Capturing Context-Related Change in Emotional Dynamics via Fixed Moderated Time Series Analysis

Much of recent affect research relies on intensive longitudinal studies to assess daily emotional experiences. The resulting data are analyzed with dynamic models to capture regulatory processes involved in emotional functioning. Daily contexts, however, are commonly ignored. This may not only result in biased parameter estimates and wrong conclusions, but also ignores the opportunity to investigate contextual effects on emotional dynamics. With fixed moderated time series analysis, we present an approach that resolves this problem by estimating context-dependent change in dynamic parameters in single-subject time series models. The approach examines parameter changes of known shape and thus addresses the problem of observed intra-individual heterogeneity (e.g., changes in emotional dynamics due to observed changes in daily stress). In comparison to existing approaches to unobserved heterogeneity, model estimation is facilitated and different forms of change can readily be accommodated. We demonstrate the approach's viability given relatively short time series by means of a simulation study. In addition, we present an empirical application, targeting the joint dynamics of affect and stress and how these co-vary with daily events. We discuss potentials and limitations of the approach and close with an outlook on the broader implications for understanding emotional adaption and development.     

Bayesian adaptive estimation: The next dimension

We propose a new psychometric model for two-dimensional stimuli, such as color differences, based on parameterizing the threshold of a one-dimensional psychometric function as an ellipse. The Ψ Bayesian adaptive estimation method applied to this model yields trials that vary in multiple stimulus dimensions simultaneously. Simulations indicate that this new procedure can be much more efficient than the more conventional procedure of estimating the psychometric function on one-dimensional lines independently, requiring only one-fourth or less the number of trials for equivalent performance in typical situations. In a real psychophysical experiment with a yes-no task, as few as 22 trials per estimated threshold ellipse were enough to consistently demonstrate certain color appearance phenomena. We discuss the practical implications of the multidimensional adaptation. In order to make the application of the model practical, we present two significantly faster algorithms for running the Ψ method: a discretized algorithm utilizing the Fast Fourier Transform for better scaling with the sampling rates and a Monte Carlo particle filter algorithm that should be able to scale into even more dimensions.     

Testing for selectivity in the dependence of random variables on external factors

Random variables A and B, whose joint distribution depends on factors (x,y), are selectively influenced by x and y, respectively, if A and B can be represented as functions of, respectively, (x,S_A,C) and (y,S_B,C), where S_A,S_B,C are stochastically independent and do not depend on (x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of A may depend on y. But parameters characterizing stochastic interdependence of A and B, such as their mixed moments, are generally functions of both x and y. We derive two simple necessary conditions for selective dependence of (A,B) on (x,y), which can be used to conduct a potential infinity of selectiveness tests. One condition is that, for any factor values x,x^′ and y,y^′,

s_xy≤s_xy^′+s_x^′y^′+s_x^′y,     

A new definition of well-behaved discrimination functions

A discrimination function shows the probability or degree with which stimuli are discriminated from each other when presented in pairs. In a previous publication [Kujala, J.V., & Dzhafarov, E.N. (2008). On minima of discrimination functions. Journal of Mathematical Psychology, 52, 116–127] we introduced a condition under which the conformity of a discrimination function with the law of Regular Minimality (which says, essentially, that “being least discriminable from” is a symmetric relation) implies the constancy of the function’s minima (i.e., the same level of discriminability of every stimulus from the stimulus least discriminable from it). This condition, referred to as “well-behavedness,” turns out to be unnecessarily restrictive. In this note we give a significantly more general definition of well-behavedness, applicable to all Hausdorff arc-connected stimulus spaces. The definition employs the notion of the smallest transitively and topologically closed extension of a relation. We provide a transfinite-recursive construction for this notion and illustrate it by examples.     

Regular Minimality and Thurstonian-type modeling

A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision rules. It has also been shown, however, that a broad class of Thurstonian-type models, called “well-behaved” (and including, e.g., models with multivariate normal perceptual representations whose parameters are smooth functions of stimuli) cannot simultaneously account for two empirically plausible properties of same–different comparisons, Regular Minimality (which essentially says that “being least discriminable from” is a symmetric relation) and nonconstancy of the minima of discrimination probabilities (the fact that different pairs of least discriminable stimuli are discriminated with different probabilities). These results have been obtained for stimulus spaces represented by regions of Euclidean spaces. In this paper, the impossibility for well-behaved Thurstonian-type models to simultaneously account for Regular Minimality and nonconstancy of minima is established for a much broader notion of well-behavedness applied to a much broader class of stimulus spaces (any Hausdorff arc-connected ones). The universality of Thurstonian-type models with independent perceptual images and deterministic decision rules is shown (by a simpler proof than before) to hold for arbitrary stimulus spaces.     

Low Self-Esteem as a Risk Factor for Loneliness in Adolescence: Perceived - but not Actual - Social Acceptance as an Underlying Mechanism

Low self-esteem has been shown to relate to concurrent and later feelings of loneliness in adolescence. However, it remains unclear why low self-esteem puts adolescents at risk for experiencing loneliness. Further, longitudinal research on the direction of effects between loneliness and self-esteem is virtually non-existent. The present study aims to fill these gaps in the literature. First, the direction of effects between loneliness and self-esteem was investigated in two independent longitudinal studies: a five-wave study sampling Dutch adolescents (M age?=?15.22 years at T1; 47 % female; N?=?428) and a three-wave study sampling Belgian adolescents (M age?=?14.95 years at T1; 63 % female; N?=?882). Second, the underlying role of social acceptance was investigated in the latter sample by applying a multi-method approach that included actual (i.e., peer-reported) and perceived (i.e., self-reported) social acceptance. Results indicated that self-esteem and loneliness influenced one another in a reciprocal manner. Furthermore, the dominant path from self-esteem to loneliness was partially mediated by perceived—but not actual—social acceptance. The importance of distinguishing actual from perceived social acceptance is discussed, and suggestions for future research are outlined.     

Obtaining the best value for money in adaptive sequential estimation

In [Kujala, J. V., Richardson, U., &; Lyytinen, H. (2010). A Bayesian-optimal principle for learner-friendly adaptation in learning games. Journal of Mathematical Psychology, 54(2), 247–255], we considered an extension of the conventional Bayesian adaptive estimation framework to situations where each observable variable is associated with a certain random cost of observation. We proposed an algorithm that chooses each placement by maximizing the expected gain in utility divided by the expected cost. In this paper, we formally justify this placement rule as an asymptotically optimal solution to the problem of maximizing the expected utility of an experiment that terminates when the total cost overruns a given budget. For example, the cost could be defined as the random time taken by each trial in an experiment, and one might wish to maximize the expected total information gain over as many trials as can be completed in 15 min. A simple, analytically tractable example is considered.     

On minima of discrimination functions

A discrimination function ψ(x,y) assigns a measure of discriminability to stimulus pairs x,y (e.g., the probability with which they are judged to be different in a same-different judgment scheme). If for every x there is a single y least discriminable from x, then this y is called the point of subjective equality (PSE) for x, and the dependence h(x) of the PSE for x on x is called a PSE function. The PSE function g(y) is defined in a symmetrically opposite way. If the graphs of the two PSE functions coincide (i.e., g≡h⁻¹), the function is said to satisfy the Regular Minimality law. The minimum level functions are restrictions of ψ to the graphs of the PSE functions. The conjunction of two characteristics of ψ, (1) whether it complies with Regular Minimality, and (2) whether the minimum level functions are constant, has consequences for possible models of perceptual discrimination. By a series of simple theorems and counterexamples, we establish set-theoretic, topological, and analytic properties of ψ which allow one to relate to each other these two characteristics of ψ.     

Lonely adolescents exhibit heightened sensitivity for facial cues of emotion

Contradicting evidence exists regarding the link between loneliness and sensitivity to facial cues of emotion, as loneliness has been related to better but also to worse performance on facial emotion recognition tasks. This study aims to contribute to this debate and extends previous work by (a) focusing on both accuracy and sensitivity to detecting positive and negative expressions, (b) controlling for depressive symptoms and social anxiety, and (c) using an advanced emotion recognition task with videos of neutral adolescent faces gradually morphing into full-intensity expressions. Participants were 170 adolescents (49% boys; M_age?=?13.65 years) from rural, low-income schools. Results showed that loneliness was associated with increased sensitivity to happy, sad, and fear faces. When controlling for depressive symptoms and social anxiety, loneliness remained significantly associated with sensitivity to sad and fear faces. Together, these results suggest that lonely adolescents are vigilant to negative facial cues of emotion.