Effects of different type of covariates and sample size on parameter estimation for multinomial logistic regression model

Abstract

The sample size and distributions of covariate may affect many statistical modeling techniques. This paper investigates the effects of sample size and data distribution on parameter estimates for multinomial logistic regression. A simulation study was conducted for different distributions (symmetric normal, positively skewed, negatively skewed) for the continuous covariates. In addition, we simulate categorical covariates to investigate their effects on parameter estimation for the multinomial logistic regression model. The simulation results show that the effect of skewed and categorical covariate reduces as sample size increases. The parameter estimates for normal distribution covariate apparently are less affected by sample size. For multinomial logistic regression model with a single covariate study, a sample size of at least 300 is required to obtain unbiased estimates when the covariate is positively skewed or is a categorical covariate. A much larger sample size is required when covariates are negatively skewed.