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Suppose we have a data set $X$. This data set consists of ordinal data (4 levels). To get estimates of the threshold coefficients and probit slope ($\beta_1, \dots, \beta_3$ and $\beta_4$ respectively), do most computational packages use maximum likelihood estimation? That is, given the data, MLE chooses the parameters that maximizes the probability of observing the data?

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Small note: If you have 4 ordinal levels, you should have only 3 thresholds. –  gung Dec 21 '12 at 19:36
    
Just to be clear, the number of $\beta$s depends on the number of explanatory variables, not on the number of levels. –  Dimitriy V. Masterov Dec 21 '12 at 21:13
    
As far as I know, MLE is the only way to estimate these. –  Dimitriy V. Masterov Dec 22 '12 at 1:57

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