[U] User's Guide

[ U ] 26.9 Exact estimators 363In the context denoted by the name conditional logistic regression—mentioned above—subjectsare members of pools, and one or more are chosen, typically to be infected by some disease or tohave some other unfortunate event befall them. Thus the characteristics of the chosen and not chosenare known, and the issue of the characteristics of the chooser never arises. Either way, it is the samemodel.In their choice-model interpretations, mlogit and clogit assume that the odds ratios are independentof other alternatives, known as the independence of irrelevant alternatives (IIA) assumption. Thisassumption is often rejected by the data and the nested logit model does not impose this condition.nlogit is also popular for fitting the random utility choice model.asmprobit is for use with outcomes that have no natural ordering and with regressors that arealternative specific. It is weakly related to mlogit. Unlike mlogit, asmprobit does not assume theIIA.mprobit is also for use with outcomes that have no natural ordering but with models that do nothave alternative-specific regressors.26.8 Count dependent-variable modelsThese models concern dependent variables that count the number of occurrences of an event. Inthis category, we include Poisson and negative binomial regression. For the Poisson model,E(count) = E j exp(x j β)where E j is the exposure time. poisson fits this model. There is also an exact Poisson estimator;see [U] 26.9 Exact estimators.Negative-binomial regression refers to estimating with data that are a mixture of Poisson counts.One derivation of the negative binomial model is that individual units follow a Poisson regressionmodel but there is an omitted variable that follows a gamma distribution with variance α. Negativebinomialregression estimates β and α. nbreg fits such models. A variation on this, unique to Stata,allows you to model α. gnbreg fits those models.Zero inflation refers to count models in which the number of 0 counts is more than would beexpected in the regular model, and that is due to there being a probit or logit process that must firstgenerate a positive outcome before the counting process can begin.Stata’s zip command fits zero-inflated Poisson models.Stata’s zinb command fits zero-inflated negative binomial models.ztp and ztnb fit zero-truncated Poisson and negative binomial models. In zero-inflated models,you observe too many zeros, so you fit a separate model to them. In zero-truncated models, you donot observe the zeros.26.9 Exact estimatorsExact estimators refer to models which, rather than being estimated by asymptotic formulas, areestimated by enumerating the conditional distribution of the sufficient statistics and then computingthe maximum likelihood estimate using that distribution. Standard errors cannot be estimated, butconfidence intervals can be and are obtained from the enumerations.exlogistic fits logistic models of binary data in this way.expoisson fits Poisson models of count data in this way.