具有固定和非正态潜变量的相关样本
Correlated samples with fixed and nonnormal latent variables
摘要：
一般结构方程模型适用于由$I$相关样本组成的面板数据集。相关样本可以是来自相关总体的数据或来自面板数据场合的相关观测。我们考虑的情况下，完全的伪正态可能性不能使用，例如，在高度不平衡的数据中，参与的个人没有出现在连续几年。该模型是由部分似然估计，这将是独立和正常样本的完整和正确的可能性。证明了渐近标准误差（a.s.e.）的）的最重要的参数和整体拟合测量是相同的，相应的正态性和独立性的标准假设下得出的所有观察。这些结果是非常重要的，因为它们使我们能够应用经典的统计方法进行推断，只使用一阶和二阶矩，相关和非正态数据。通过模拟研究，我们表明，a.s.e.基于前两个矩的具有可忽略的偏差，并且提供比a.s.e.更少的可变性。的计算的替代鲁棒估计，利用高达四阶矩。我们的方法和结果被应用到真实的面板数据，它表明，相关的样本不能制定和分析作为独立的样本。我们还提供强大的a.s.e.的剩余参数。此外，我们在模拟中表明，不考虑样本相关性的效率损失很小，在随机变量和固定变量的情况下可以忽略不计。
英文摘要：
A general structural equation model is fitted on a panel data set that consists of $I$ correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider cases in which the full pseudo-normal likelihood cannot be used, for example, in highly unbalanced data where the participating individuals do not appear in consecutive years. The model is estimated by a partial likelihood that would be the full and correct likelihood for independent and normal samples. It is proved that the asymptotic standard errors (a.s.e.'s) for the most important parameters and an overall-fit measure are the same as the corresponding ones derived under the standard assumptions of normality and independence for all the observations. These results are very important since they allow us to apply classical statistical methods for inference, which use only first- and second-order moments, to correlated and nonnormal data. Via a simulation study we show that the a.s.e.'s based on the first two moments have negligible bias and provide less variability than the a.s.e.'s computed by an alternative robust estimator that utilizes up to fourth moments. Our methodology and results are applied to real panel data, and it is shown that the correlated samples cannot be formulated and analyzed as independent samples. We also provide robust a.s.e.'s for the remaining parameters. Additionally, we show in the simulation that the efficiency loss for not considering the correlation over the samples is small and negligible in the cases with random and fixed variables.
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