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Exact logistic regression

Stata’s command for exact logistic regression provides more reliable statistical inference with small-sample datasets.

  • exlogistic fits exact logistic regression models. The dependent variable can be Bernoulli (0 or 1) or binomial (the number of successes in n trials). Exact joint hypothesis tests can be performed, and predictions with exact confidence intervals can be obtained.

Example

Stata’s exact logistic regression command provides better coverage in small samples than does standard logistic regression.

It also provides parameter estimates and confidence intervals where standard asymptotic methods cannot.

Such cases include small-data problems with binary regressors for which the outcome is 1 whenever the regressor is 1.

In the example below, every treated patient exhibits a positive response. Standard logistic regression cannot estimate the treatment effect. Stata’s exlogistic command can:

. exlogistic response treatment x2 x3 Enumerating sample-space combinations: observation 1: enumerations = 2 observation 2: enumerations = 4 (omitted) observation 57: enumerations = 1659 observation 58: enumerations = 900 note: CMLE estimate for treatment is +inf; computing MUE Exact logistic regression Number of obs = 58 Model score = 13.87402 Pr >= score = 0.0020
response Odds Ratio Suff. 2*Pr(Suff.) [95% Conf. Interval]
treatment 2.101107* 16 0.5277 .2616515 +Inf
x2 .5183876 13 0.7180 .0690557 4.336805
x3 .11389 7 0.0068 .0172465 .6023146
(*) median unbiased estimates (MUE)

Parameter estimates, standard errors, and CIs are calculated on the basis of permutation without recourse to asymptotic assumptions and results.

Not only is the treatment effect estimated, but tests of significance and reported confidence intervals are based on exact methods.

Stata also includes exact Poisson regression for count data.

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