Connecting Theory to Methods in Longitudinal Research

Advances in methods for longitudinal data collection and analysis have prompted a surge of research on psychological processes. However, decisions about how to time assessments are often not explicitly tethered to theories about psychological processes but are instead justified on methodological (e.g., power) or practical (e.g., feasibility) grounds. In many cases, methodological decisions are not explicitly justified at all. The disconnect between theories about processes and the timing of assessments in longitudinal research has contributed to misspecified models, interpretive errors, mixed findings, and nonspecific conclusions. In this article, we argue that higher demands should be placed on researchers to connect theories to methods in longitudinal research. We review instances of this disconnect and offer potential solutions as they pertain to four general questions for longitudinal researchers: how time should be scaled, how many assessments are needed, how frequently assessments should occur, and when assessments should happen.

Consequences of violating assumptions of integrated population models on parameter estimates

While ecologists know that models require assumptions, the consequences of their violation become vague as model complexity increases. Integrated population models (IPMs) combine several datasets to inform a population model and to estimate survival and reproduction parameters jointly with higher precision than is possible using independent models. However, accuracy actually depends on an adequate fit of the model to datasets. We first investigated bias of parameters obtained from integrated population models when specific assumptions are violated. For instance, a model may assume that all females reproduce although there are non-breeding females in the population. Our second goal was to identify which diagnostic tests are sensitive to detect violations of the assumptions of IPMs. We simulated data mimicking a short- and a long-lived species under five scenarios in which a specific assumption is violated. For each simulated scenario, we fitted an IPM that violates the assumption (simple IPM) and an IPM that does not violate each specific assumption. We estimated bias and uncertainty of parameters and performed seven diagnostic tests to assess the fit of the models to the data. Our results show that the simple IPM was quite robust to violation of many assumptions and only resulted in small bias of the parameter estimates. Yet, the applied diagnostic tests were not sensitive to detect such small bias. The violation of some assumptions such as the absence of immigrants resulted in larger bias to which diagnostic tests were more sensitive. The parameters informed by the least amount of data were the most biased in all scenarios. We provide guidelines to identify misspecified models and to diagnose the assumption being violated. Simple models should often be sufficient to describe simple population dynamics, and when data are abundant, complex models accounting for specific processes will be able to shed light on specific biological questions.

Learning With Heterogeneous Misspecified Models: Characterization and Robustness

This paper develops a general framework to study how misinterpreting information impacts learning. Our main result is a simple criterion to characterize long‐run beliefs based on the underlying form of misspecification. We present this characterization in the context of social learning, then highlight how it applies to other learning environments, including individual learning. A key contribution is that our characterization applies to settings with model heterogeneity and provides conditions for entrenched disagreement. Our characterization can be used to determine whether a representative agent approach is valid in the face of heterogeneity, study how differing levels of bias or unawareness of others' biases impact learning, and explore whether the impact of a bias is sensitive to parametric specification or the source of information. This unified framework synthesizes insights gleaned from previously studied forms of misspecification and provides novel insights in specific applications, as we demonstrate in settings with partisan bias, overreaction, naive learning, and level‐k reasoning.

Statistical finite elements for misspecified models

We present a statistical finite element method for nonlinear, time-dependent phenomena, illustrated in the context of nonlinear internal waves (solitons). We take a Bayesian approach and leverage the finite element method to cast the statistical problem as a nonlinear Gaussian state–space model, updating the solution, in receipt of data, in a filtering framework. The method is applicable to problems across science and engineering for which finite element methods are appropriate. The Korteweg–de Vries equation for solitons is presented because it reflects the necessary complexity while being suitably familiar and succinct for pedagogical purposes. We present two algorithms to implement this method, based on the extended and ensemble Kalman filters, and demonstrate effectiveness with a simulation study and a case study with experimental data. The generality of our approach is demonstrated in SI Appendix, where we present examples from additional nonlinear, time-dependent partial differential equations (Burgers equation, Kuramoto–Sivashinsky equation).

Estimating and assessing second-order constructs using PLS-PM: the case of composites of composites

PurposeThe purpose of this study is threefold: (1) to propose partial least squares path modeling (PLS-PM) as a way to estimate models containing composites of composites and to compare the performance of the PLS-PM approaches in this context, (2) to provide and evaluate two testing procedures to assess the overall fit of such models and (3) to introduce user-friendly step-by-step guidelines.Design/methodology/approachA simulation is conducted to examine the PLS-PM approaches and the performance of the two proposed testing procedures.FindingsThe simulation results show that the two-stage approach, its combination with the repeated indicators approach and the extended repeated indicators approach perform similarly. However, only the former is Fisher consistent. Moreover, the simulation shows that guidelines neglecting model fit assessment miss an important opportunity to detect misspecified models. Finally, the results show that both testing procedures based on the two-stage approach allow for assessment of the model fit.Practical implicationsAnalysts who estimate and assess models containing composites of composites should use the authors’ guidelines, since the majority of existing guidelines neglect model fit assessment and thus omit a crucial step of structural equation modeling.Originality/valueThis study contributes to the understanding of the discussed approaches. Moreover, it highlights the importance of overall model fit assessment and provides insights about testing the fit of models containing composites of composites. Based on these findings, step-by-step guidelines are introduced to estimate and assess models containing composites of composites.

BAYESIAN ESTIMATION OF A SMALL-SCALE NEW KEYNESIAN MODEL WITH HETEROGENEOUS EXPECTATIONS

This paper uses Bayesian methods to estimate a small-scale New Keynesian model with heterogeneous expectations (HE). Agents form expectations via Euler equation adaptive learning (AL) and differ by the model they use to forecast. Type A agents use a correctly specified model, while type B and type C agents use misspecified models. Quarterly US data from the pre-Great Moderation and Great Moderation periods are used to jointly estimate the degree of agent heterogeneity, the AL parameters, and the deep model parameters. Results show that the data exhibit significant expectational heterogeneity, and that the HE model fits the data better than a model with homogeneous agent AL.