Behavioral economic demand methodology is increasingly being used in various fields such as substance use and consumer behavior analysis. Traditional analytical techniques to fitting demand data have proven useful yet some of these approaches require preprocessing of data, ignore dependence in the data, and present statistical limitations. We term these approaches "fit to group" and "two stage" with the former interested in group or population level estimates and the latter interested in individual subject estimates. As an extension to these regression techniques, mixed-effect (or multilevel) modeling can serve as an improvement over these traditional methods. Notable benefits include providing simultaneous group (i.e., population) level estimates (with more accurate standard errors) and individual level predictions while accommodating the inclusion of "nonsystematic" response sets and covariates. These models can also accommodate complex experimental designs including repeated measures. The goal of this article is to introduce and provide a high-level overview of mixed-effects modeling techniques applied to behavioral economic demand data. We compare and contrast results from traditional techniques to that of the mixed-effects models across two datasets differing in species and experimental design. We discuss the relative benefits and drawbacks of these approaches and provide access to statistical code and data to support the analytical replicability of the comparisons.

Human postural sway during quiet standing has been characterized as a proportional-integral-derivative controller with intermittent activation. In the model, patterns of sway result from both instantaneous, passive, mechanical resistance and delayed, intermittent resistance signaled by the central nervous system. A Kalman-Filter framework was designed to directly estimate from experimental data the parameters of the model’s stochastic delay differential equations with discrete dynamic switching conditions. Simulations showed that all parameters could be estimated over a variety of possible data-generating configurations with varying degrees of bias and variance depending on their empirical identification. Applications to experimental data reveal distributions of each parameter that correspond well to previous findings, suggesting that many useful, physiological measures may be extracted from sway data. Individuals varied in degree and type of deviation from theoretical expectations, ranging from harmonic oscillation to non-equilibrium Langevin dynamics.

Understanding the factors that contribute to behavioral traits is a complex task, and partitioning variance into latent genetic and environmental components is a useful beginning, but it should not also be the end. Many constructs are influenced by their contextual milieu, and accounting for background effects (such as gene-environment correlation) is necessary to avoid bias. This study introduces a method for examining the interplay between traits, in a longitudinal design using differential items in sibling pairs. The model is validated via simulation and power analysis, and we conclude with an application to paternal praise and ADHD symptoms in a twin sample. The model can help identify what type of genetic and environmental interplay may contribute to the dynamic relationship between traits using a cross-lagged panel framework. Overall, it presents a way to estimate and explicate the developmental interplay between a set of traits, free from many common sources of bias.

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Damped Linear Oscillators estimated by 2nd-order Latent Differential Equation have assumed a constant equilibrium and one oscillatory component. Lower-frequency oscillations may come from seasonal background processes, which non-randomly contribute to deviation from equilibrium at each occasion and confound estimation of dynamics over shorter timescales. Boker (2015) proposed a model of individual change on multiple timescales, but implementation, simulation, and applications to data have not been demonstrated. This study implemented a generalization of the proposed model; examined robustness to varied timescale ratios, measurement error, and occasions-per-person in simulated data; and tested for dynamics at multiple timescales in experience sampling affect data. Results show small standard errors and low bias to dynamic estimates at timescale ratios greater than 3:1. Below 3:1, estimate error was sensitive to noise and total occasions; rates of non-convergence increased. For affect data, model comparisons showed statistically significant dynamics at both timescales for both participants.