It is usually impossible to impose experimental conditions in large-scale longitudinal (observational) studies in education. This increases the risk of bias due to for instance unobserved heterogeneity, missing background variables, and dropouts. A flexible statistical model is required for the nature of the observational assessment data and to account for the unexplained heterogeneity. A general class of longitudinal item response theory (IRT) models is proposed, where growth in performance can be monitored using a skewed multivariate normal distribution for the latent variables. Change in performance and unexplained heterogeneity is addressed through structured covariance patterns and skewed multivariate latent variable distributions. The Cholesky decomposition of the covariance matrix is considered to model the dependence structure. A novel multivariate skew-normal distribution is defined by the antedependence model with centered skew-normal distributed errors. A hybrid MCMC approach is developed for parameter estimation, model-fit assessment, and model comparison. Results of simulation studies show good parameter recovery. A longitudinal assessment study by the Brazilian federal government is considered to show the performance of the general LIRT model.

通常不可能在教育的大规模纵向（观察）研究中强加实验条件。由于未观察到的异质性、缺少背景变量和辍学等原因，这会增加偏差的风险。观察评估数据的性质需要灵活的统计模型，并解释无法解释的异质性。提出了一类通用的纵向项目响应理论 (IRT) 模型，其中可以使用潜在变量的偏态多元正态分布来监控性能的增长。性能变化和无法解释的异质性通过结构化协方差模式和倾斜的多元潜在变量分布来解决。协方差矩阵的 Cholesky 分解被认为是对依赖结构建模。一种新颖的多元偏正态分布由具有中心偏态正态分布误差的前依赖模型定义。为参数估计、模型拟合评估和模型比较开发了一种混合 MCMC 方法。模拟研究的结果显示出良好的参数恢复。巴西联邦政府的一项纵向评估研究被认为显示了一般 LIRT 模型的性能。