The Appropriate Sample Size to Avoid the Biasness of the Parameters Estimation in Binary Logistic Regression Models

In general, the maximum likelihood method with Newton-Raphson iteration is used to estimate the parameters of the binary logistic regression models, and also can be estimated using an iterative (re-)weighted least squares (IWLS) whose iterations are equivalent to the Newton-Raphson iterations. However, it is known that these methods produce bias estimates if small sample sizes are used. The main aim of this paper is to determine the appropriate sample size to achieve the unbiasedness of parameters estimates in the binary logistic regression model. To investigate the appropriate sample size three models were suggested and generated with known parameters. The estimates of the suggested models were collected via simulation study, using different sample sizes. The expected values for the collected parameters by the simulation where compared with the actual values of parameters of the suggested models. From the results of the simulation study, it was found that the appropriate sample size to achieve the unbiasness for such models, is 80 or more.