Sy-Miin Chow

Automated Measurement of Facial Expression in Infant-Mother Interaction: A Pilot Study.

Automated facial measurement using computer vision has the potential to objectively document continuous changes in behavior. To examine emotional expression and communication, we used automated measurements to quantify smile strength, eye constriction, and mouth opening in two six-month-old/mother dyads who each engaged in a face-to-face interaction. Automated measurements showed high associations with anatomically based manual coding (concurrent validity); measurements of smiling showed high associations with mean ratings of positive emotion made by naive observers (construct validity). For both infants and mothers, smile strength and eye constriction (the Duchenne marker) were correlated over time, creating a continuous index of smile intensity. Infant and mother smile activity exhibited changing (nonstationary) local patterns of association, suggesting the dyadic repair and dissolution of states of affective synchrony. The study provides insights into the potential and limitations of automated measurement of facial action.

An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models.

In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log–likelihood of nonlinear state–space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple–subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction.

Dynamic infant-parent affect coupling during the face-to-face/still-face.

We examined dynamic infant-parent affect coupling using the Face-to-Face/Still-Face (FFSF). The sample included 20 infants whose older siblings had been diagnosed with Autism Spectrum Disorders (ASD-sibs) and 18 infants with comparison siblings (COMP-sibs). A series of mixed effects bivariate autoregressive models was used to represent the self-regulation and interactive dynamics of infants and parents during the FFSF. Significant bidirectional affective coupling was found between infants and parents, with infant-to-parent coupling being more prominent than parent-to-infant coupling. Further analysis of within-dyad dynamics revealed ongoing changes in concurrent infant-parent linkages both within and between different FFSF episodes. The importance of considering both inter- and intradyad differences is discussed.

Dynamic Factor Analysis Models With Time-Varying Parameters.

Dynamic factor analysis models with time-varying parameters offer a valuable tool for evaluating multivariate time series data with time-varying dynamics and/or measurement properties. We use the Dynamic Model of Activation proposed by Zautra and colleagues (Zautra, Potter, & Reich, 1997) as a motivating example to construct a dynamic factor model with vector autoregressive relations and time-varying cross-regression parameters at the factor level. Using techniques drawn from the state-space literature, the model was fitted to a set of daily affect data (over 71 days) from 10 participants who had been diagnosed with Parkinsons disease. Our empirical results lend partial support and some potential refinement to the Dynamic Model of Activation with regard to how the time dependencies between positive and negative affects change over time. A simulation study is conducted to examine the performance of the proposed techniques when (a) changes in the time-varying parameters are represented using the true model of change, (b) supposedly time-invariant parameters are represented as time-varying, and (c) the time-varying parameters show discrete shifts that are approximated using an autoregressive model of differences.

Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior

Parameters in time series and other dynamic models often show complex range restrictions and their distributions may deviate substantially from multivariate normal or other standard parametric distributions. We use the truncated Dirichlet process (DP) as a non-parametric prior for such dynamic parameters in a novel nonlinear Bayesian dynamic factor analysis model. This is equivalent to specifying the prior distribution to be a mixture distribution composed of an unknown number of discrete point masses (or clusters). The stick-breaking prior and the blocked Gibbs sampler are used to enable efficient simulation of posterior samples. Using a series of empirical and simulation examples, we illustrate the flexibility of the proposed approach in approximating distributions of very diverse shapes.

Age differences in dynamical emotion-cognition linkages.

The ability to maintain the separation between positive emotion and negative emotion in times of stress has been construed as a resilience mechanism. Emotional resiliency is particularly relevant in old age given concomitant declines in cognitive performance. In the present study, the authors examined the dynamical linkages among positive emotion, negative emotion, and cognition as individuals performed a complex cognitive task. Comparisons were made between younger (n = 63) and older (n = 52) age groups. Older adults manifested significant unidirectional coupling from negative emotion to cognitive performance; younger adults manifested significant unidirectional coupling from negative emotion to positive emotion and from cognitive performance to both positive and negative emotions. Implications for age differences in emotion regulatory strategies are discussed.

Bayesian Lasso for Semiparametric Structural Equation Models

There has been great interest in developing nonlinear structural equation models and associated statistical inference procedures, including estimation and model selection methods. In this paper a general semiparametric structural equation model (SSEM) is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables. A basis representation is used to approximate these nonparametric functions in the structural equation and the Bayesian Lasso method coupled with a Markov Chain Monte Carlo (MCMC) algorithm is used for simultaneous estimation and model selection. The proposed method is illustrated using a simulation study and data from the Affective Dynamics and Individual Differences (ADID) study. Results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model.

Nonlinear Regime-Switching State-Space (RSSS) Models

Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases—namely, latent “regimes” or classes—during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.

Regime-Switching Bivariate Dual Change Score Model

Mixture structural equation model with regime switching (MSEM-RS) provides one possible way of representing over-time heterogeneities in dynamic processes by allowing a system to manifest qualitatively or quantitatively distinct change processes conditional on the latent “regime” the system is in at a particular time point. Unlike standard mixture structural equation models such as growth mixture models, MSEM-RS allows individuals to transition between latent classes over time. This class of models, often referred to as regime-switching models in the time series and econometric applications, can be specified as regime-switching mixture structural equation models when the number of repeated measures involved is not large. We illustrate the empirical utility of such models using one special case—a regime-switching bivariate dual change score model in which two growth processes are allowed to manifest regime-dependent coupling relations with one another. The proposed model is illustrated using a set of longitudinal reading and arithmetic performance data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 study (ECLS-K; U.S. Department of Education, National Center for Education Statistics, 2010).

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.