Analysis of Quadratic Pathway with Resampling Bootstrap on Simulation Data

Abstract

The purpose of this study is to determine whether bootstrap resampling can be used in overcoming violations of the normality assumption residual quadratic path analysis. Data with simulation studies in this study were generated with one exogenous variable, one pure endogenous variable, and one endogenous mediating variable. The residuals are raised following the Weibull distribution to represent normality conditions not met, then after testing the normality of residuals, a p-value of <2.2e-16 is generated and the value is less than , so it can be proven that the residuals are not normally distributed. Estimation of parameters in quadratic resampling bootstrap path analysis produces a quadratic model which shows that each increase in the variable   will increase the variable  , but at the peak point of (0.167; 0.151), the variable   can decrease with the assumption that the other variables are fixed. Also, each increase in variables   will increase the variable   , but at the peak point (0.667; 0.298)   will decrease with the assumption that the other variables are fixed. The results of testing the remaining normality assumption using Kolmogorov Smirnov, the resulting p-value of 0.2884 and 0.116. These values are more than α=0,05, so it can be concluded that the remainder follows the normal distribution. The conclusion of this research is bootstrap resampling can overcome the violation of the normality assumption residual on quadratic path analysis.

Keywords: Quadratic Path Analysis, Simulation, Bootstrap Resampling.