Model specification searches and modifications are commonly employed in covariance structure analysis (CSA) or structural equation modeling (SEM) to improve the goodness-of-fit. However, these practices can be susceptible to capitalizing on chance, as a model that fits one sample may not generalize to another sample from the same population. This paper introduces the improved Lagrange Multipliers (LM) test, which provides a reliable method for conducting a thorough model specification search and effectively identifying missing parameters. By leveraging the stepwise bootstrap method in the standard LM and Wald tests, our data-driven approach enhances the accuracy of parameter identification. The results from Monte Carlo simulations and two empirical applications in political science demonstrate the effectiveness of the improved LM test, particularly when dealing with small sample sizes and models with large degrees of freedom. This approach contributes to better statistical fit and addresses the issue of capitalization on chance in model specification.

翻译：模型设定搜索与修正常被用于协方差结构分析（CSA）或结构方程模型（SEM）中，以提升模型拟合优度。然而，这些操作易受巧合性利用的影响——即某一样本拟合良好的模型未必能推广至同一总体的其他样本。本文提出改进的拉格朗日乘数（LM）检验，该方法为进行彻底的模型设定搜索和有效识别缺失参数提供了可靠途径。通过将逐步自助法引入标准LM检验与Wald检验，本文提出的数据驱动方法增强了参数识别的准确性。蒙特卡洛模拟结果及政治学领域两项实证应用表明，改进的LM检验在处理小样本量和高自由度模型时尤为有效。该方法不仅有助于提升统计拟合度，还能有效解决模型设定中因巧合性利用产生的问题。