Abstract：
Research in psychology has seen a rapid increase in the usage of experience sampling methods and daily diary methods. The data that result from using these methods are typically analyzed with a mixed-effects or a multilevel model because it allows testing hypotheses about the time course of the longitudinally assessed variable or the influence of time-varying predictors in a simple way. Here, we describe an extension of this model that does not only allow to include random effects for the mean structure but also for the residual variance, for the parameter of an autoregressive process of order 1 and/or the parameter of a moving average process of order 1. After we have introduced this extension, we show how to estimate the parameters with maximum likelihood. Because the likelihood function contains complex integrals, we suggest using adaptive Gauss-Hermite quadrature and Quasi-Monte Carlo integration to approximate it. We illustrate the models using a real data example and also report the results of a small simulation study in which the two integral approximation methods are compared.
摘要：
心理学研究发现，经验抽样方法和日常日记方法的使用迅速增加。通常使用混合效应或多水平模型分析使用这些方法产生的数据，因为它允许以简单的方式测试关于纵向评估变量的时间过程或时变预测因子的影响的假设。这里,我们描述了这个模型的扩展，它不仅允许包括均值结构的随机效应，还包括残差方差的随机效应，用于阶数为1的自回归过程的参数和/或阶数为1的移动平均过程的参数。在我们引入这个扩展之后，我们展示了如何用最大似然估计参数。因为似然函数包含复杂积分，我们建议使用自适应高斯-埃尔米特正交和拟蒙特卡罗积分来逼近它。我们使用真实的数据示例说明了模型，并报告了一个小型模拟研究的结果，其中比较了两种积分逼近方法。
