Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models

Assessing mediational processes using piecewise linear growth curve models with individual measurement occasions

Longitudinal processes often unfold concurrently where the growth patterns of two or more longitudinal outcomes are associated. Additionally, if the study under investigation is long, the growth curves may exhibit nonconstant change with respect to time. Multiple existing studies have developed multivariate growth models with nonlinear functional forms to explore joint development where two longitudinal records are correlated over time. However, the relationship between multiple longitudinal outcomes may also be unidirectional. Accordingly, it is of interest to estimate regression coefficients of such unidirectional paths. One statistical tool for such analyses is longitudinal mediation models. In this study, we develop two models to evaluate mediational processes where the linear-linear piecewise functional form is utilized to capture the change patterns. We define the mediational process as either the baseline covariate or the change in covariate influencing the change in the mediator, which, in turn, affects the change in the outcome. We present the proposed models through simulation studies and real-world data analyses. Our simulation studies demonstrate that the proposed mediational models can provide unbiased and accurate point estimates with target coverage probabilities with a 95% confidence interval. The empirical analyses demonstrate that the proposed models can estimate covariates' direct and indirect effects on the change in the outcome. We also provide the corresponding code for the proposed models.

The Impact of Functional Form Complexity on Model Overfitting for Nonlinear Mixed-Effects Models

Nonlinear mixed-effects models (NLMEMs) allow researchers to model curvilinear patterns of growth, but there is ambiguity as to what functional form the data follow. Often, researchers fit multiple nonlinear functions to data and use model selection criteria to decide which functional form fits the data "best." Frequently used model selection criteria only account for the number of parameters in a model but overlook the complexity of intrinsically nonlinear functional forms. This can lead to overfitting and hinder the generalizability and reproducibility of results. The primary goal of this study was to evaluate the performance of eight model selection criteria via a Monte Carlo simulation study and assess under what conditions these criteria are sensitive to model overfitting as it relates to functional form complexity. Results highlighted criteria with the potential to capture overfitting for intrinsically nonlinear functional forms for NLMEMs. Information criteria and the stochastic information complexity criterion recovered the true model more often than the average or conditional concordance correlation. Results also suggest that the amount of residual variance and sample size have an impact on model selection for NLMEMs. Implications for future research and recommendations for application are also provided.

Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies

BACKGROUND

Longitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories.

METHODS

This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5-40 years. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts.

RESULTS

Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence.

CONCLUSIONS

LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software.

Linear-linear piecewise growth mixture models with unknown random knots: A primer for school psychology

Studying change over time requires rigorous and sometimes novel statistical methods that can support increasingly complex applied research questions. In this article, we provide an overview of the potential of piecewise growth mixture models. This type of longitudinal model can be used to advance our understanding of group and individual growth that may follow a segmented, or disjointed, pattern of change, and where the data come from a mixture of two or more latent classes. We then demonstrate the practical utility of piecewise growth mixture models by applying it to a subsample of students from the Early Childhood Longitudinal Study - Kindergarten Cohort of 1998 (ECLS-K) to ascertain whether mathematics achievement is characterized by one or two latent classes akin to students with and without mathematics difficulties. We discuss the applicability for school psychological research and provide supplementary online files that include an instructional sample dataset and corresponding R routine with explanatory annotations to assist in understanding the R routine before applying this approach in novel applications (https://doi.org/10.1016/j.jsp.2019.03.004).