A maximum likelihood estimation routine for two-level structural equation models with random slopes for latent covariates is presented. Because the likelihood function does not typically have a closed-form solution, numerical integration over the random effects is required. The routine relies upon a method proposed by du Toit and Cudeck (Psychometrika 74(1):65–82, 2009) for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically, reducing the computational burden of high-dimensional numerical integration. The method is demonstrated and assessed using a small-scale simulation study and an empirical example.

中文翻译：

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潜在协变量随机斜率多级结构方程模型的最大似然估计

介绍了具有潜在协变量随机斜率的两级结构方程模型的最大似然估计例程。由于似然函数通常没有封闭形式的解，因此需要对随机效应进行数值积分。该例程依赖于 du Toit 和 Cudeck (Psychometrika 74(1):65–82, 2009) 提出的用于重新制定似然函数的方法，以便可以分析整合通常较大的随机效应子集，从而减少计算负担高维数值积分。使用小规模模拟研究和经验示例来演示和评估该方法。