Econometrica: Sep 1981, Volume 49, Issue 5

Maximum Likelihood Estimator for Choice-Based Samples

https://doi.org/0012-9682(198109)49:5<1289:MLEFCS>2.0.CO;2-I
p. 1289-1316

Stephen R. Cosslett

A discrete-choice probability model can be estimated from a sample stratified on the choice variable by maximizing the "pseudo-likelihood," a quantity closely related to the log likelihood for a random sample. We investigate the asymptotic properties of the estimator, and show that it is consistent, asymptotically normally distributed, and satisfies a commonly used criterion for asymptotic efficiency.
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