Bootstrapping technique in structural equation modeling: a Monte Carlo study

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Structural Equation Modeling (SEM) is a powerful statistical technique that used to measure the causal relationships between variables. SEM is common among social science researchers, but not with clinical researchers as in the clinical field, data commonly available in smaller sample size. Hence, it is affecting the performance of SEM. This study was to propose the use of Double Bootstrap method on SEM (DBSEM) with smaller samples. DBSEM is an extension of Bootstrap method on SEM (BSEM) in which we resample residuals from original model SEM. With the estimated residual errors with sample size = n as a population, a bootstrap sample of n persons with residual errors was drawn randomly with replacement. The DBSEM was expected to offer a practical and efficient performance compared to the original SEM. The double residual bootstrap method (resample with replacement) was used on SEM. A Monte Carlo simulation with the normal data distribution (n = 30, 50, 75, and 100) was used to test the performance of models. Several point estimators such as Standard Error (SE), Mean Square Error (MSE) and Root Mean Square Error (RMSE) were used to measure models performance. The performance of DBSEM model is far well better compared to the original model, SEM. All point estimators for DBSEM showed a decreasing value compared to SEM (point estimators values are high). The result shows that for BSEM and DBSEM model, there are steep decreasing values in SE, MSE and RMSE. Since the point estimates values for DBSEM are relatively lesser compared to SEM, we can conclude that double bootstrap increase model’s accuracy and its reliability.