We propose a latent linear mixed model to analyze multivariate longitudinal data of multiple ordinal variables, which are manifestations of fewer continuous latent variables. We focus on the latent level where the effects of observed covariates on the latent variables are of interest. We incorporate serial correlation into the variance component rather than assuming independent residuals. We show that misleading inference may be drawn when misspecifying the variance component. Furthermore, we provide a graphical tool depicting latent empirical semi‐variograms to detect serial correlation for latent stationary linear mixed models. We apply our proposed model to examine the treatment effect on patients having the amyotrophic lateral sclerosis disease. The result shows that the treatment can slow down progression of latent cervical and lumbar functions.

中文翻译：

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潜在线性混合模型中的序列相关结构，用于分析多元纵向序数响应

我们提出了一个潜在的线性混合模型来分析多个有序变量的多元纵向数据，这是较少连续连续变量的体现。我们关注潜在水平，在该水平上观察到的协变量对潜在变量的影响是令人感兴趣的。我们将序列相关性纳入方差成分，而不是假设独立残差。我们表明，错误指定方差成分时可能会产生误导性推断。此外，我们提供了描述潜在经验半变异函数的图形工具，以检测潜在平稳线性混合模型的序列相关性。我们应用我们提出的模型来检查对肌萎缩性侧索硬化病患者的治疗效果。