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在协方差结构分析（CSA）或结构方程建模（SEM）中常被用于提高模型拟合优度。然而，这些实践容易受到偶然性影响，因为拟合某个样本的模型可能无法推广到来自同一总体的其他样本。本文提出了改进的拉格朗日乘子（LM）检验，为进行全面的模型设定搜索和有效识别缺失参数提供了可靠方法。通过在标准LM检验和Wald检验中采用逐步自助法，我们的数据驱动方法提升了参数识别的准确性。蒙特卡洛模拟以及政治学领域两项实证应用的结果表明，改进的LM检验在处理小样本和自由度较大的模型时尤为有效。该方法不仅有助于获得更好的统计拟合，还解决了模型设定中偶然性利用的问题。