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We demonstrate how developmental theories may be instantiated as statistical models, using hierarchical continuous‐time dynamic systems. This approach offers a flexible specification and an often more direct link between theory and model parameters than common modeling frameworks. We address developmental theories of the relation between the academic competencies of mathematics and language, using data from the online learning system Mindsteps. We use ability estimates from 160,164 observation occasions, across N = 4623 3rd to 9th grade students and five ability domains. Model development is step‐by‐step from simple to complex, with ramifications for theory and modeling discussed at each step.

Standardized tests of learning and memory are sensitive to changes associated with both aging and superimposed neurodegenerative diseases. Unfortunately, repeated behavioral test administration can be confounded by practice effects (PE), which may obscure declines in level of abilities and contribute to misdiagnoses. Growing evidence, however, suggests PE over successive longitudinal measurements may differentially predict cognitive status and risk for progressive decline associated with aging, mild cognitive impairment (MCI), and dementia. Thus, when viewed as a reflection of neurocognitive plasticity, PE may reveal residual abilities that can add to our understanding of age- and disease-related changes in learning and memory. The present study sought to evaluate differences in PE and verbal recall in a clinically characterized aging cohort assessed on multiple occasions over 3 years. Participants included 256 older adults recently diagnosed as cognitively unimpaired (CU; n = 126), or with MCI of amnestic (n = 65) or non-amnestic MCI (n = 2085), and multi-domain amnestic dementia of the Alzheimer’s type (DAT; n = 45). We applied a continuous time structural equation modeling (ctsem) approach to verbal recall performance on the Hopkins Verbal Learning Test in order to distinguish PE from individual occasion performance, coupled random changes, age trends, and differing measurement quality. Diagnoses of MCI and dementia were associated with lower recall performance on all trials, reduced PE gain per occasion, and differences in non-linear dynamic parameters. Practice self-feedback is a dynamic measure of the decay or acceleration in PE process changes over longitudinal occasions. As with PE and mean recall, estimated practice self-feedback followed a gradient from positive in CU participants to null in participants with diagnosed MCI and negative for those with dementia diagnoses. Evaluation of sensitivity models showed this pattern of variation in PE was largely unm

Personality traits and physical health both change over the life span. Theoretical models and empirical evidence suggest that these changes are related. The current study investigated the dynamic relations between personality traits and physical health at both the between-person and the within-person levels. Data were drawn from three longitudinal studies: the Veterans Affairs Normative Aging Study (NAS; N = 1,734), the Longitudinal Internet Studies for the Social Sciences (LISS; N = 13,559), and the Swedish Adoption/Twin Study of Aging (SATSA, N = 2,209). Using random intercept cross-lagged panel models (RI-CLPMs) and the continuous time (CT) models, after controlling the between-person variance, generally, evidence was found for bidirectional associations between changes in neuroticism and extraversion and changes in self-rated health and general disease level. Bidirectional associations between changes in neuroticism and change in cardiovascular diseases and central nervous system diseases were observed only when time was modeled as continuous. We also found within-person associations between changes in neuroticism and extraversion and changes in performance-based ratings of motor functioning impairment. According to the current findings, the dynamic within-person relations between personality traits and health outcomes were largely in the direction consistent with their between-person connections, although the within-person relationships were substantially smaller in strength when compared their between-person counterparts. Findings from the current study highlight the importance of distinguishing between-person and within-person effects when examining the longitudinal relationship between personality traits and health.

Well-being and smartphone use are thought to influence each other. However, previous studies mainly focused on one direction (looking at the effects of smartphone use on well-being) and considered between-person effects, with self-reported measures of smartphone use. By using 2548 assessments of well-being and trace data of smartphone use collected for 45 consecutive days in 82 adolescent participants (M$_{age}$ = 13.47, SD$_{age}$ = 1.62, 54% females), the present study disentangled the reciprocal and individual dynamics of well-being and smartphone use. Hierarchical Bayesian Continuous Time Dynamic Models were used to estimate how a change in frequency and duration of smartphone use predicted a later change in well-being, and vice versa. Results revealed that (i) when participants used the smartphone frequently and for a longer period, they also reported higher levels of well-being; (ii) well-being positively predicted subsequent duration of smartphone use; (iii) usage patterns and system dynamics showed heterogeneity, with many subjects showing reciprocal effects close to zero; finally, (iv) changes in well-being tend to persist longer than changes in the frequency and duration of smartphone use.

Im Rahmen dieser Dissertation bemühe ich mich, den statistischen Ansatz der zeitkontinuierlichen dynamischen Modellierung, der die Rolle der Zeit explizit berücksichtigt, zu erweitern und praktisch anwendbar zu machen. Diese Dissertation ist so strukturiert, dass ich in Kapitel 1 die Natur dynamischer Modelle bespreche, verschiedene Ansätze zum Umgang mit mehreren Personen betrachte und ein zeitkontinuierliches dynamisches Modell mit Input-Effekten (wie Interventionen) und einem Gaußschen Messmodell detailliert darstelle. In Kapitel 2 beschreibe ich die Verwendung der Software ctsem für R, die als Teil dieser Dissertation entwickelt wurde und die Modellierung von Strukturgleichungen und Mixed-Effects über einen frequentistischen Schätzansatz realisiert. In Kapitel 3 stelle ich einen hierarchischen, komplett Random-Effects beinhaltenden Bayesschen Schätzansatz vor, unter dem sich Personen nicht nur in Interceptparametern, sondern in allen Charakteristika von Mess - und Prozessmodell unterscheiden können, wobei die Schätzung individueller Parameter trotzdem von den Daten aller Personen profitiert. Kapitel 4 beschreibt die Verwendung der Bayesschen Erweiterung der Software ctsem. In Kapitel 5} betrachte ich die Natur experimenteller Interventionen vor dem Hintergrund zeitkontinuierlicher dynamischer Modellierung und zeige Ansätze, die die Art und Weise adressieren, mit der Interventionen auf psychologische Prozesse über die Zeit wirken. Das berührt Fragen, wie: 'Nach welcher Zeit zeigt eine Intervention ihre maximale Wirkung', 'Wie ändert sich die Form des Effektes im Laufe der Zeit' und 'Für wen ist die Wirkung am stärksten oder dauert am längsten an'. Viele Bei-spiele, die sowohl frequentistische als auch bayessche Formen der Software ctsem verwenden, sind enthalten. Im letzten Kapitel fasse ich die Dissertation zusammen, zeige Limitationen der angebotenen Ansätze auf und stelle meine Gedanken zu möglichen zukünftigen Entwicklungen dar., With this dissertation I endeavor to extend, and make practically applicable for psychology, the statistical approach of continuous time dynamic modelling, in which the role of time is made explicit. The structure of this dissertation is such that in Chapter 1, I discuss the nature of dynamic models, consider various approaches to handling multiple subjects, and detail a continuous time dynamic model with input effects (such as interventions) and a Gaussian measurement model. In Chapter 2, I describe the usage of the ctsem software for R developed as part of this dissertation, which provides a frequentist, mixed effects, structural equation modelling approach to estimation. Chapter 3 details a hierarchical Bayesian, fully random effects approach to estimation, allowing for subjects to differ not only in intercept parameters but in all characteristics of the measurement and dynamic models -- while still benefiting from other subjects data for parameter estimation. Chapter 4 describes the usage of the Bayesian extension to the ctsem software. In Chapter 5 I consider the nature of experimental interventions in the continuous time dynamic modelling framework, and show approaches to address questions regarding the way interventions influence psychological processes over time, with questions such as 'how long does a treatment take to reach maximum effect', `how does the shape of the effect change over time', and 'for whom is the effect strongest, or longest lasting'. Many examples using both frequentist and Bayesian forms of the ctsem software are given. For the final chapter I summarise the dissertation, consider limitations of the approaches offered, and provide some thoughts on possible future developments.