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：模型设定搜索与修改常用于协方差结构分析或结构方程模型中以提升拟合优度。然而，这类操作易受偶然因素影响——适用于某一样本的模型可能无法推广至同一总体的另一样本。本文提出改进的拉格朗日乘子检验，通过系统化执行模型设定搜索并有效识别缺失参数，提供了可靠方法。基于标准LM检验与Wald检验中的逐步自助法，本数据驱动方法提升了参数识别的精确性。蒙特卡洛模拟与政治科学领域两项实证应用的结果表明，改进的LM检验在处理小样本规模及高自由度模型时尤为有效。该方法既优化了统计拟合度，又解决了模型设定中偶然因素利用的固有问题。