Simulating Parametric and Nonparametric Models

Abstract

The purpose of this paper was to investigate the performance of the parametric bootstrap data generating processes (DGPs) methods and to compare the parametric and nonparametric bootstrap (DGPs) methods for estimating the standard error of simple linear regression (SLR) under various assessment conditions. When the performance of the parametric bootstrap method was investigated, simple linear models were employed to fit the data. With the consideration of the different bootstrap levels and sample sizes, a total of twelve parametric bootstrap models were examined. Three hypothetical and one real datasets were used as the basis to define the population distributions and the “true” SEEs. A bootstrap paper was conducted on different parametric and nonparametric bootstrap (DGPs) methods reflecting three levels for group proficiency differences, three levels of sample sizes, three test lengths and three bootstrap levels. Bias of the SLR, standard errors of the SLR, root mean square errors of the SLR, were calculated and used to evaluate and compare the bootstrap results. The main findings from this bootstrap paper were as follows: (i) The parametric bootstrap DGP models with larger bootstrap levels generally produced smaller bias likewise a larger sample size. (ii) The parametric bootstrap models with a higher bootstrap level generally yielded more accurate estimates of the standard error than the corresponding models with lower bootstrap level. (iii) The nonparametric bootstrap method generally produced less accurate estimates of the standard error than the parametric bootstrap method. However, as the sample size increased, the differences between the two bootstrap methods became smaller. When the sample size was equal to or larger than 3,000, say 10000, the differences between the nonparametric bootstrap DGP method and the parametric bootstrap DGP model that produced the smallest RMSE were very small. (4) Of all the models considered in this paper, parametric bootstrap DGP models with higher bootstrap performed better under most bootstrap conditions. (5) Aside from method effects, sample size and test length had the most impact on estimating the Simple Linear Regression.