Comparison of Bootstrap Confidence Interval Methods for GSCA Using a Monte Carlo Simulation.

Kwanghee Jung,Vibhuti Gupta,Jaehoon Lee,Gyeongcheol Cho

doi:10.3389/fpsyg.2019.02215

Abstract

Generalized structured component analysis (GSCA) is a theoretically well-founded approach to component-based structural equation modeling (SEM). This approach utilizes the bootstrap method to estimate the confidence intervals of its parameter estimates without recourse to distributional assumptions, such as multivariate normality. It currently provides the bootstrap percentile confidence intervals only. Recently, the potential usefulness of the bias-corrected and accelerated bootstrap (BCa) confidence intervals (CIs) over the percentile method has attracted attention for another component-based SEM approach—partial least squares path modeling. Thus, in this study, we implemented the BCa CI method into GSCA and conducted a rigorous simulation to evaluate the performance of three bootstrap CI methods, including percentile, BCa, and Student's t methods, in terms of coverage and balance. We found that the percentile method produced CIs closer to the desired level of coverage than the other methods, while the BCa method was less prone to imbalance than the other two methods. Study findings and implications are discussed, as well as limitations and directions for future research.

Highlights

Generalized structured component analysis (GSCA; Hwang and Takane, 2004, 2014) is an approach to component-based structure equation modeling (SEM), where constructs are represented by weighted composites or components of indicators
We focus on the three bootstrap confidence intervals (CIs) methods that are most popular in practice: percentile, bias-corrected and accelerated CI, and Student’s t (Efron and Tibshirani, 1993; Chernick, 2011)
We provide the results of the simulation study, displaying a series of plots that show the performance of the three bootstrap CI methods in terms of coverage and balance averaged over the six latent variables

Summary

INTRODUCTION

Generalized structured component analysis (GSCA; Hwang and Takane, 2004, 2014) is an approach to component-based structure equation modeling (SEM), where constructs are represented by weighted composites or components of indicators (observed variables; Tenenhaus, 2008; Rigdon, 2012). Instead, it utilizes the bootstrap method (Efron, 1982) to obtain the standard errors and confidence intervals non-parametrically. GSCA With Different CI Methods parameters are estimated using each bootstrap sample. The bootstrap standard errors and confidence intervals can be used to test statistical significance of the parameter estimates. Α 2 percentiles of the distribution of θ estimates obtained from resampling, where θ represents a parameter of interest and α is the level of significance (e.g., α = 0.05 for 95% CIs) (Efron, 1982). We applied GSCA to fit the model to each sample and, subsequently, obtained the percentile, BCa, and Student’s t CIs for the loading and path coefficient estimates based on 1,000 bootstrap samples (B = 1,000). There was no case of model non-convergence or inadmissible solution in the current simulation

EVALUATION CRITERIA

RESULTS

DISCUSSION