Entropy Fit Indices: New Fit Measures for Assessing the Structure and Dimensionality of Multiple Latent Variables.

The accurate identification of the content and number of latent factors underlying multivariate data is an important endeavor in many areas of Psychology and related fields. Recently, a new dimensionality assessment technique based on network psychometrics was proposed (Exploratory Graph Analysis, EGA), but a measure to check the fit of the dimensionality structure to the data estimated via EGA is still lacking. Although traditional factor-analytic fit measures are widespread, recent research has identified limitations for their effectiveness in categorical variables. Here, we propose three new fit measures (termed entropy fit indices) that combines information theory, quantum information theory and structural analysis: Entropy Fit Index (EFI), EFI with Von Neumman Entropy (EFI.vn) and Total EFI.vn (TEFI.vn). The first can be estimated in complete datasets using Shannon entropy, while EFI.vn and TEFI.vn can be estimated in correlation matrices using quantum information metrics. We show, through several simulations, that TEFI.vn, EFI.vn and EFI are as accurate or more accurate than traditional fit measures when identifying the number of simulated latent factors. However, in conditions where more factors are extracted than the number of factors simulated, only TEFI.vn presents a very high accuracy. In addition, we provide an applied example that demonstrates how the new fit measures can be used with a real-world dataset, using exploratory graph analysis.

A Rejoinder.

Three commentaries on the Nesselroade and Molenaar target article in this issue are responded to in the interest of elaborating and defending the points of view expressed in our article. The commentaries feature philosophy of science, general structural modeling, and broad behavioral research perspectives. Responding to the commentaries afforded us the opportunity to clarify further matters that we deem critical to the fundamental matter of measurement in behavioral science, especially as it emphasizes (properly, we believe) the individual as the primary unit of analysis.

Some Behaviorial Science Measurement Concerns and Proposals.

Primarily from a measurement standpoint, we question some basic beliefs and procedures characterizing the scientific study of human behavior. The relations between observed and unobserved variables are key to an empirical approach to building explanatory theories and we are especially concerned about how the former are used as proxies for the latter. We believe that behavioral science can profitably reconsider the prevailing version of this arrangement because of its vulnerability to limiting idiosyncratic aspects of observed/unobserved variable relations. We describe a general measurement approach that takes into account idiosyncrasies that should be irrelevant to the measurement process but can intrude and may invalidate it in ways that distort and weaken relations among theoretically important variables. To clarify further our major concerns, we briefly describe one version of the measurement approach that fundamentally supports the individual as the primary unit of analysis orientation that we believe should be preeminent in the scientific study of human behavior.

Estimation of subject-specific heritabilities from intra-individual variation: iFACE.

A new genetic factor model for multivariate phenotypic time series, iFACE, is presented which allows for the estimation of subject-specific model parameters of genetic and environmental factors. The iFACE was applied to multivariate EEG registrations obtained with single dizygotic twin pairs. The results showed evidence for considerable subject-specificity in heritabilities and environmental effects. The assumption that the population is homogeneous (i.e., that each case in the population obeys the same parametric model), does not hold for these psychophysiological data, and its use should be critically reconsidered. We conclude that the iFACE provides a powerful new methodology to assess heterogeneity (subject-specificity) based on phenotypic observations.

On Standardized Measurement in Behavioral Science.

That standardized measurement procedures are a sine qua non of "good" science is generally not questioned. Here we examine the meaning and use of standardized measurement in behavioral science. Procedures and methods of measurement that have served the physical sciences so well should not blindly be assumed to work in the same manner and with the same effectiveness in behavioral science. There seems to be general agreement that social/behavioral science is "different" among the sciences. Problems arising from how behavioral science is "different" begin, we believe, with measurement. We put forward the argument that the source of the difference is unique to animate objects and is first evident at the stage of measuring the behavioral attributes of interest. It is at that point in conducting scientific inquiry that the matters raised might be resolved by developing and applying alternatives to standardized measurement. One such alternative discussed is the idiographic filter (Nesselroade, Gerstorf, Hardy, & Ram, 2007).

Analyzing intra-person variation: hybridizing the ACE model with P-technique factor analysis and the idiographic filter.

Integrating idiographic and nomothetic approaches to the study of behavior has met with success via the idiographic filter (IF) which separates irrelevant inter-individual differences from relevant inter-individual similarities at the level of construct measurement in order to facilitate drawing conclusions regarding nomothetic relationships among the constructs. We propose an integration of the IF and the ACE behavior genetics models through the use of P-technique factor analysis and its dynamic factor analysis extensions and examine how it can strengthen the modeling of genetic and environmental effects in behavioral data representing intra-person variation, change, and process.

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.

Development and structural dynamics of personal life investment in old age.

The development of personal life investment (PLI) during old age was investigated with longitudinal and cross-sectional data from the Berlin Aging Study (N = 516, ages = 70-103 years). PLI measures motivational energy expended in life domains that require (obligatory PLI) or do not require (optional PLI) investment in old age. The authors used structural modeling to determine developmental trajectories and dynamics of the PLI types. On average, obligatory PLI remained unchanged between 70 and 101 years. Optional PLI declined during the transition to the 4th age (between 80 and 90 years). When change on the intraindividual level was considered, reductions in optional PLI were not related to changes in obligatory PLI, but declining obligatory PLI was associated with declining optional PLI.

Short-term variability in cognitive performance and the calibration of longitudinal change.

Recent studies have documented that normal adults exhibit considerable variability in cognitive performance from one occasion to another. We investigated this phenomenon in a study in which 143 adults ranging from 18 to 97 years of age performed different versions of 13 cognitive tests in three separate sessions. Substantial within-person variability was apparent across 13 different cognitive variables, and there were also large individual differences in the magnitude of within-person variability. Because people differ in the amount of short-term variability, we propose that this variability might provide a meaningful basis for calibrating change in longitudinal research. Correlations among the measures of within-person variability were very low, even after we adjusted for reliability, and there was little evidence that increased age was associated with a larger amount of within-person variability.

Test Reliability at the Individual Level.

Reliability has a long history as one of the key psychometric properties of a test. However, a given test might not measure people equally reliably. Test scores from some individuals may have considerably greater error than others. This study proposed two approaches using intraindividual variation to estimate test reliability for each person. A simulation study suggested that the parallel tests approach and the structural equation modeling approach recovered the simulated reliability coefficients. Then in an empirical study, where forty-five females were measured daily on the Positive and Negative Affect Schedule (PANAS) for 45 consecutive days, separate estimates of reliability were generated for each person. Results showed that reliability estimates of the PANAS varied substantially from person to person. The methods provided in this article apply to tests measuring changeable attributes and require repeated measures across time on each individual. This article also provides a set of parallel forms of PANAS.

Cognitive performance inconsistency: intraindividual change and variability.

Although many studies have examined inconsistency of cognitive performance, few have examined how inconsistency changes over time. 91 older adults (age 52 to 79) were tested weekly for 36 consecutive weeks on a series of multitrial memory speed (i.e., letter recognition) tasks. A number of multivariate techniques were used to examine how individuals' level of inconsistency changed across weeks and how this change was related to interindividual differences in age and intelligence. Results indicated that (a) inconsistency of performance is a construct separate from the underlying performance ability (i.e., memory speed); (b) inconsistency reduces exponentially with practice; (c) individuals with higher scores on tests of fluid general intelligence (G-sub(f)) reached lower asymptotic levels of inconsistency compared to lower scorers; and (d) after controlling for the systematic effects of practice, variability in inconsistency from week-to-week was more pronounced for individuals with lower G-sub(f) scores compared to individuals with higher scores.

Assessing psychological change in adulthood: an overview of methodological issues.

This article reviews the current status of methods available for the analysis of psychological change in adulthood and aging. Enormous progress has been made in designing statistical models that can capture key aspects of intraindividual change, as reflected in techniques such as latent growth curve models and multilevel (random-effects) models. However, the rapid evolution of statistical innovations may have obscured the critical importance of addressing rival explanations for statistical outcomes, such as cohort differences or practice effects that could influence estimates of age-related change. Choice of modeling technique and implementation of a specific modeling approach should be grounded in and reflect both the theoretical nature of the developmental phenomenon and the features of the sampling design that selected persons, variables, and contexts for empirical observation.

Modeling affective processes in dyadic relations via dynamic factor analysis.

An intraindividual variability design, including application of dynamic factor models, was used to examine the affective processes of a husband-wife dyad over 182 consecutive days. Structural equation analyses indicated differences in the affective structure between the husband and the wife, and these differences were characterized in terms of their factorial configuration and temporal organization. Examination of the dyad's affective dynamics revealed unidirectional (i.e., from the husband to the wife) interpersonal influences with a defined structure over time.

General slowing or decreased inhibition? Mathematical models of age differences in cognitive functioning.

Researchers have attempted to explain age-related decrements in cognitive performance in terms of reduced processing speed or decreased ability to inhibit irrelevant thoughts. We present these ideas in the context of a dynamic model derived from extensions of the classical predator-prey equation. Reduced processing speed among older adults is represented by use of delays in the dynamic model, whereas the interference imposed by distractors is captured by use of the predator-prey interaction term. We demonstrate the versatility of this modeling approach, and its pertinence to age-related behavioral change, by means of numerical simulations. In showing the applicability of these models, we identify several unresolved methodological and measurement issues that have to be addressed.

Methodological and theoretical implications of intraindividual variability in perceptual-motor performance.

As an individual differences variable, lability (within-person variability) has often been neglected even though it has been shown to predict key outcomes such as mortality. We examine intraindividual variability in perceptual-motor performance and relate it to chronological age in a sample of adults. The magnitude of between-session variability was found to average between 25% and 50% of the between-person variability and was equivalent in magnitude to the variation that was apparent across an age range of 12 to 27 years in cross-sectional comparisons. Age is related to the magnitude of intraindividual variability, which in turn is negatively related to performance on other cognitive tasks. Various implications of the findings are discussed.

An idiographic approach to estimating models of dyadic interactions with differential equations.

We present an idiographic approach to modeling dyadic interactions using differential equations. Using data representing daily affect ratings from romantic relationships, we examined several models conceptualizing different types of dyadic interactions. We fitted each model to each of the dyads and the resulting AICc values were used to classify the most likely configuration of interaction for each dyad. Additionally, the AICc from the different models were used in parameter averaging across models. Averaged parameters were used in models involving predictors of relationship dynamics, as indexed by these parameters, as well as models wherein the parameters predicted distal outcomes of the dyads such as relationship satisfaction and status. Results indicated that, within our sample, the most likely interaction style was that of independence, without evidence of emotional interrelations between the two individuals in the couple. Attachment-related avoidance and anxiety showed significant relations with model parameters, such that ideal levels of affect for males were negatively influenced by higher levels of avoidance from their partner while their own levels of anxiety had positive effects on their levels of dyadic coregulation. For females coregulation was negatively influenced by both time in the relationship and their partner's level of avoidance. Analysis involving distal outcomes showed modest influences from the individual's level of ideal affect.

Emotional experience improves with age: evidence based on over 10 years of experience sampling.

Recent evidence suggests that emotional well-being improves from early adulthood to old age. This study used experience-sampling to examine the developmental course of emotional experience in a representative sample of adults spanning early to very late adulthood. Participants (N = 184, Wave 1; N = 191, Wave 2; N = 178, Wave 3) reported their emotional states at five randomly selected times each day for a one week period. Using a measurement burst design, the one-week sampling procedure was repeated five and then ten years later. Cross-sectional and growth curve analyses indicate that aging is associated with more positive overall emotional well-being, with greater emotional stability and with more complexity (as evidenced by greater co-occurrence of positive and negative emotions). These findings remained robust after accounting for other variables that may be related to emotional experience (personality, verbal fluency, physical health, and demographic variables). Finally, emotional experience predicted mortality; controlling for age, sex, and ethnicity, individuals who experienced relatively more positive than negative emotions in everyday life were more likely to have survived over a 13 year period. Findings are discussed in the theoretical context of socioemotional selectivity theory.

Dealing with short-term fluctuation in longitudinal research.

OBJECTIVES: Many analytical methods are not very sensitive to change because of the difficulty of distinguishing short-term fluctuation from the developmental change of primary interest. The current project investigated one possible solution to this problem in the form of a measurement-burst design in which research participants perform several versions of each test at each measurement occasion. METHODS: Over 1,200 adults across a wide-age range performed different versions of cognitive tests on several sessions at each measurement occasion. RESULTS: Four methods of incorporating short-term variability were compared with respect to the magnitude of the correlations of the ability measures with each other and with respect to the magnitude of their relations with age. CONCLUSIONS: The results revealed that more sensitive assessments of change can be obtained by taking short-term fluctuation into account with measurement-burst designs. In particular, capitalizing on the availability of multiple measures at each occasion to form latent constructs representing the level and change in cognitive performance may provide the most sensitive assessment of cognitive change.

The Recoverability of P-technique Factor Analysis.

It seems that just when we are about to lay P-technique factor analysis finally to rest as obsolete because of newer, more sophisticated multivariate time-series models using latent variables-dynamic factor models-it rears its head to inform us that an obituary may be premature. We present the results of some simulations demonstrating that even though it does not explicitly model lagged information, P-technique's ability to recover the parameters of underlying dynamic processes involving lagged relations among the manifest variables is apparently robust and accurate. An empirical example is presented using 103 days of affective mood self-ratings from a young pregnant woman. Implications of the simulation and empirical findings are briefly discussed.