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Estimating knots and their association in parallel bilinear spline growth curve models in the framework of individual measurement occasions.
Psychological Methods ( IF 7.6 ) Pub Date : 2021-03-29 , DOI: 10.1037/met0000309
Jin Liu 1 , Robert A Perera 2
Affiliation  

Latent growth curve models with spline functions are flexible and accessible statistical tools for investigating nonlinear change patterns that exhibit distinct phases of development in manifested variables. Among such models, the bilinear spline growth model (BLSGM) is the most straightforward and intuitive but useful. An existing study has demonstrated that the BLSGM allows the knot (or change-point), at which two linear segments join together, to be an additional growth factor other than the intercept and slopes so that researchers can estimate the knot and its variability in the framework of individual measurement occasions. However, developmental processes usually unfold in a joint development where two or more outcomes and their change patterns are correlated over time. As an extension of the existing BLSGM with an unknown knot, this study considers a parallel BLSGM (PBLSGM) for investigating multiple nonlinear growth processes and estimating the knot with its variability of each process as well as the knot-knot association in the framework of individual measurement occasions. We present the proposed model by simulation studies and a real-world data analysis. Our simulation studies demonstrate that the proposed PBLSGM generally estimate the parameters of interest unbiasedly, precisely and exhibit appropriate confidence interval coverage. An empirical example using longitudinal reading scores, mathematics scores, and science scores shows that the model can estimate the knot with its variance for each growth curve and the covariance between two knots. We also provide the corresponding code for the proposed model.

中文翻译:

在单个测量场合的框架内估计结点及其在平行双线性样条增长曲线模型中的关联。

具有样条函数的潜在增长曲线模型是灵活且易于访问的统计工具,用于研究在显性变量中表现出不同发展阶段的非线性变化模式。在这些模型中,双线性样条增长模型(BLSGM)是最直接、最直观但最有用的。一项现有研究表明,BLSGM 允许两个线性段连接在一起的结点(或变化点)成为除截距和斜率之外的额外增长因子,以便研究人员可以估计结点及其在个别测量场合的框架。然而,发展过程通常以联合发展的形式展开,其中两个或多个结果及其变化模式随时间相关。作为现有 BLSGM 的一个未知结的扩展,本研究考虑使用并行 BLSGM (PBLSGM) 来研究多个非线性生长过程,并估计结及其每个过程的可变性以及个体测量场合框架内的结-结关联。我们通过模拟研究和真实世界的数据分析来展示所提出的模型。我们的模拟研究表明,所提出的 PBLSGM 通常可以无偏、准确地估计感兴趣的参数,并表现出适当的置信区间覆盖。使用纵向阅读分数、数学分数和科学分数的经验示例表明,该模型可以估计结及其每个生长曲线的方差和两个结之间的协方差。我们还为所提出的模型提供了相应的代码。我们通过模拟研究和真实世界的数据分析来展示所提出的模型。我们的模拟研究表明,所提出的 PBLSGM 通常可以无偏、准确地估计感兴趣的参数,并表现出适当的置信区间覆盖。使用纵向阅读分数、数学分数和科学分数的经验示例表明,该模型可以估计结及其每个生长曲线的方差和两个结之间的协方差。我们还为所提出的模型提供了相应的代码。我们通过模拟研究和真实世界的数据分析来展示所提出的模型。我们的模拟研究表明,所提出的 PBLSGM 通常可以无偏、准确地估计感兴趣的参数,并表现出适当的置信区间覆盖。使用纵向阅读分数、数学分数和科学分数的经验示例表明,该模型可以估计结及其每个生长曲线的方差和两个结之间的协方差。我们还为所提出的模型提供了相应的代码。科学分数表明,该模型可以根据每个生长曲线的方差和两个结点之间的协方差来估计结点。我们还为所提出的模型提供了相应的代码。科学分数表明,该模型可以根据每个生长曲线的方差和两个结点之间的协方差来估计结点。我们还为所提出的模型提供了相应的代码。
更新日期:2021-03-29
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