Time-varying Effect Models Research Articles

Number of Subjects and Time Points Needed for Multilevel Time-Series Analysis: A Simulation Study of Dynamic Structural Equation Modeling

Dynamic structural equation modeling (DSEM) is a novel, intensive longitudinal data (ILD) analysis framework. DSEM models intraindividual changes over time on Level 1 and allows the parameters of these processes to vary across individuals on Level 2 using random effects. DSEM merges time series, structural equation, multilevel, and time-varying effects models. Despite the well-known properties of these analysis areas by themselves, it is unclear how their sample size requirements and recommendations transfer to the DSEM framework. This article presents the results of a simulation study that examines the estimation quality of univariate 2-level autoregressive models of order 1, AR(1), using Bayesian analysis in Mplus Version 8. Three features are varied in the simulations: complexity of the model, number of subjects, and number of time points per subject. Samples with many subjects and few time points are shown to perform substantially better than samples with few subjects and many time points.

Sexual Behavior and Heavy Episodic Drinking Across the Transition to Adulthood: Differences by College Attendance.

Despite a growing literature on college students' sexual behaviors, little is known about how sexual behaviors, and their associations with alcohol, differ for college and noncollege attenders, and whether these patterns represent changes during college or an extension of pre-college behaviors. This paper applied time-varying effect models to data from the National Longitudinal Study of Adolescent to Adult Health to examine (1) prevalence of four sexual behaviors from ages 14 to 24 and (2) how their association with frequent heavy episodic drinking varied across these ages for college and noncollege attenders. Nonattenders have higher prevalence of all sexual behaviors than college attenders across most ages; however, the association between heavy episodic drinking and sexual behaviors is stronger for college attenders during ages 18-20.

A time-varying effect model of the dynamic association between alcohol use and consequences over the first two years of college

College students experience myriad negative consequences from alcohol misuse. The strength of the association between level of alcohol use and consequences may change across the initial years of college, as students develop tolerance or learn to avoid negative effects of drinking. Time varying effect models (TVEM) allow for statistical examination of the changing strength of associations between two variables as they unfold across time. Goals of the present study were to test the hypothesis that the association between weekly quantity of alcohol use and the odds of an alcohol consequence that week would decrease in strength from the first week of freshman year to the end of sophomore year, and to examine gender differences in the association between use and consequences over time. Participants (N=812 college student drinkers, 60% female) completed 36 assessments of alcohol use and consequences across two years (every other week). TVEM models revealed that the proportion of those for whom alcohol use led to a consequence declined across time. Aside from the first few weeks of college, the association between alcohol use and odds of a consequence was consistently stronger for women than men. Among men, the odds of a consequence declined relatively steadily over time. Among women, the strength of this association was more dynamic. This study provides initial insight into the complex relationship between drinking and consequences. Future research focusing on understanding factors that explain the decreasing association between use and consequences with time can contribute to college student alcohol education and interventions.

Modeling the complexity of dynamic, momentary interpersonal behavior: Applying the time-varying effect model to test predictions from interpersonal theory

This paper demonstrates a recently-popularized quantitative method, the time-varying effect model (TVEM), in describing dynamic, momentary interpersonal processes implicated by Interpersonal Theory. We investigated moment-to-moment complementarity in affiliation and control behaviors (i.e., correspondence in affiliation and reciprocity in control between married dyad members) in a five-minute interaction (N=135), and how complementarity changed over time. Overall, results supported complementarity in affiliation and control. Moreover, effects were time-varying: Complementarity in affiliation increased over time and complementary in control changed over time in a cyclical manner. Dyadic adjustment moderated the strength in complementarity in control during specific timeframes. We discuss implications of these results and future directions. The findings support the utility of TVEM for studying dynamic and time-dependent interpersonal processes.

Decentering in the process of cultivating mindfulness: An experience-sampling study in time and context.

Through intensive experience sampling, we studied the practice and development of mindfulness as a dynamic process in time and context. We focused on role(s) and salutary function(s) of mindfulness and decentering for emotional experience over the course of mindfulness practice and development. Eighty-two meditation-naive adults from the general community, 52% women, Mage (SD) = 25.05 (3.26) years, participated in a 1-month, 6-session, Mahasi-based mindfulness-training intervention (Mahasi, 1978). We collected 52 digital experience samples of mindfulness, decentering, and emotional experience, in the context of daily living and meditative states, over the course of the program. Data were analyzed via time-varying effects models (TVEMs) and mixed-linear models (MLMs) within a single-subject, multiple-baseline experimental design. First, over the course of the intervention, participants grew more mindful and decentered in daily living and meditative states. Second, the association between mindfulness and decentering was significant in daily living, although the magnitude of this association was stronger in meditative states. Third, we observed the same contextualized pattern of relations between mindfulness and emotional valence (happy > sad) as well as arousal (calm > nervous). Finally, whereas decentering mediated the effect of mindfulness on reduced emotional arousal in meditative states, it did not similarly mediate the effect of mindfulness on positive emotional valence. The present findings illustrate the insights that may be gained about mindfulness mechanisms broadly and decentering specifically through the study of mindfulness as a dynamic, contextualized developmental process over time. (PsycINFO Database Record

Age-varying associations between nonmarital sexual behavior and depressive symptoms across adolescence and young adulthood.

Research has demonstrated associations between adolescent sexual behavior and depressive symptoms, but no single study has examined individuals at different ages throughout adolescence and young adulthood in order to determine at what ages sexual behavior may be associated with higher or lower levels of depressive symptoms. Using nationally representative longitudinal data and an innovative method, the time-varying effect model (TVEM), which examines how the strength of an association changes over time, this study examines how nonmarital sexual intercourse is associated with depressive symptoms at different ages, which behaviors and contexts may contribute to these associations, and whether associations differ for male and female participants. Findings indicate that sexual behavior in adolescence is associated with a higher level of depressive symptoms, particularly for female adolescents, and this association is relatively consistent across different partner types and adolescent contexts. Associations between sexual behavior and depressive symptoms in young adulthood are more dependent on partner factors and adolescent contexts; sexual behavior in young adulthood is associated with fewer depressive symptoms for women who have sex with a single partner and for men whose parents did not strongly disapprove of adolescent sexual behavior. Findings suggest that delaying sexual behavior into young adulthood may have some benefits for mental health, although contextual and relationship factors also play a role. (PsycINFO Database Record

Varied effects of age-related neuropathologies on the trajectory of late life cognitive decline.

The objective of this study was to examine whether the effects of age-related neuropathologies on cognition change over time. Participants were 1096 deceased persons from two clinical-pathologic studies. All were without dementia at baseline, completed a detailed battery of cognitive tests annually over up to 21 years, died, and underwent detailed neuropathologic examinations to identify Alzheimer's disease pathology, vascular pathologies (i.e. macro- and microscopic infarcts, atherosclerosis, arteriolar sclerosis, and cerebral amyloid angiopathy), Lewy bodies, transactive response DNA-binding protein 43 (TDP-43) pathology, and hippocampal sclerosis. A time-varying effects model was used to flexibly characterize the trajectory of global cognition and assess whether the effects of demographics and each neuropathologic index on cognition changed over time. Results indicated that the mean trajectory of global cognition was characterized by gradual cognitive decline beginning ∼15 years before death and accelerated decline in the last few years. With the exception of microinfarcts and arteriolar sclerosis, all neuropathologies were associated with the cognitive trajectory. However, the nature of their associations varied. Alzheimer's disease pathology, macroscopic infarcts, Lewy bodies, TDP-43 pathology, and hippocampal sclerosis were associated with progressive cognitive decline, with their deleterious effects increasing over time. By contrast, atherosclerosis and cerebral amyloid angiopathy pathology were associated with a lower level of cognition but their effects were relatively stable over time. These results suggest that age-related neuropathologies are differentially related to late life cognitive trajectories. Whereas some contribute to progressive cognitive deterioration, others lower the level of cognition but exert relatively stable effects over time.

The shape of change in perceived stress, negative affect, and stress sensitivity during mindfulness-based stress reduction.

Both daily stress and the tendency to react to stress with heightened levels of negative affect (i.e., stress sensitivity) are important vulnerability factors for adverse mental health outcomes. Mindfulness-based stress reduction (MBSR) may help to reduce perceived daily stress and stress sensitivity. The purpose of this study was to examine how change in perceived stress, negative affect (NA), and the decoupling between perceived stress and NA evolved over the course of a MBSR program, without making any a priori assumptions on the shape of change. Seventy-one adults from the general population participating in MBSR provided daily diary assessments of perceived stress and NA during MBSR. The time-varying effect model (TVEM) indicated that perceived stress and NA decreased in a linear fashion rather than in a non-linear fashion, both as a function of time and as a function of the cumulative number of days of mindfulness practice. Both TVEM and multilevel growth modeling showed that the association between perceived stress and NA did not decrease over the course of MBSR. The findings support the hypothesis that MBSR reduces NA and also reduces the extent to which individuals perceive their days as stressful. Also, the results suggest that there is a dose-response relationship between the amount of mindfulness practice and reductions in daily stress and NA.

A time-varying effect model for examining group differences in trajectories of zero-inflated count outcomes with applications in substance abuse research.

This study proposes a time-varying effect model for examining group differences in trajectories of zero-inflated count outcomes. The motivating example demonstrates that this zero-inflated Poisson model allows investigators to study group differences in different aspects of substance use (e.g., the probability of abstinence and the quantity of alcohol use) simultaneously. The simulation study shows that the accuracy of estimation of trajectory functions improves as the sample size increases; the accuracy under equal group sizes is only higher when the sample size is small (100). In terms of the performance of the hypothesis testing, the type I error rates are close to their corresponding significance levels under all settings. Furthermore, the power increases as the alternative hypothesis deviates more from the null hypothesis, and the rate of this increasing trend is higher when the sample size is larger. Moreover, the hypothesis test for the group difference in the zero component tends to be less powerful than the test for the group difference in the Poisson component. Copyright © 2016 John Wiley & Sons, Ltd.

Time-varying SMART design and data analysis methods for evaluating adaptive intervention effects.

BackgroundIn a standard two-stage SMART design, the intermediate response to the first-stage intervention is measured at a fixed time point for all participants. Subsequently, responders and non-responders are re-randomized and the final outcome of interest is measured at the end of the study. To reduce the side effects and costs associated with first-stage interventions in a SMART design, we proposed a novel time-varying SMART design in which individuals are re-randomized to the second-stage interventions as soon as a pre-fixed intermediate response is observed. With this strategy, the duration of the first-stage intervention will vary.MethodsWe developed a time-varying mixed effects model and a joint model that allows for modeling the outcomes of interest (intermediate and final) and the random durations of the first-stage interventions simultaneously. The joint model borrows strength from the survival sub-model in which the duration of the first-stage intervention (i.e., time to response to the first-stage intervention) is modeled. We performed a simulation study to evaluate the statistical properties of these models.ResultsOur simulation results showed that the two modeling approaches were both able to provide good estimations of the means of the final outcomes of all the embedded interventions in a SMART. However, the joint modeling approach was more accurate for estimating the coefficients of first-stage interventions and time of the intervention.ConclusionWe conclude that the joint modeling approach provides more accurate parameter estimates and a higher estimated coverage probability than the single time-varying mixed effects model, and we recommend the joint model for analyzing data generated from time-varying SMART designs. In addition, we showed that the proposed time-varying SMART design is cost-efficient and equally effective in selecting the optimal embedded adaptive intervention as the standard SMART design.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0202-7) contains supplementary material, which is available to authorized users.

Early-Emerging Nicotine Dependence Has Lasting and Time-Varying Effects on Adolescent Smoking Behavior.

Novice and light adolescent smokers can develop symptoms of nicotine dependence, which predicts smoking behavior several years into the future. However, little is known about how the association between these early - emerging symptoms and later smoker behaviors may change across time from early adolescence into young adulthood. Data were drawn from a 7-year longitudinal study of experimental (<100 cigarettes/lifetime; N = 594) and light (100+ cigarettes/lifetime, but ≤5 cigarettes/day; N = 152) adolescent smokers. Time-varying effect models were used to examine the relationship between baseline nicotine dependence (assessed at age 15 ± 2years) and future smoking frequency through age 24, after controlling for concurrent smoking heaviness. Baseline smoking status, race, and sex were examined as potential moderators of this relationship. Nicotine dependence symptoms assessed at approximately age 15 significantly predicted smoking frequency through age 24, over and above concurrent smoking heaviness, though it showed declining trends at older ages. Predictive validity was weaker among experimenters at young ages (<16), but stronger at older ages (20-23), relative to light smokers. Additionally, nicotine dependence was a stronger predictor of smoking frequency for white smokers around baseline (ages 14.5-16), relative to nonwhite smokers. Nicotine dependence assessed in mid-adolescence predicts smoking frequency well into early adulthood, over and above concurrent smoking heaviness, especially among novice smokers and nonwhite smokers. Early-emerging nicotine dependence is a promising marker for screening and interventions aimed at preventing smoking progression.

Synergistic effects of social media and traditional marketing on brand sales: capturing the time-varying effects

As social media gains more importance, managers are challenged to quantify its return on sales. The academic understanding in the effectiveness of social media is limited, and in fact the synergistic effects between social media and traditional marketing efforts have rarely been investigated. Despite the dynamics in marketing effectiveness on sales, the time-varying effectiveness of social media has never been studied either. In this study, we capture the time-varying effects of social media and the time-varying synergistic effects of social media and traditional marketing with a time-varying effect model (TVEM) approach. The empirical analyses of a large U.S. ice-cream brand sales reveal that a) the effectiveness of social media and traditional marketing vary over time, b) the synergistic effects vary over time for social media with product sampling and with in-store promotions, c) the proposed TVEM approach has a higher predictive accuracy than the benchmark models, and d) the proposed TVEM approach saves marketing costs by $0.4 million per year, compared to the time-invariant benchmark model. Overall, this study enables managers to not only better understand the synergistic effects of social media marketing and traditional marketing, but also the time-varying effectiveness of their marketing efforts with TVEM approach for better resource allocation.

Timing of First Sexual Intercourse and Young Adult Health Outcomes

PurposeTo examine how age of onset of sexual intercourse is associated with past-year and lifetime sexually transmitted infections (STIs) and depression in young adulthood. MethodsWe examined how occurrence of a lifetime and past-year STI, lifetime diagnosis of depression, and past-week depressive symptoms differed as a function of age of onset of sexual intercourse using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health; N = 8,938 individuals). Time-varying effect models were used to examine how age of onset, measured as continuous age, was associated with these outcomes in young adulthood, with all analyses stratified to examine gender differences. ResultsIndividuals who engaged in first intercourse before age 16 reported higher than average rates of all outcomes studied; for example, an estimated 35% of women and 12% of men who initiated at age 14 years reported a lifetime STI, compared with about 5% of those who initiated at age 24 years. Timing of first intercourse past the mid-twenties was associated with lower than average rates of STIs and lifetime depression diagnoses but was associated with a somewhat higher level of past-year depressive symptoms. Patterns were similar by gender, although there was little difference in men's depression diagnoses by age of onset. ConclusionsResults suggest that sexual intercourse before age 16 years may be associated with higher rates of STIs and depression. Findings provide support for comprehensive programs that both promote delay of first intercourse and provide safe sex and psychological support for those who initiate early.

Overweight and isolated

This longitudinal study investigates whether there are particularly salient ages when being overweight is related to problems in interpersonal relationships (i.e., physical, relational, and verbal victimization, lack of friend social support, dating status, and romantic relationship worries). Participants were from a large, six-wave longitudinal study (N = 662, 48% males, M age at T1 = 15.5 years, SD = 1.9 years). We use time-varying effect models to estimate how the associations between weight status and interpersonal problems differ from ages 12 to 28. Gender differences are also investigated. Findings show that youth who are overweight are more likely to experience verbal victimization, feel less supported by their peers, and are less likely to date than youth who are not overweight from mid-adolescence into early young adulthood. Further, females who are overweight are more likely to be physically victimized at ages 15 to 22 than females who are not overweight. The results provide a better understanding of age-related changes in interpersonal problems among youth who are overweight from adolescence into young adulthood.

Using Big Data to Model Time-Varying Effects for Marketing Resource (RE) Allocation

Marketing resource allocation has been a topic of intense scrutiny, yet the literature on the topic has not paid adequate attention to the fact that the effectiveness of marketing-mix elements varies over time. Despite the fact that firms collect volumes of data on their customers, existing estimation approaches do not readily lend themselves to modeling the temporal variations for big data and provide little guidance to managers in terms of their resource allocation decisions. We address this gap and argue that marketing-mix effectiveness varies with the evolution of the consumer-brand relationship and explicitly model these temporal variations using a time-varying effects model (TVEM) that accounts for self-selection of customers into receiving marketing communications and endogeneity of the number of such communications. The proposed TVEM framework handles the complexities associated with big data analytics and provides novel insights for data-driven decision making. We combine transaction data from a Fortune 500 retailer with demographic information obtained from Acxiom Corp for over a quarter million customers to test our framework. The results provide strong support for our proposed framework. Specifically, we find that the influence of marketing mailers, other transaction characteristics (coupon redemption, returns, and cross-buy), and demographic factors (age, income, household size, and interests) on sales varies significantly over the customer life cycle and ignoring such temporal variations can lead to gross misallocation of marketing investments. Specifically, our results suggest that firms can increase their revenues by over 17 percent by just reallocating their resources based on the proposed framework. To facilitate adoption of our proposed framework, we provide guidance and actionable insights for managerial relevance.

Time-varying associations between confidence and motivation to abstain from marijuana during treatment among adolescents

IntroductionAn important goal of addictions treatment is to develop a positive association between high levels of confidence and motivation to abstain from substance use. This study modeled the time-varying association between confidence and motivation to abstain from marijuana use among youth in treatment, and the time-varying effect of pre-treatment covariates (marijuana abstinence goal and perceived peer marijuana use) on motivation to abstain. Method150 adolescents (75% male, 83% White) in community-based intensive outpatient treatment in Pennsylvania completed a pre-treatment assessment of abstinence goal, perceived peer marijuana use, and motivation and confidence to abstain from marijuana. Ratings of motivation and confidence to abstain also were collected after each session. A time-varying effect model (TVEM) was used to characterize changes in the association between confidence and motivation to abstain (lagged), and included covariates representing pre-treatment abstinence goal and perceived peer marijuana use. ResultsConfidence and motivation to abstain from marijuana generally increased during treatment. The association between confidence and motivation strengthened across sessions 1–4, and was maintained through later sessions. Pre-treatment abstinence goal had an early time-limited effect (through session 6) on motivation to abstain. Pre-treatment perception of peer marijuana use had a significant effect on motivation to abstain only at session 2. ConclusionsEarly treatment sessions represent a critical period during which the association between confidence and motivation to abstain generally increased. The time-limited effects of pre-treatment characteristics suggest the importance of early sessions in addressing abstinence goal and peer substance use that may impact motivation to abstain from marijuana.

Analyzing Long-Duration and High-Frequency Data Using the Time-Varying Effect Model.

With the rapid development of methods for electronic data capture, longitudinal data sets with many assessment points have become common in mental health services and addiction research. These data typically exhibit complex and irregular patterns of change, and the relationship between variables may also change over time. Existing statistical methods are not flexible enough to capture this complexity, but a new method, the time-varying effect model (TVEM), permits modeling nearly any shape of change, and allows the effect of an independent variable on outcome to change over time. This paper introduces TVEM and illustrates its application using data from a 16-year study of 223 participants with serious mental illness and substance abuse.

A Time-Varying True Individual Effects Model with Endogenous Regressors

We propose a fairly general individual effects stochastic frontier model which allows both heterogeneity and inefficiency to change over time. Moreover, our model handles the endogeneity problems if either at least one of the regressors or one-sided error term is correlated with the two-sided error term. Our Monte Carlo experiments show that our estimator performs good. We employ our methodology to the US banking data, which supports our findings from the Monte Carlo experiments.

Modeling intensive longitudinal data with mixtures of nonparametric trajectories and time-varying effects.

Behavioral scientists increasingly collect intensive longitudinal data (ILD), in which phenomena are measured at high frequency and in real time. In many such studies, it is of interest to describe the pattern of change over time in important variables as well as the changing nature of the relationship between variables. Individuals' trajectories on variables of interest may be far from linear, and the predictive relationship between variables of interest and related covariates may also change over time in a nonlinear way. Time-varying effect models (TVEMs; see Tan, Shiyko, Li, Li, & Dierker, 2012) address these needs by allowing regression coefficients to be smooth, nonlinear functions of time rather than constants. However, it is possible that not only observed covariates but also unknown, latent variables may be related to the outcome. That is, regression coefficients may change over time and also vary for different kinds of individuals. Therefore, we describe a finite mixture version of TVEM for situations in which the population is heterogeneous and in which a single trajectory would conceal important, interindividual differences. This extended approach, MixTVEM, combines finite mixture modeling with non- or semiparametric regression modeling, to describe a complex pattern of change over time for distinct latent classes of individuals. The usefulness of the method is demonstrated in an empirical example from a smoking cessation study. We provide a versatile SAS macro and R function for fitting MixTVEMs.

Race and Justice System Attitude Formation During the Transition to Adulthood

Although attitudes towards the justice system are directly related to crime commission, few studies have examined how these attitudes develop from adolescence through early adulthood. Further, despite knowledge that minority youth experience disproportionate contact with the justice system, it is unknown how legal socialization differs by racial group. This study investigates how attitudes towards the justice system develop as youth transition into adulthood, examines how personal experiences with the justice system affect legal socialization, and determines whether developmental processes differ for Black, White, and Latino youth. Data were obtained from a 7-year longitudinal study of male offenders (N = 1114). Individual growth curve models were used to examine attitude formation from adolescence into adulthood. Time-varying effects models were used to examine how experiences with the justice system affect legal socialization. Findings indicate that Black youth hold the most negative views of the system during adolescence, followed by Latino youth, and White youth. These racial differences become more pronounced as youth transition into adulthood. Further, although legitimacy and legal cynicism follow similar developmental trajectories, personal contacts with the justice system only affect legitimacy. Legal socialization from adolescence into young adulthood varies by race. The mechanisms that affect Black youth’s attitudes do not affect Latino youths’ attitudes, indicating that aggregating racial groups may mask meaningful differences. Despite engaging in the same amount of offending as White and Latino youth, Black youth are disproportionately contacted by the system. These disproportionate justice system contacts erode their perceptions of its legitimacy.