Predicte probability after estimating an ordered logit model in STATA

In STATA, the cumulative probability Cij is considred as the probability that the ith individual is in the jth or higher category:
Cij = Pr(yij <= j) = Pr(yi = 1) + Pr(yi = 2) + …+ Pr(yi = j)

This cumulative probability is transformed into the cumulative logit and modelled as a linear function of IVs:
logit(Cij) = log(Cij/(1 – Cij)) = Aj – Beta*Xi

where Aj (known as the cutpoints) indicates the logit of the odds of being equal to or less than category j for the baseline group.

The prediction of probability after obtaining the coefficient estimates can be calculated as:
Pr(yi = 1) = exp(A1 – Beta*Xi) / (1+exp(A1 – Beta*Xi))
Pr(yi = 2) = exp(A2 – Beta*Xi) / (1+exp(A2 – Beta*Xi)) –  exp(A1 – Beta*Xi) / (1+exp(A1 – Beta*Xi))
Pr(yi = 3) = exp(A3 – Beta*Xi) / (1+exp(A3 – Beta*Xi)) –  exp(A2 – Beta*Xi) / (1+exp(A2 – Beta*Xi))

Pr(yi = j) = exp(Aj – Beta*Xi) / (1+exp(Aj – Beta*Xi)) –  exp(Ak – Beta*Xi) / (1+exp(Ak – Beta*Xi))
where k = j -1

About Hongwei Xu

I'm a social demographer, a single-child, a husband, and a father.
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