Modeling within-person change over time and between-person differences in change over time is a primary goal in prevention science. When modeling change in an observed score over time with multilevel or structural equation modeling approaches, each observed score counts toward the estimation of model parameters equally. However, observed scores can differ in terms of their precision—both within and across participants. We propose an approach to weight observed scores by their level of precision, which is estimated as the inverse of their standard error of measurement in the context of item response modeling. Thus, scores with lower standard errors of measurement have greater weight, and scores with higher standard errors of measurement are down weighted. We discuss the weighting approaches and illustrate how to apply this approach with commonly available software. We then compare this approach to modeling change without weighting based on standard errors of measurement.

对人际变化随时间变化以及人际变化随时间变化进行建模是预防科学的主要目标。当使用多级或结构方程建模方法对观察到的分数随时间的变化进行建模时，每个观察到的分数将平均计入模型参数的估计中。但是，观察到的分数在参与者内部和参与者之间的准确性可能会有所不同。我们提出了一种方法，可以根据其得分的准确性对所观察到的分数进行加权，这可以通过在项目响应建模的情况下将其视为标准测量误差的倒数来估算。因此，具有较低标准测量误差的分数具有较大的权重，而具有较高标准测量误差的分数具有较低的权重。我们讨论加权方法，并说明如何将这种方法与常用软件一起应用。然后，我们将这种方法与不采用基于标准测量误差的加权的建模变化进行比较。