Performance of the likelihood ratio test when fitting logistic regression models with small samples

In using the likelihood ratio test for the hypothesis concerning the slope parameter in logistic regression model, we usually make use of the fact that the null distribution of the test statistic is approximately chi-square with one degree of freedom (chi(1)(2)). The performance of the chi(1)(2) approximation for small sample sizes is investigated. It is found that theoretically the size of the test at the nominally 5% level can range from 6% to 14%. Furthermore as the value of the parameter which is not of interest varies, the type I error is fairly stable at around 0.05 when the probability of the least frequent outcome is not far from 0.50, but it deviates fairly severely from 0.05 when the probability of the least frequent outcome is near to 0.