Assessing the Effect of Different Covariates Distributions on Parameter Estimates for Multinomial Logistic Regression (MLR)

In fitting a multinomial logistic regression model, one of the most important part is estimating the parameter. In Multinomial Logistic Regression (MLR), Maximum Likelihood Estimation (MLE) method is used to estimate the parameters. MLE is the suitable method to be applied to the problems associated with categorical response variables since it has several benefits such as sufficiency, consistency, efficiency and parameterization invariance. This study investigates the different type of continuous distributions (normal, negatively skewed, positively skewed) on parameter estimation via Monte Carlo simulation. From the simulation result, it shows that as the sample size increases, the effect of covariate distribution reduces. The estimated parameter also less affected for model with normal covariate distribution. At sample size 300 and above, the estimated parameter with normal covariate distribution is considered as close to the true parameter value. Interestingly, for the positively skewed, the estimated parameter also obtained unbiased parameter at sample size 300 and above. However, for negatively skewed, it requires a larger sample size to get closer to the true parameter value. The estimated parameters deviate too far from the true parameter at small sample size. As expected, as sample size increases the parameter estimates for all distributions are getting close to the true parameter value. Lastly, the distribution for MLR with more than one covariate give the same effect as the MLR model with only one covariate on parameter estimations.