Estimated asymptotic variances for the estimates of the parameters in a logit-probit model for binary response data are unreliable for moderate sized samples. We show how bootstrapping gives a bctter idea of the sampling distribution of the estimators, and can also allow an assessment of the reliability of the scoring of individuals on the latent scale. lntroductionWhen a one-factor logit-probit model is fitted by maximum likelihood to binary (0, I ) response data, one very often wishes to score the observed response patterns on the scale of the latent variable. We prefer to score with the estimated conditional mean of the latent variable for the given response pattern, though Bartholomew (1984) has suggested scoring the response patterns by their component scores: thesc are defined as the sum of the estimated discrimination parameters for items responding 1. A difficulty with both methods of scoring is that little is known about the sampling properties of the estimators of the discrimination parameters. Usually one depends on the first-order asymptotic distribution theory for maximum likelihood estimators which suggests that the discrimination parameters have a sampling distribution which is asymptotically normal. The covariance matrix of the estimators is estimated from the observed information matrix. For logit-probit models for binary response with their usually large number of parameters it is not clear that sample sizes are great enough in practice to justify the use of this procedure. One would like to know whether the distributions of the estimators are approximately normal. One also needs a guide to the reliability of the scoring of the response patterns, and this is difficult to obtain from standard asymptotic theory.A common way to investigate questions of this type when exact mathematical results are not feasible is to generate bootstrap samples, and use these as a substitute for the t Requests for reprints