Browsing by Subject "Bivariate processes"

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    Bayesian Modeling of Associations in Bivariate Mixed-Effects Models for Segmented Growth Curves
    (2018-11) Peralta Torres, Yadira
    Developmental processes rarely occur in isolation; often the growth curves of two or more variables are interdependent. In addition, frequently, growth curves do not portray a constant pattern of change. Different stages or segments of development are present in the data. Bivariate piecewise linear mixed-effects models (BPLMEM) are a useful statistical framework to simultaneously describe two processes that portray segmented linear trajectories and to investigate their associations over time. Interrelations between the growth curves are measured by assuming a joint distribution of the random-effects parameters of each outcome variable. Furthermore, associations in the outcome variables collected from the same subject should be taken into account when they are modeled jointly. This association is modeled by correlating the error variance parameters of each outcome variable. There are several drawbacks in the literature of bivariate piecewise mixed-effects models. An important limitation in the BPLMEMs literature is that researchers have assumed uncorrelated residual errors across the two longitudinal processes, which is something unlikely to hold in practice. Also, current modeling choices for the random-effects in bivariate piecewise mixed-effects model have shortcomings. For instance, researchers have unintentionally imposed dependencies among the elements of the covariance matrix associated with the random-effects; or they have modeled only few of its covariance parameters determined by the research interest. In addition, simulation studies using BPLMEMs are scarce. Little is known about the performance of bivariate piecewise mixed-effects models under different correlational scenarios of the random-effects parameters and the error variances. Furthermore, a criticism to the piecewise linear model is a hypothesized abrupt change between one linear segment to another because this performance may not be true for all empirical scenarios. However, although a smooth transition or adaptation period between linear segments might be more realistic, the piecewise linear model is extensively used in practice. Thus, it is natural to wonder under which scenarios this is an acceptable choice. The purpose of the present study was to develop a BPLMEM using a Bayesian inference approach allowing the estimation of the association between error variances and providing a more robust modeling choice for the random-effects. Furthermore, the performance of the BPLMEM was investigated via a Monte Carlo simulation study focusing on the strength of the associations of the error variance parameters and the growth curves (represented by the random-effects’ correlational structure). An additional purpose was to empirically characterize scenarios for which the piecewise linear model gives a reasonable approximation to an underlying smoothed segmented trajectory given by a quadratic bend joining the linear phases of growth. Lastly, the contribution of bivariate mixed-effects modeling approaches is illustrated by using a BPLMEM to investigate the joint development of mathematics and reading achievement and the association between their longitudinal trajectories. This constitutes a novel approach to examine associations between educational domains over time. Simulation results showed that the strength of the association between the growth curves and the sample size had a significant effect on the performance of the BPLMEM. Specifically, lower relative bias of parameter estimates and higher model convergence was related to a stronger correlational structure between the random-effects of the growth curves. Likewise, slightly higher coverage rates and better convergence were associated with a smaller sample size. In addition, it was possible to identify cases for which the piecewise linear model had an acceptable performance when the true underlying trajectory had an adaptation period or bend between linear segments. Scenarios with small or centered bends were accurately described by a piecewise linear model. Results from the illustrative example suggested that mathematics and reading achievement are positively associated all along their segmented trajectories and that the strength of such association decreases over time. In addition, evidence of the same patterns of association of reading over mathematics and mathematics over reading were found.