Studying Multivariate Change Using Multilevel Models and Latent Curve Models

Growth Curves for Headache Research: A Multilevel Modeling Perspective

OBJECTIVE

To introduce growth curve modeling for longitudinal headache research.

BACKGROUND

Longitudinal data play an important role in the study of headache-related outcomes by allowing researchers to test hypotheses about change over time. However, headache researchers are often unfamiliar with the flexibility and power that growth curves can offer in analyzing longitudinal data. The goals of this paper are to introduce growth curve models within the multilevel modeling framework for analyzing longitudinal headache-related data and to show how these models can be applied in practice.

METHODS

Longitudinal data for the empirical example came from publicly available data from Wave I to Wave IV of the National Longitudinal Study of Adolescent to Adult Health. In total, 5608 individuals were included in the study and multilevel models were fit to examine, for individuals with and without adolescent migraine, longitudinal changes in depression from age 13 to 27 years old.

RESULTS

Findings showed that individuals varied in their longitudinal depression trajectories. A cubic time trend best approximated the data with depression increasing through adolescence, decreasing during young adulthood, and then beginning to increase again in adulthood. Further, results also indicated that individuals with adolescent migraine had higher levels of depression throughout the age span compared those without adolescent migraine, but the shape of change did not differ across the groups.

CONCLUSION

Growth curve models offer a flexible alternative to traditional statistical methods and can rigorously evaluate a wide array of headache-related hypotheses.

Modeling empathy as synchrony in clinician and patient vocally encoded emotional arousal: A failure to replicate

Empathy is a well-defined active ingredient in clinical encounters. To measure empathy, the current gold standard is behavioral coding (i.e., trained coders attribute overall ratings of empathy to clinician behaviors within an encounter), which is labor intensive and subject to important reliability challenges. Recently, an alternative measurement has been proposed: capturing empathy as synchrony in vocally encoded arousal, which can be measured as the mean fundamental frequency of the voice (mean F0). This method has received preliminary support by one study (Imel, Barco, et al., 2014). We aimed to replicate this study by using 2 large samples of clinical interactions (alcohol brief motivational interventions with young adults, N = 208; general practice consultations, N = 204). Audio files were segmented to identify respective speakers and mean F0 was measured using speech signal processing software. All sessions were independently rated by behavioral coders using 2 validated empathy scales. Synchrony between clinician and patient F0 was analyzed using multivariate multilevel models and compared with high and low levels of empathy derived from behavioral coding. Findings showed no support for our hypothesis that mean F0 synchrony between clinicians and patients would be higher in high-empathy sessions. This lack of replication was consistent for both clinical samples, both behavioral coding instruments, and using measures of F0 synchrony occurring at both the session-level and minute-level. We considered differences in culture and language, patients' characteristics, and setting as explanations for this failure to replicate. Further replication testing and new developments regarding measurement methods and modeling are needed. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

The Differential Time-Varying Effect Model (DTVEM): A tool for diagnosing and modeling time lags in intensive longitudinal data

With the recent growth in intensive longitudinal designs and the corresponding demand for methods to analyze such data, there has never been a more pressing need for user-friendly analytic tools that can identify and estimate optimal time lags in intensive longitudinal data. The available standard exploratory methods to identify optimal time lags within univariate and multivariate multiple-subject time series are greatly underpowered at the group (i.e., population) level. We describe a hybrid exploratory-confirmatory tool, referred to herein as the Differential Time-Varying Effect Model (DTVEM), which features a convenient user-accessible function to identify optimal time lags and estimate these lags within a state-space framework. Data from an empirical ecological momentary assessment study are then used to demonstrate the utility of the proposed tool in identifying the optimal time lag for studying the linkages between nervousness and heart rate in a group of undergraduate students. Using a simulation study, we illustrate the effectiveness of DTVEM in identifying optimal lag structures in multiple-subject time-series data with missingness, as well as its strengths and limitations as a hybrid exploratory-confirmatory approach, relative to other existing approaches.

Modeling competence development in the presence of selection bias

A major challenge for representative longitudinal studies is panel attrition, because some respondents refuse to continue participating across all measurement waves. Depending on the nature of this selection process, statistical inferences based on the observed sample can be biased. Therefore, statistical analyses need to consider a missing-data mechanism. Because each missing-data model hinges on frequently untestable assumptions, sensitivity analyses are indispensable to gauging the robustness of statistical inferences. This article highlights contemporary approaches for applied researchers to acknowledge missing data in longitudinal, multilevel modeling and shows how sensitivity analyses can guide their interpretation. Using a representative sample of N = 13,417 German students, the development of mathematical competence across three years was examined by contrasting seven missing-data models, including listwise deletion, full-information maximum likelihood estimation, inverse probability weighting, multiple imputation, selection models, and pattern mixture models. These analyses identified strong selection effects related to various individual and context factors. Comparative analyses revealed that inverse probability weighting performed rather poorly in growth curve modeling. Moreover, school-specific effects should be acknowledged in missing-data models for educational data. Finally, we demonstrated how sensitivity analyses can be used to gauge the robustness of the identified effects.

Change in Cognitive Performance From Midlife Into Old Age: Findings from the Midlife in the United States (MIDUS) Study

OBJECTIVES

A substantial body of research has documented age-related declines in cognitive abilities among adults over 60, yet there is much less known about changes in cognitive abilities during midlife. The goal was to examine longitudinal changes in multiple cognitive domains from early midlife through old age in a large national sample, the Midlife in the United States (MIDUS) study.

METHODS

The Brief Test of Adult Cognition by Telephone (BTACT) was administered on two occasions (MIDUS 2, MIDUS 3), an average of 9 years apart. At MIDUS 3, those with the cognitive assessment (N=2518) ranged in age from 42 to 92 years (M=64.30; SD=11.20) and had a mean education of 14.68 years (SD=2.63). The BTACT includes assessment of key aging-sensitive cognitive domains: immediate and delayed free recall, number series, category fluency, backward digit span, processing speed, and reaction time for attention switching and inhibitory control, which comprise two factors: episodic memory and executive functioning.

RESULTS

As predicted, all cognitive subtests and factors showed very small but significant declines over 9 years, with differences in the timing and extent of change. Processing speed showed the earliest and steepest decrements. Those with higher educational attainment scored better on all tests except reaction time. Men had better executive functioning and women performed better on episodic memory.

CONCLUSIONS

Examining cognitive changes in midlife provides opportunities for early detection of cognitive impairments and possibilities for preventative interventions. (JINS, 2018, 24, 805-820).

On Measuring and Modeling Physiological Synchrony in Dyads

Physiological synchrony within a dyad, or the degree of temporal correspondence between two individuals' physiological systems, has become a focal area of psychological research. Multiple methods have been used for measuring and modeling physiological synchrony. Each method extracts and analyzes different types of physiological synchrony, where 'type' refers to a specific manner through which two different physiological signals may correlate. Yet, to our knowledge, there is no documentation of the different methods, how each method corresponds to a specific type of synchrony, and the statistical assumptions embedded within each method. Hence, this article outlines several approaches for measuring and modeling physiological synchrony, connects each type of synchrony to a specific method, and identifies the assumptions that need to be satisfied for each method to appropriately extract each type of synchrony. Furthermore, this article demonstrates how to test for between-dyad differences of synchrony via inclusion of dyad-level (i.e., time-invariant) covariates. Finally, we complement each method with an empirical demonstration, as well as online supplemental material that contains Mplus code.

Sources of Variability in the Detection of B-Lines, Using Lung Ultrasound

Lung ultrasound (LUS) is a largely employed diagnostic tool but an operational protocol for implementation has never been proposed. The lack of standardization clearly introduces variability in LUS results. We enrolled adult patients presenting for acute dyspnea with a clinical suspect of etiology related to heart failure. We calculated agreement among four providers in assessing B-lines. We varied probes, depth, evaluation time and scanning areas and we estimated the importance of each factors on B-lines assessment. Overall agreement among raters varied from a kappa of 0.70 to 0.81. The mean number of B-lines was 5.44 (95% confidence interval, CI, 4.1-6.8). This estimate did not suffer variation by the depth used (0.03, 95% CI -0.2-0.2, more B-lines, using 19 cm versus 10 cm). The use of a convex probe and expertise in LUS reduced the number of artifacts by 1.7 (95% CI 1.5-1.9) and 1.1 in comparison with a phased array probe and naive operators. Evaluation time increased estimates by 1.2 (95% CI 1-1.5) and 2.9 (95% CI 2.7-3.9) B-lines for 4" and 7" clips (reference was 2" clips). This study suggests that the probe, the evaluation time and the level of expertise might affect the results of quantitative assessment of B-lines.

APOEε4 Genotype and Hypertension Modify 8-year Cortical Thinning: Five Occasion Evidence from the Seattle Longitudinal Study

We investigated individual differences in longitudinal trajectories of brain aging in cognitively normal healthy adults from the Seattle Longitudinal Study covering 8 years of longitudinal change (across 5 occasions) in cortical thickness in 249 midlife and older adults (52-95 years old). We aimed to understand true brain change; examine the influence of salient risk factors that modify an individual's rate of cortical thinning; and compare cross-sectional age-related differences in cortical thickness to longitudinal within-person cortical thinning. We used Multivariate Multilevel Modeling to simultaneously model dependencies among 5 lobar composites (Frontal, Parietal, Temporal, Occipital, and Cingulate [CING]) and account for the longitudinal nature of the data. Results indicate (1) all 5 lobar composites significantly atrophied across 8 years, showing nonlinear longitudinal rate of cortical thinning decelerated over time, (2) longitudinal thinning was significantly altered by hypertension and Apolipoprotein-E ε4 (APOEε4), varying by location: Frontal and CING thinned more rapidly in APOEε4 carriers. Notably, thinning of parietal and occipital cortex showed synergistic effect of combined risk factors, where individuals who were both APOEε4 carriers and hypertensive had significantly greater 8-year thinning than those with either risk factor alone or neither risk factor, (3) longitudinal thinning was 3 times greater than cross-sectional estimates of age-related differences in thickness in parietal and occipital cortices.

IV. DEVELOPMENTS IN THE ANALYSIS OF LONGITUDINAL DATA

Longitudinal data analytic techniques include a complex array of statistical techniques from repeated-measures analysis of variance, mixed-effects models, and time-series analysis, to longitudinal latent variable models (e.g., growth models, dynamic factor models) and mixture models (longitudinal latent profile analysis, growth mixture models). In this article, we focus our attention on the rationales of longitudinal research laid out by Baltes and Nesselroade (1979) and discuss the advancements in the analysis of longitudinal data since their landmark paper. We highlight the developments in growth and change analysis and its derivatives because these models best capture the rationales for conducting longitudinal research. We conclude with additional rationales of longitudinal research brought about by the development of new analytic techniques.

Comparison of progress monitoring data from general outcome measures and specific subskill mastery measures for reading

Interventionists often monitor the progress of students receiving supplemental interventions with general outcome measures (GOMs) such as curriculum-based measurement of reading (CBM-R). However, some researchers have suggested that interventionists should collect data more closely related to instructional targets, specific subskill mastery measures (SSMMs) because outcomes from GOMs such as CBM-R may not be sufficiently sensitive to gauge intervention effects. In turn, interventionists may prematurely terminate an effective intervention or continue to deliver an ineffective intervention if they do not monitor student progress with the appropriate measure. However, such recommendations are based upon expert opinion or studies with serious methodological shortcomings. We used multi-variate multilevel modeling to compare pre-intervention intercepts and intervention slopes between GOM and SSMM data collected concurrently in a sample of 96 first, 44 second, and 53 third grade students receiving tier 2 phonics interventions. Statistically significant differences were observed between slopes from SSMM consonant-vowel-consonant words and CBM-R data. Statistically significant differences in slopes were not observed for consonant blend, digraph or consonant-vowel-consonant-silent e (CVCe) SSMMs. Results suggest that using word lists to monitor student response to instruction for early struggling readers is beneficial but as students are exposed to more complex phonetic patterns, the distinction between SSMMs and CBM-R become less meaningful.

Joint modeling of multivariate hearing thresholds measured longitudinally at multiple frequencies

Pure-tone thresholds are used to estimate hearing acuity and, when measured longitudinally, can characterize age-related changes in hearing. Measured at multiple-frequencies, multiple-irregular time points, for right and left ears, these longitudinal studies of age-related hearing loss produce data of inherent complexity due to: 1) multivariate outcomes at different frequencies; 2) longitudinal measurements taken at subject-specific time intervals; and 3) inter-ear correlations due to clustering and nesting. To address limitations in existing methods, we propose a multivariate generalized linear mixed model(mGLMM) and assess its performance. We demonstrate its application using a unique dataset from a cohort study of age-related hearing loss.

Reduced impact of alcohol use on next-day tiredness in older relative to younger adults: A role for sleep duration

Recent work has suggested that older adults may be less susceptible to the next-day effects of alcohol relative to younger adults. The effects of alcohol in younger adults may be mediated by sleep duration, but due to age differences in the contexts of alcohol use, this mediation process may not generalize to older adults. The present study examined age-group (younger vs. older adults) differences in how alcohol use influenced next-day tiredness during daily life. Reports of alcohol use, sleep duration, and next-day tiredness obtained on ∼101 days from 91 younger adults (ages 20-31 years) and 75 older adults (ages 65-80 years) were modeled using a multilevel, moderated mediation framework. Findings indicated that (a) greater-than-usual alcohol use was associated with greater-than-usual tiredness in younger adults only, (b) greater-than-usual alcohol use was associated with shorter-than-usual sleep duration in younger adults only, and (c) shorter-than-usual sleep duration was associated with greater tiredness in both younger and older adults. For the prototypical younger adult, a significant portion (43%) of the association between alcohol use and next-day tiredness could be explained assuming mediation through sleep duration, whereas there was no evidence of mediation for the prototypical older adult. Findings of age differences in the mediation process underlying associations among alcohol use, sleep, and tiredness provide insight into the mechanisms driving recent observations of reduced next-day effects of alcohol in older relative to younger adults. (PsycINFO Database Record

Latent Growth Curve Models: Tracking Changes Over Time

The latent growth curve model (LGCM) is a useful tool in analyzing longitudinal data. It is particularly suitable for gerontological research because the LGCM can track the trajectories and changes of phenomena (e.g., physical health and psychological well-being) over time. Specifically, the LGCM compares lines of change across a set of individuals and determines the overall model's line of change. LGCMs can be used to track either linear or curvilinear trajectories. Since the technique uses structural equation modeling, models are also adjusted for measurement error. This article will present a step-by-step approach to setting up, analyzing, and interpreting an LGCM using post-hospitalization recovery in depressive symptomatology as an example. This article will demonstrate how to test linear, quadratic, and freely estimated lines of change using LGCMs with the purpose of finding the line of trajectory for depressive symptoms that best fits the data.

Life course indices for social determinants of self-rated health trajectory in Korean elderly

OBJECTIVES

This study investigated the self-rated health trajectories of the Korean older population and revealed life-course factors that affect the trajectories over the life course.

METHODS

Around 1000 older adults were randomly allocated by stratified multi-stage sampling based on the population census, and underwent face-to-face interviews. Self-rated health status, socioeconomic variables over the life course, and demographic variables were included in the analysis. A group-based trajectory model was used to investigate the association between self-rated health and explanatory variables.

RESULTS

The enrolled men and women were divided into three groups by trajectory analysis, which showed marked differences in self-rated health trajectories from childhood to senescence. Among older men, those who experienced skipping meals in childhood and those with chronic disease conditions were more likely to be in the lower trajectory groups. Compared to the older men, the likelihood of being in the lower trajectory groups in older women was increased by experience of skipping meals, lower household income, housekeeping labor, receiving Basic Livelihood Security and chronic disease conditions.

CONCLUSION

Various self-rated health trajectories of the Korean older population were identified, and differed according to socioeconomic variables during their life course. Therefore, socioeconomic variables during the life course should be monitored, and health policies directed at the elderly should focus on initial health status from the perspective of a life-course approach.

Growth Curve Modeling to Studying Change: A Comparison of Approaches Using Longitudinal Dyadic Data With Distinguishable Dyads

Although methodology articles have increasingly emphasized the need to analyze data from two members of a dyad simultaneously, the most popular method in substantive applications is to examine dyad members separately. This might be due to the underappreciation of the extra information simultaneous modeling strategies can provide. Therefore, the goal of this study was to compare multiple growth curve modeling approaches for longitudinal dyadic data (LDD) in both structural equation modeling and multilevel modeling frameworks. Models separately assessing change over time for distinguishable dyad members are compared to simultaneous models fitted to LDD from both dyad members. Furthermore, we compared the simultaneous default versus dependent approaches (whether dyad pairs' Level 1 [or unique] residuals are allowed to covary and differ in variance). Results indicated that estimates of variance and covariance components led to conflicting results. We recommend the simultaneous dependent approach for inferring differences in change over time within a dyad.

Multivariate Longitudinal Analysis with Bivariate Correlation Test

In the context of multivariate multilevel data analysis, this paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the dimensional residual terms are assumed uncorrelated. Using the EM algorithm, we suggest more general expressions of the model's parameters estimators. These estimators can be used in the framework of the multivariate longitudinal data analysis as well as in the more general context of the analysis of multivariate multilevel data. By using a likelihood ratio test, we test the significance of the correlations between the random effects of two dependent variables of the model, in order to investigate whether or not it is useful to model these dependent variables jointly. Simulation studies are done to assess both the parameter recovery performance of the EM estimators and the power of the test. Using two empirical data sets which are of longitudinal multivariate type and multivariate multilevel type, respectively, the usefulness of the test is illustrated.

Implicit Theories Relate to Youth Psychopathology, But How? A Longitudinal Test of Two Predictive Models

Research shows relations between entity theories-i.e., beliefs that traits and abilities are unchangeable-and youth psychopathology. A common interpretation has been that entity theories lead to psychopathology, but another possibility is that psychopathology predicts entity theories. The two models carry different implications for developmental psychopathology and intervention design. We tested each model's plausibility, examining longitudinal associations between entity theories of thoughts, feelings, and behavior and psychopathology in early adolescents across one school year (N = 59, 52 % female, ages 11-14, 0 % attrition). Baseline entity theories did not predict increases in psychopathology; instead, baseline psychopathology predicted increased entity theories over time. When symptom clusters were assessed individually, greater youth internalizing (but not externalizing) problems predicted subsequent increases in entity theories. Findings suggest that the commonly proposed predictive model may not be the only one warranting attention. They suggest that youth psychopathology may contribute to the development of certain kinds of entity theories.

Nonlinear latent curve models for multivariate longitudinal data

Latent curve models have become a useful approach to analyzing longitudinal data, due in part to their allowance of and emphasis on individual differences in features that describe change. Common applications of latent curve models in developmental studies rely on polynomial functions, such as linear or quadratic functions. Although useful for describing linear forms of change and some that are nonlinear, latent curve models based on polynomial functions are not suitable for describing many developmental processes that change in a nonlinear manner. This article considers nonlinear latent curve models that permit researchers to consider a variety of nonlinear functions to characterize developmental processes. An example is provided that considers simultaneous development of two behaviors.

Advanced Applications of Structural Equation Modeling in Counseling Psychology Research

Structural equation modeling (SEM) is a data-analytic technique that allows researchers to test complex theoretical models. Most published applications of SEM involve analyses of cross-sectional recursive (i.e., unidirectional) models, but it is possible for researchers to test more complex designs that involve variables observed at multiple points in time or variables implicated in reciprocal feedback loops (i.e., bidirectional models). Given SEM’s popularity among counseling psychology researchers, this article aims to introduce three SEM designs not often seen in the counseling psychology literature: cross-lagged panel analyses, latent growth curve modeling, and nonrecursive mediated model analysis. For each design, the authors provide a brief rationale regarding its purpose, procedures for specifying a model to test the design, and a worked illustration.

A Didactic Example of Latent Curve Analysis Applicable to the Study of Aging

Objectives: This article provides an example and application of growth curve analysis for modeling individual differences in behavioral rates of change in aging. The latent curve modeling approach to the analysis of change allows researchers to describe change as a continuous process and to address issues related to individual differences in change over time. Methods: Data are used from the Longitudinal Study of Aging (LSOA) on change in activities of daily living (ADLs) in the elderly. Analyses involved direct maximum likelihood estimation using complete and incomplete cases. Results: It is possible to statistically capture developmental changes. Change in participants’ ADLs was characterized by a negative linear trajectory, and there was evidence of significant individual variability in the starting point of the trajectory and the rate of change over time. Discussion: The article discusses the utility of latent curve analysis in aging research as well as other techniques that are extensions of latent curve analysis.

The Conceptualization and Analysis of Change Over Time: An Integrative Approach Incorporating Longitudinal Mean and Covariance Structures Analysis (LMACS) and Multiple Indicator Latent Growth Modeling (MLGM)

The concept of change over time is fundamental to many phenomena investigated in organizational research. This didactically oriented article proposes an integrative approach incorporating longitudinal mean and covariance structures analysis and multiple indicator latent growth modeling to aid organizational researchers in directly addressing fundamental questions concerning the conceptualization and analysis of change over time. The approach is illustrated using a numerical example involving several organizationally relevant variables. Advantages, limitations, and extensions of the approach are discussed.

Applications of Hierarchical Linear Models for Evaluations of Health Interventions

Despite the wide availability of statistical programs designed to deal with longitudinal data from a multilevel perspective, many applied researchers remain unfamiliar with the benefits of this methodology, particularly for the evaluation of interventions. The authors present an example of multilevel modeling as part of the analysis of evaluation data from an HIV intervention study. Strategies for understanding multilevel models using longitudinal (panel) data are demonstrated and discussed. The authors illustrate how multiple linear regression models provide a convenient conceptual background to understanding how hierarchical linear models can be developed and interpreted. Multilevel analysis results are compared and contrasted with typical approaches through general linear models for repeated-measures data. Analyses are presented using the SPSS and HLM 5 software.

A longitudinal analysis of sentence interpretation in bilingual children

This longitudinal study used sentence interpretation tasks to consider growth in language processing among school-aged children learning Vietnamese and English. Thirty-two children participated yearly over three time points. Children were asked to identify the agent of sentences that manipulated linguistic cues relevant to Vietnamese (animacy) and English (word order). Hierarchical linear modeling was used to examine change in cue use over time as well as the relation between cue use and proficiency in each language. Findings include exclusive reliance on word order by the end point, nearly identical group-level cue-use patterns across languages with individual variation, and positive relationships between language proficiency and cue use. Findings are discussed within the unified competition model (MacWhinney, 2004) and the literature on sequential bilingualism.

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

Unconscious deception detection measured by finger skin temperature and indirect veracity judgments-results of a registered report

A pre-registered experiment was conducted to examine psychophysiological responses to being lied to. Bridging research on social cognition and deception detection, we hypothesized that observing a liar compared to a truth-teller would decrease finger skin temperature of observers. Participants first watched two targets while not forewarned that they would later be asked to judge (direct and indirect) veracity, and then watched another two targets while forewarned about this. During both these phases finger skin temperature was measured. Findings pertaining to temperature partly confirmed our main hypothesis. When participants were observing a liar, irrespective of being forewarned, on average finger skin temperature declined over time. In the forewarned phase, temperature trajectories of truth-tellers were higher than those of liars, however, in the not forewarned phase, this pattern was reversed. Results confirmed our further hypotheses that participants judge liars as less likeable and less trustworthy than truth-tellers-an indication of indirect deception detection. Our hypothesis that the effect size for trustworthiness would be bigger than that of liking was not supported by the data. Additionally, and also confirming our hypothesis, participants performed around chance level when directly judging whether the target person was lying. Exploratory analyses are reported with regard to truth bias and dependency between direct and indirect veracity judgments. Limitations and directions for future work related to the existence of psychophysiological indicators of deception detection are discussed.

Analytical strategies in human growth research

Human growth research requires knowledge of longitudinal statistical methods that can be analytically challenging. Even the assessment of growth between two ages is not as simple as subtracting the first measurement from the second, for example. This article provides an overview of the key analytical strategies available to human biologists in increasing order of complexity, starting with a review on how to express cross-sectional measurements of size, before covering growth (conditional regression models, regression with conditional growth measures), growth curves (individual growth curves, mixed effects growth curves, latent growth curves), and patterns of growth (growth mixture modeling). The article is not a statistical treatise and has been written by a human biologist for human biologists; as such, it should be accessible to anyone with training in at least basic statistics. A summary table linking each analytical strategy to its applications is provided to help investigators match their hypotheses and measurement schedules to an analysis plan. In addition, worked examples using data on non-Hispanic white participants in the Fels Longitudinal Study are used to illustrate how the analytical strategies might be applied to gain novel insight into human growth and its determinants and consequences. All too often, serial measurements are treated as cross-sectional in analyses that do not harness the power of longitudinal data. The broad goal of this article is to encourage the rigorous application of longitudinal statistical methods to human growth research.

Analyzing multiple outcomes in clinical research using multivariate multilevel models

OBJECTIVE

Multilevel models have become a standard data analysis approach in intervention research. Although the vast majority of intervention studies involve multiple outcome measures, few studies use multivariate analysis methods. The authors discuss multivariate extensions to the multilevel model that can be used by psychotherapy researchers.

METHOD AND RESULTS

Using simulated longitudinal treatment data, the authors show how multivariate models extend common univariate growth models and how the multivariate model can be used to examine multivariate hypotheses involving fixed effects (e.g., does the size of the treatment effect differ across outcomes?) and random effects (e.g., is change in one outcome related to change in the other?). An online supplemental appendix provides annotated computer code and simulated example data for implementing a multivariate model.

CONCLUSIONS

Multivariate multilevel models are flexible, powerful models that can enhance clinical research.

A longitudinal examination of the interrelationship of multiple health behaviors

BACKGROUND

Evaluating the interrelationship of health behaviors could assist in the development of effective public health interventions. Furthermore, the ability to identify cognitive mediators that may influence multiple behavioral changes requires evaluation.

PURPOSE

To evaluate covariation among health behaviors, specifically alcohol consumption, leisure-time physical activity, and smoking, and examine whether mastery acts as a mediating social-cognitive mechanism that facilitates multiple health behavior change in a longitudinal analysis.

METHODS

In 2010, secondary data analysis was conducted on the first seven cycles of the Canadian National Population Health Survey. Data collection began in 1994-1995 and has continued biennially. At the time of this analysis, only seven cycles of data (2006-2007) were available. Parallel process growth curve models were used to analyze covariation between health behaviors and the potential mediating effects of perceived mastery.

RESULTS

Increases in leisure-time physical activity were associated with reductions in tobacco use, whereas declines in alcohol consumption were associated with decreases in tobacco use. Covariation between alcohol consumption and leisure-time physical activity did not reach statistical significance. For the most part, mastery was unsuccessful in mediating the interrelationship of multiple behavioral changes.

CONCLUSIONS

Health behaviors are not independent but rather interrelated. In order to optimize limited prevention resources, these results suggest that population-level intervention efforts targeting multiple modifiable behavioral risk factors may not need to occur simultaneously.

Longitudinal changes in health-related quality of life for chronic diseases: an example in hemophilia A

BACKGROUND

Patients with well-managed rare chronic diseases such as hemophilia maintain a stable health state and health-related quality of life (HrQoL) that may be affected by acute events. Longitudinal HrQoL assessments analyzed using multivariate multilevel (MVML) modelling can determine the impact of such events on individuals (within-person effect) and identify factors influencing within-population differences (between-person effect).

OBJECTIVES

To demonstrate the application of MVML modelling in a longitudinal study of HrQoL in hemophilia A.

METHODS/DESIGN/PARTICIPANTS

Using data on 136 adults and 125 children from a two-year observational cohort study of burden of illness in US hemophilia A patients, MVML modelling determined the effect of time-invariant (sociodemographic and clinical characteristics) and time-varying factors (bleeding frequency, emergency room visits, and missed work/school days) on within-person and between-person HrQoL changes. HrQoL was assessed using the SF-12 health survey (adults) and PedsQL inventory (children) at baseline, then every 6 months.

RESULTS

In children, within-person (p < 0.0001) and between-person (p < 0.0001) psychosocial functioning was reduced by each additional bleed and missed day (within-person: p = 0.0089; between-person: p = 0.0060). Within-person physical functioning was reduced by each additional bleed (p < 0.0001), emergency room (ER) visit (p = 0.0284), and missed day (p = 0.0473). Between-persons, additional missed days (p < 0.0001) significantly decreased physical functioning. In adults, each additional missed day reduced SF-12 Health Survey mental (p = 0.0025) and physical (p = 0.0093) component summary scores. Each additional bleed also decreased physical component summary (PCS) significantly (p = 0.0093).

CONCLUSIONS

This study demonstrated the applicability of MVML modelling in identifying time-invariant and time-varying factors influencing HrQoL in a rare chronic disease population. Small but significant within-person and between-person changes in HrQoL with each additional acute event experienced were identified, which if frequent, could have a large cumulative impact. The results suggest that MVML modelling may be applied to future studies of longitudinal change in HrQoL in other rare chronic disease populations.

The Extensiveness of Corporate Social and Environmental Commitment across Firms over Time

Corporate social commitment (CSC) and corporate environmental commitment (CEC) are often combined under the general rubric of corporate social responsibility. Although the two sets of activities are similar, they are also very different. Both CSC and CEC respond to issues raised by stakeholders, but CEC tends to be more “technical”. This characteristic demands that CEC fit with the organization, which exposes greater economic opportunities than CSC. As a result, we argue that the extent to which these practices are implemented differs across firms over time. We analyze the extensiveness of implementation of CSC and CEC across 266 firms from 1991 to 2003, using latent growth curve modeling and one-way ANOVA. We find that firms moved towards at least a moderate level of CSC over time, but tended to bifurcate in the extent to which they implemented CEC practices, towards either the high or low end of the scale, over time. In this paper, we contribute to the institutional analysis of practice diffusion by examining how the characteristics of different kinds of practices shape the extensiveness of firm adoption patterns. As well, this research also speaks to corporate social responsibility researchers, pointing to the need to sometimes discriminate between social and environmental practices.

Longitudinal design considerations to optimize power to detect variances and covariances among rates of change: simulation results based on actual longitudinal studies

We investigated the power to detect variances and covariances in rates of change in the context of existing longitudinal studies using linear bivariate growth curve models. Power was estimated by means of Monte Carlo simulations. Our findings show that typical longitudinal study designs have substantial power to detect both variances and covariances among rates of change in a variety of cognitive, physical functioning, and mental health outcomes. We performed simulations to investigate the interplay among number and spacing of occasions, total duration of the study, effect size, and error variance on power and required sample size. The relation between growth rate reliability (GRR) and effect size to the sample size required to detect power greater than or equal to .80 was nonlinear, with rapidly decreasing sample sizes needed as GRR increases. The results presented here stand in contrast to previous simulation results and recommendations (Hertzog, Lindenberger, Ghisletta, & von Oertzen, 2006; Hertzog, von Oertzen, Ghisletta, & Lindenberger, 2008; von Oertzen, Ghisletta, & Lindenberger, 2010), which are limited due to confounds between study length and number of waves, error variance with growth curve reliability, and parameter values that are largely out of bounds of actual study values. Power to detect change is generally low in the early phases (i.e., first years) of longitudinal studies but can substantially increase if the design is optimized. We recommend additional assessments, including embedded intensive measurement designs, to improve power in the early phases of long-term longitudinal studies.

Aggregating and Testing Intra-Individual Correlations: Methods and Comparisons

From a longitudinal study, we have repeatedly measured data from multiple individuals at multiple occasions. For each individual, the relation between 2 variables can be measured by the Pearson's correlation. The question is how to aggregate the multiple correlations and conduct statistical inference on the aggregated intra-individual correlation. Several methods are proposed to aggregate and test intra-individual correlations: (a) a meta-analysis method based on Fisher's Z transformed correlations, (b) a meta-analysis method based on the Pearson's correlations, and (c) a multilevel modeling method using data standardized within each individual. The performance of the methods after bias corrections was compared using simulations with considering factors including numbers of individuals, numbers of time points, population effect sizes, and their distribution forms (homogeneous vs heterogeneous). The results from the simulation studies show that estimation biases were found using the meta-analytic methods and suggestions on when and how to correct biases were provided based on the simulation results. Furthermore, the performance of the 3 methods after necessary bias corrections was found to be comparable and reasonably good, indicating that all 3 methods worked for aggregating and testing intra-individual correlations. An empirical daily diary data set was then used to illustrate the applications of the 3 methods. The assumptions, advantages and disadvantages, and possible extensions of the 3 methods were discussed.

Trajectories of change in emotion regulation and social anxiety during cognitive-behavioral therapy for social anxiety disorder

Cognitive-behavioral therapy (CBT) for social anxiety disorder (SAD) may decrease social anxiety by training emotion regulation skills. This randomized controlled trial of CBT for SAD examined changes in weekly frequency and success of cognitive reappraisal and expressive suppression, as well as weekly intensity of social anxiety among patients receiving 16 weekly sessions of individual CBT. We expected these variables to (1) differ from pre-to-post-CBT vs. Waitlist, (2) have differential trajectories during CBT, and (3) covary during CBT. We also expected that weekly changes in emotion regulation would predict (4) subsequent weekly changes in social anxiety, and (5) changes in social anxiety both during and post-CBT. Compared to Waitlist, CBT increased cognitive reappraisal frequency and success, decreased social anxiety, but had no impact on expressive suppression. During CBT, weekly cognitive reappraisal frequency and success increased, whereas weekly expressive suppression frequency and social anxiety decreased. Weekly decreases in social anxiety were associated with concurrent increases in reappraisal success and decreases in suppression frequency. Granger causality analysis showed that only reappraisal success increases predicted decreases in subsequent social anxiety during CBT. Reappraisal success increases pre-to-post-CBT predicted reductions in social anxiety symptom severity post-CBT. The trajectory of weekly changes in emotion regulation strategies may help clinicians understand whether CBT is effective and predict decreases in social anxiety.

CLINICALTRIALSGOV IDENTIFIER

NCT00380731; http://www.clinicaltrials.gov/ct2/show/NCT00380731?term=social+anxiety+cognitive+behavioral+therapy+Stanford&rank=1.

On Fitting a Multivariate Two-Part Latent Growth Model

A 2-part latent growth model can be used to analyze semicontinuous data to simultaneously study change in the probability that an individual engages in a behavior, and if engaged, change in the behavior. This article uses a Monte Carlo (MC) integration algorithm to study the interrelationships between the growth factors of 2 variables measured longitudinally where each variable can follow a 2-part latent growth model. A SAS macro implementing Mplus is developed to estimate the model to take into account the sampling uncertainty of this simulation-based computational approach. A sample of time-use data is used to show how maximum likelihood estimates can be obtained using a rectangular numerical integration method and an MC integration method.

The association of therapist empathy and synchrony in vocally encoded arousal

Empathy is a critical ingredient in motivational interviewing (MI) and in psychotherapy generally. It is typically defined as the ability to experience and understand the feelings of another. Basic science indicates that empathy is related to the development of synchrony in dyads. However, in clinical research, empathy has proved difficult to operationalize and measure, and has mostly relied on the felt sense of observers, clients, or therapists. We extracted estimates of therapist and standardized patient (SP) vocally encoded arousal (mean fundamental frequency; mean f₀) in 89 MI sessions with high and low empathy ratings from independent observers. We hypothesized (a) therapist and SP mean f₀ would be correlated and (b) the correlation of therapist and SP mean f₀ would be greater in sessions with high empathy as compared with low. On the basis of a multivariate mixed model, the correlation between therapist and SP mean f₀ was large (r = .71) and close to 0 in randomly assigned therapist-SP dyads (r = -.08). The association was higher in sessions with high empathy ratings (r = .80) than in sessions with low ratings (r = .36). There was strong evidence for vocal synchrony in clinical dyads as well as for the association of synchrony with empathy ratings, illustrating the relevance of basic psychological processes to clinical interactions. These findings provide initial evidence for an objective and nonobtrusive method for assessing therapist performance. Novel indicators of therapist empathy may have implications for the study of MI process as well as the training of therapists generally. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

A longitudinal study of lexical development in children learning Vietnamese and English

This longitudinal study modeled lexical development among children who spoke Vietnamese as a first language (L1) and English as a second language (L2). Participants (n = 33, initial mean age of 7.3 years) completed a total of eight tasks (four in each language) that measured vocabulary knowledge and lexical processing at four yearly time points. Multivariate hierarchical linear modeling was used to calculate L1 and L2 trajectories within the same model for each task. Main findings included (a) positive growth in each language, (b) greater gains in English resulting in shifts toward L2 dominance, and (c) different patterns for receptive and expressive domains. Timing of shifts to L2 dominance underscored L1 skills that are resilient and vulnerable to increases in L2 proficiency.

Comparing statistical methods for analyzing skewed longitudinal count data with many zeros: an example of smoking cessation

Count data with skewness and many zeros are common in substance abuse and addiction research. Zero-adjusting models, especially zero-inflated models, have become increasingly popular in analyzing this type of data. This paper reviews and compares five mixed-effects Poisson family models commonly used to analyze count data with a high proportion of zeros by analyzing a longitudinal outcome: number of smoking quit attempts from the New Hampshire Dual Disorders Study. The findings of our study indicated that count data with many zeros do not necessarily require zero-inflated or other zero-adjusting models. For rare event counts or count data with small means, a simpler model such as the negative binomial model may provide a better fit.

Multivariate multilevel spline models for parallel growth processes: application to weight and mean arterial pressure in pregnancy

Growth models are commonly used in life course epidemiology to describe growth trajectories and their determinants or to relate particular patterns of change to later health outcomes. However, methods to analyse relationships between two or more change processes occurring in parallel, in particular to assess evidence for causal influences of change in one variable on subsequent changes in another, are less developed. We discuss linear spline multilevel models with a multivariate response and show how these can be used to relate rates of change in a particular time period in one variable to later rates of change in another variable by using the variances and covariances of individual-level random effects for each of the splines. We describe how regression coefficients can be calculated for these associations and how these can be adjusted for other parameters such as random effect variables relating to baseline values or rates of change in earlier time periods, and compare different methods for calculating the standard errors of these regression coefficients. We also show that these models can equivalently be fitted in the structural equation modelling framework and apply each method to weight and mean arterial pressure changes during pregnancy, obtaining similar results for multilevel and structural equation models. This method improves on the multivariate linear growth models, which have been used previously to model parallel processes because it enables nonlinear patterns of change to be modelled and the temporal sequence of multivariate changes to be determined, with adjustment for change in earlier time periods.

Order-restricted inference for multivariate longitudinal data with applications to the natural history of hearing loss

Multivariate outcomes are often measured longitudinally. For example, in hearing loss studies, hearing thresholds for each subject are measured repeatedly over time at several frequencies. Thus, each patient is associated with a multivariate longitudinal outcome. The multivariate mixed-effects model is a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, it is known that hearing thresholds, at every frequency, increase with age. Moreover, this age-related threshold elevation is monotone in frequency, that is, the higher the frequency, the higher, on average, is the rate of threshold elevation. This means that there is a natural ordering among the different frequencies in the rate of hearing loss. In practice, this amounts to imposing a set of constraints on the different frequencies' regression coefficients modeling the mean effect of time and age at entry to the study on hearing thresholds. The aforementioned constraints should be accounted for in the analysis. The result is a multivariate longitudinal model with restricted parameters. We propose estimation and testing procedures for such models. We show that ignoring the constraints may lead to misleading inferences regarding the direction and the magnitude of various effects. Moreover, simulations show that incorporating the constraints substantially improves the mean squared error of the estimates and the power of the tests. We used this methodology to analyze a real hearing loss study.

Distinguishing between-person and within-person relationships in longitudinal health research: arthritis and quality of life

BACKGROUND

Many health measures (e.g., blood pressure, quality of life) have meaningful fluctuation over time around a relatively stable mean level for each person.

PURPOSE

This didactic paper describes two closely related statistical models for examining between-person and within-person relationships between two or more sets of measures collected over time: the latent intercept model with correlated residuals (LI) in structural equation modeling framework and the multivariate multilevel model (MVML) in multilevel modeling framework.

RESULTS

We illustrated that the basic LI model and the MVML model are equivalent. We presented an illustrative example using a national arthritis data resource to examine between-person and within-person relationships of symptom status, functional health, and quality of life in arthritis patients.

DISCUSSION

Additional design and modeling issues for the treatment of missing data are considered. We discuss contexts in which one of the two models may be preferred. Mplus and SAS syntax are available.