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In longitudinal studies, it is of fundamental importance to understand the dynamics in the mean function, variance function and correlations of the repeated or clustered measurements. For modelling the covariance structure, Cholesky‐type decomposition‐based approaches have been demonstrated to be effective. However, parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored, and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure. We propose a novel joint mean–variance correlation modelling approach for longitudinal studies. By applying hyperspherical co‐ordinates, we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness, and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization. The modelling framework proposed is parsimonious, interpretable and flexible for analysing longitudinal data. Extensive data examples and simulations support the effectiveness of the approach proposed.

The use of multilevel VAR(1) models to unravel within-individual process dynamics is gaining momentum in psychological research. These models accommodate the structure of intensive longitudinal datasets in which repeated measurements are nested within individuals. They estimate within-individual auto- and cross-regressive relationships while incorporating and using information about the distributions of these effects across individuals. An important quality feature of the obtained estimates pertains to how well they generalize to unseen data. Bulteel and colleagues (Psychol Methods 23(4):740–756, 2018a) showed that this feature can be assessed through a cross-validation approach, yielding a predictive accuracy measure. In this article, we follow up on their results, by performing three simulation studies that allow to systematically study five factors that likely affect the predictive accuracy of multilevel VAR(1) models: (i) the number of measurement occasions per person, (ii) the number of persons, (iii) the number of variables, (iv) the contemporaneous collinearity between the variables, and (v) the distributional shape of the individual differences in the VAR(1) parameters (i.e., normal versus multimodal distributions). Simulation results show that pooling information across individuals and using multilevel techniques prevent overfitting. Also, we show that when variables are expected to show strong contemporaneous correlations, performing multilevel VAR(1) in a reduced variable space can be useful. Furthermore, results reveal that multilevel VAR(1) models with random effects have a better predictive performance than person-specific VAR(1) models when the sample includes groups of individuals that share similar dynamics.

Missing data are inevitable in mobile health (mHealth) and ubiquitous health (uHealth) research and are often driven by distinct within- and between-person factors that influence compliance. Understanding these distinct mechanisms underlying nonresponse can inform strategies to improve compliance and strengthen the validity of inferences about health behaviors. However, current missing data handling techniques rarely disentangle these different sources of nonresponse, especially when data are missing not at random. We demonstrate the usability of joint modeling in the mHealth context, showing how simultaneously accounting for the dynamics of health behavior and both within- and between-person missingness mechanisms can affect the validity of health behavior inferences. We also illustrate how joint modeling can inform distinct sources of (possibly nonignorable) missingness in studies using ecological momentary assessment and wearable devices. We provide a practical workflow for applying joint models to empirical data. We applied joint modeling on empirical data comprising 1 year of daily smartphone-based ecological momentary assessment data (affect and energetic feeling) and smartwatch-tracked physical activity (PA). The approach combined (1) a multilevel vector autoregressive model for examining the reciprocal influences between daily affect and PA, and (2) a multilevel probit model for missingness. Unlike conventional 2-stage imputation methods-which first impute missing data before fitting the main model-joint modeling handles missingness during model fitting without explicit imputation. Sensitivity analyses compared results from the proposed method to other missing data approaches that do not explicitly model missingness. A simulation study designed to mirror the temporally clustered (eg, consecutive days of missing data) and person-specific missingness patterns of the empirical data validated the feasibility of the proposed approach. Sensitivity analysis indicated relative robustness of the autoregressive effects across missing data handling approaches, whereas cross-regressive effects could be detected only under the joint modeling but not with methods that did not simultaneously model missingness mechanisms. Specifically, under joint modeling approaches, participants had higher levels of PA on days following a previous day with higher self-report energy levels (95% credible interval [CrI] 0.012-0.049). Furthermore, the missing data model revealed both missing not at random and missing at random mechanisms. For example, lower PA predicted higher missingness in PA at the within-person level (95% CrI -1.528 to -1.441). Being employed was associated with higher missingness in device-tracked PA at the between-person level (95% CrI 0.148-0.574). Finally, simulation showed that joint modeling could improve the accuracy of estimates and identify nonignorable missingness. We recommend joint modeling with multilevel decomposition for addressing nonignorable missingness in mHealth/uHealth studies collecting intensive longitudinal data. We also suggest using a missing data model to explore the missingness mechanism and inform data collection strategies.

Research in psychology is experiencing a rapid increase in the availability of intensive longitudinal data. To use such data for predicting feelings, beliefs, and behavior, recent methodological work suggested combinations of the longitudinal mixed-effect model with Lasso regression or with regression trees. The present article adds to this literature by suggesting an extension of these models that—in addition to a random effect for the mean level—also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After introducing the extended mixed-effect location scale ( E-MELS ), the extended mixed-effect location-scale Lasso model ( Lasso E-MELS ), and the extended mixed-effect location-scale tree model ( E-MELS trees ), we show how its parameters can be estimated using a marginal maximum likelihood approach. Using real and simulated example data, we illustrate how to use E-MELS, Lasso E-MELS, and E-MELS trees for building prediction models to forecast individuals’ daily nervousness. The article is accompanied by an R package (called mels) and functions that support users in the application of the suggested models.

This paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are as follows: (1) testing the null hypothesis that the mean of a functional process is parametric against a general alternative modelled by penalized splines; and (2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo-likelihood ratio test is proposed, and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite-sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized δ-power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls.

With the advent of new data collection technologies, intensive longitudinal data (ILD) are collected more frequently than ever. Along with the increased prevalence of ILD, more methods are being developed to analyze these data. However, relatively few methods have yet been applied for making long- or even short-term predictions from ILD in behavioral settings. Applications of forecasting methods to behavioral ILD are still scant. We first establish a general framework for modeling ILD and then extend that frame to two previously existing forecasting methods: these methods are Kalman prediction and ensemble prediction. After implementing Kalman and ensemble forecasts in free and open-source software, we apply these methods to daily drug and alcohol use data. In doing so, we create a simple, but nonlinear dynamical system model of daily drug and alcohol use and illustrate important differences between the forecasting methods. We further compare the Kalman and ensemble forecasting methods to several simpler forecasts of daily drug and alcohol use. Ensemble forecasts may be more appropriate than Kalman forecasts for nonlinear dynamical systems models, but further forecasting evaluation methods must be put into practice.

In this paper, we present and evaluate a novel Bayesian regime-switching zero-inflated multilevel Poisson (RS-ZIMLP) regression model for forecasting alcohol use dynamics. The model partitions individuals’ data into two phases, known as regimes, with: (1) a zero-inflation regime that is used to accommodate high instances of zeros (non-drinking) and (2) a multilevel Poisson regression regime in which variations in individuals’ log-transformed average rates of alcohol use are captured by means of an autoregressive process with exogenous predictors and a person-specific intercept. The times at which individuals are in each regime are unknown, but may be estimated from the data. We assume that the regime indicator follows a first-order Markov process as related to exogenous predictors of interest. The forecast performance of the proposed model was evaluated using a Monte Carlo simulation study and further demonstrated using substance use and spatial covariate data from the Colorado Online Twin Study (CoTwins). Results showed that the proposed model yielded better forecast performance compared to a baseline model which predicted all cases as non-drinking and a reduced ZIMLP model without the RS structure, as indicated by higher AUC (the area under the receiver operating characteristic (ROC) curve) scores, and lower mean absolute errors (MAEs) and root-mean-square errors (RMSEs). The improvements in forecast performance were even more pronounced when we limited the comparisons to participants who showed at least one instance of transition to drinking.

Motivated by an empirical analysis of the Childhood Asthma Management Project, CAMP, we introduce a new screening procedure for varying coefficient models with ultrahigh-dimensional longitudinal predictor variables. The performance of the proposed procedure is investigated via Monte Carlo simulation. Numerical comparisons indicate that it outperforms existing ones substantially, resulting in significant improvements in explained variability and prediction error. Applying these methods to CAMP, we are able to find a number of potentially important genetic mutations related to lung function, several of which exhibit interesting nonlinear patterns around puberty.

In this article, we propose penalized spline (P‐spline)‐based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time‐varying coefficients, functional subject‐specific random effects, and residual measurement error processes. Using P‐splines, we propose nonparametric estimation of the population mean function, varying coefficient, random subject‐specific curves, and the associated covariance function that represents between‐subject variation and the variance function of the residual measurement errors which represents within‐subject variation. Proposed methods offer flexible estimation of both the population‐ and subject‐level curves. In addition, decomposing variability of the outcomes as a between‐ and within‐subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood‐based method to select multiple smoothing parameters. Furthermore, we study the asymptotics of the baseline P‐spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between‐ and within‐subject covariance decomposition is illustrated through an analysis of Berkeley growth data, where we identified clearly distinct patterns of the between‐ and within‐subject covariance functions of children's heights. We also apply the proposed methods to estimate the effect of antihypertensive treatment from the Framingham Heart Study data.

Multiple outcomes, both continuous and discrete, are routinely gathered on subjects in longitudinal studies and during routine clinical follow-up in general. To motivate our work, we consider a longitudinal study on patients with primary biliary cirrhosis (PBC) with a continuous bilirubin level, a discrete platelet count and a dichotomous indication of blood vessel malformations as examples of such longitudinal outcomes. An apparent requirement is to use all the outcome values to classify the subjects into groups (e.g., groups of subjects with a similar prognosis in a clinical setting). In recent years, numerous approaches have been suggested for classification based on longitudinal (or otherwise correlated) outcomes, targeting not only traditional areas like biostatistics, but also rapidly evolving bioinformatics and many others. However, most available approaches consider only continuous outcomes as a basis for classification, or if noncontinuous outcomes are considered, then not in combination with other outcomes of a different nature. Here, we propose a statistical method for clustering (classification) of subjects into a prespecified number of groups with a priori unknown characteristics on the basis of repeated measurements of several longitudinal outcomes of a different nature. This method relies on a multivariate extension of the classical generalized linear mixed model where a mixture distribution is additionally assumed for random effects. We base the inference on a Bayesian specification of the model and simulation-based Markov chain Monte Carlo methodology. To apply the method in practice, we have prepared ready-to-use software for use in R (http://www.R-project.org). We also discuss evaluation of uncertainty in the classification and also discuss usage of a recently proposed methodology for model comparison—the selection of a number of clusters in our case—based on the penalized posterior deviance proposed by Plummer [Biostatistics 9 (2008) 523—539].