoint, and the likelihood does not hold a special place in the frequentist school.

Stefano Nembrini
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