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I am trying to implement a robit model. The answer here has a description.

I currently have functioning code (written in R) that follows the procedure laid out in this paper. It looks like this:

1. Input data y, X, beta, nu
2. [E step] Calculate sufficient summary statistics
3. Update beta based on (2)
4. [M step] Find nu that maximizes the likelihood given y, x, and beta from (3)
5. Assess convergence based on the change in likelihood
6. Return to (1) if necessary 

However, I do not think I have the correct implementation. On page 9, the author says:

Then update nu using, for example, the half-interval method

The paper seems to be saying there is an intermediate step after (4) where a different nu is used as the update (based on the half-interval method?). This is not clear to me.

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    $\begingroup$ Have you had a look at this Koenker article? (Parametric Links for Binary Response). It contains R code. I think what you are looking for is also refereed to as The Gosset link (that's how I remembered it and that's how Koenker calls it, so you might try that). Finally, the R Package ‘glmx’ has some tools related to what you seem to be looking for (alternative links for logistic). Including the Gosset link. $\endgroup$
    – user603
    Oct 11, 2017 at 21:31
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    $\begingroup$ @user603 thanks for the link. i did come across the glmx package but did not make the connection between the t-distribution and the Gosset link. $\endgroup$ Oct 11, 2017 at 22:15

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