Continuous-time (CT) models are a flexible approach for modeling longitudinal data of psychological constructs. When using CT models, a researcher can assume one underlying continuous function for the phenomenon of interest. In principle, these models overcome some limitations of discrete-time (DT) models and allow researchers to compare findings across measures collected using different time intervals, such as daily, weekly, or monthly intervals. Theoretically, the parameters for equivalent models can be rescaled into a common time interval that allows for comparisons across individuals and studies, irrespective of the time interval used for sampling. In this study, we carry out a Monte Carlo simulation to examine the capability of CT autoregressive (CT-AR) models to recover the true dynamics of a process when the sampling interval is different from the time scale of the true generating process. We use two generating time intervals (daily or weekly) with varying strengths of the AR parameter and assess its recovery when sampled at different intervals (daily, weekly, or monthly). Our findings indicate that sampling at a faster time interval than the generating dynamics can mostly recover the generating AR effects. Sampling at a slower time interval requires stronger generating AR effects for satisfactory recovery, otherwise the estimation results show high bias and poor coverage. Based on our findings, we recommend researchers use sampling intervals guided by theory about the variable under study, and whenever possible, sample as frequently as possible.

Studying development processes, as they unfold over time, involves collecting repeated measures from individuals and modeling the changes over time. One methodological challenge in this type of longitudinal data is separating retest effects, due to the repeated assessments, from developmental processes such as maturation or age. In this article, we describe several specifications of latent change score models using age as the underlying time metric and include parameters to account for retest effects. We illustrate the models with data on fluid reasoning collected from children and adolescents in a cohort-sequential design ranging from 6 to 20 years. Our models include alternative approaches to specify retest effects at the structural or measurement level of the model, and as an observed or a latent covariate. We discuss the benefits and limitations of the different approaches for univariate and multivariate data in the context of studying developmental processes.

Continuous-time (CT) models are a flexible approach for modeling longitudinal data of psychological constructs. When using CT models, a researcher can assume one underlying continuous function for the phenomenon of interest. In principle, these models overcome some limitations of discrete-time (DT) models and allow researchers to compare findings across measures collected using different time intervals, such as daily, weekly, or monthly intervals. Theoretically, the parameters for equivalent models can be rescaled into a common time interval that allows for comparisons across individuals and studies, irrespective of the time interval used for sampling. In this study, we carry out a Monte Carlo simulation to examine the capability of CT autoregressive (CT-AR) models to recover the true dynamics of a process when the sampling interval is different from the time scale of the true generating process. We use two generating time intervals (daily or weekly) with varying strengths of the autoregressive parameter and assess its recovery when sampled at different intervals (daily, weekly, or monthly). Our findings indicate that sampling at a faster time interval than the generating dynamics can mostly recover the generating autoregressive effects. Sampling at a slower time interval requires stronger generating autoregressive effects for satisfactory recovery, otherwise the estimation results show high bias and poor coverage. Based on our findings, we recommend researchers use sampling intervals guided by theory about the variable under study, and whenever possible, sample as frequently as possible.

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Studying development processes, as they unfold over time, involves collecting repeated measures from individuals and modeling the changes over time. One methodological challenge in this type of longitudinal data is separating retest effects, due to the repeated assessments, from developmental processes such as maturation or age. In this article, we describe several specifications of latent change score models using age as the underlying time metric and include parameters to account for retest effects. We illustrate the models with data on fluid reasoning collected from children and adolescents in a cohort-sequential design ranging from 6 to 20 years. Our models include alternative approaches to specify retest effects at the structural or measurement level of the model, and as an observed or a latent covariate. We discuss the benefits and limitations of the different approaches for univariate and multivariate data in the context of studying developmental processes.