Inference in a Binary Response Model with Applications to Data Analysis*
通过蒙特卡洛模拟比较了逻辑回归系数标准误的渐近公式与自助法估计，发现自助法在小样本下更准确，并用两个实例验证了结果。
ABSTRACT Standard errors of the coefficients of a logistic regression (a binary response model) based on the asymptotic formula are compared to those obtained from the bootstrap through Monte Carlo simulations. The computer intensive bootstrap method, a nonparametric alternative to the asymptotic estimate, overestimates the true value of the standard errors while the asymptotic formula underestimates it. However, for small samples the bootstrap estimates are substantially closer to the true value than their counterpart derived from the asymptotic formula. The methodology is discussed using two illustrative data sets. The first example deals with a logistic model explaining the log‐odds of passing the ERA amendment by the 1982 deadline as a function of percent of women legislators and the percent vote for Reagan. In the second example, the probability that an ingot is ready to roll is modelled using heating time and soaking time as explanatory variables. The results agree with those obtained from the simulations. The value of the study to better decision making through accurate statistical inference is discussed.