Longitudinal data are useful for capturing and analyzing patterns of change over time. Often, these patterns follow a nonlinear form. One useful and commonly applied nonlinear function is the piecewise function, which assumes growth occurs in distinct phases, each with its own functional form. Past literature has established that Bayesian inference is preferred over likelihood-based methods for estimating piecewise models. To address this, we developed the R package BEND - Bayesian Estimation of Nonlinear Data (available on CRAN). The purpose of BEND is to provide a user friendly software for estimating nonlinear longitudinal models using a Bayesian inference approach. Given the flexibility and practicality of the piecewise models, BEND includes several extensions of it to accommodate various types of complex longitudinal datasets and applications. Bayes_PREM() can empirically identify the number and location of random changepoints in a piecewise random effects model. This function can also model multiple latent classes with different longitudinal growth patterns and incorporate covariates to predict the outcome and latent class membership. Bayes_BPREM() can jointly model the longitudinal piecewise trajectories of two interrelated outcomes. Lastly, Bayes_CREM() can estimate the impact of group membership on longitudinal growth. This paper provides an overview of the functions included in BEND and empirical examples of how to apply these models in practice.

翻译：纵向数据有助于捕捉和分析随时间变化的模式。通常，这些模式呈现非线性形式。分段函数是一种常用且实用的非线性函数，它假设增长发生在不同阶段，每个阶段具有各自的函数形式。已有文献证实，在估计分段模型时，贝叶斯推断优于基于似然的方法。为此，我们开发了R语言包BEND——非线性数据的贝叶斯估计（可在CRAN获取）。BEND旨在提供一种用户友好的工具，用于通过贝叶斯推断方法估计非线性纵向模型。鉴于分段模型的灵活性和实用性，BEND包含其多种扩展形式，以适应各种复杂纵向数据集和应用场景。函数Bayes_PREM()可经验性地识别分段随机效应模型中随机变点的数量和位置。该函数还能对具有不同纵向增长模式的多个潜在类别进行建模，并纳入协变量以预测结果变量和潜在类别归属。函数Bayes_BPREM()可对两个相互关联结果的纵向分段轨迹进行联合建模。此外，函数Bayes_CREM()可估计分组变量对纵向增长的影响。本文概述了BEND中各项函数的功能，并提供了在实践应用中如何运用这些模型的实证案例。