Linear Latent Growth Curve Research Articles

Longitudinal Changes in the Parenting Stress of Mothers of Children with Cerebral Palsy and Their Relationship with Children's Gross Motor Function System Levels.

Stress caused by children with disabilities harms the growth and development of children and their families. The present study aimed to investigate whether parenting stress of mothers of children with cerebral palsy changes and the relationship between children's gross motor function level and changes in parenting stress. Data were collected from 162 children with cerebral palsy and their mothers over a 2-year period at three time points. Gross motor function and parenting stress were assessed using the Gross Motor Function Classification System and the Korean version of the Parenting Stress Index-Short Form. Linear latent growth curve models of Wave 2 and Wave 3 variation in parenting stress were constructed. The relationship between Gross Motor Function Classification System level and parenting stress was evaluated via latent growth modeling. The results showed that the linear variation models reflected the time evolution of parenting stress. There were individual differences in parenting stress at the initial level and no individual differences in changes in parenting stress. The relationship between the initial level and the change rate of parenting stress was not significant. Higher initial values of the Gross Motor Function Classification System level were associated with higher initial values of parenting stress, but not related to a change in parenting stress. The results showed that parenting stress of mothers with children with cerebral palsy decreased over time and that Gross Motor Function Classification System level was related to parenting stress level. Based on these findings, directions for further research are put forth.

The development of early scientific literacy gaps in kindergarten children

ABSTRACT In times of climate change, worldwide diseases, and the question of sustainable energy, scientific literacy has never been more important. The acquisition of scientific literacy starts in early childhood and depends on children’s experiences in learning environments such as the parental home and kindergarten. The Starting Cohort 2 of the German National Educational Panel Study offers longitudinal data on the scientific literacy of 2,937 children from kindergarten to the third grade of primary school. We used linear latent growth curve models to analyse the data. The results show that the scientific literacy of kindergarten children grew over time and that kindergarten children already differed in their scientific literacy. Especially children from non-German-speaking homes or whose parents had lower levels of education or who came from homes with low cultural capital had a significantly lower level of scientific literacy in kindergarten. A scientific focus in kindergarten, on the other hand, had a positive effect on the scientific literacy of kindergarten children. Moreover, our study did not reveal any interindividual differences in the growth of scientific literacy over time. Thus, our study did not find any evidence to indicate that school had closed the initial gap in children’s scientific literacy.

Age of Migration and Cognitive Function Among Older Latinos in the United States.

Age of migration has been shown to have a robust association with Latino immigrant health outcomes; however, the relationship between timing of migration and cognition is less understood. To examine associations between race/ethnicity, nativity, age of migration, and cognitive aging among US-born (USB) non-Latino Whites (NLW) and USB and foreign-born Latinos 50 years and older. We used longitudinal biennial data from the Health and Retirement Study (HRS; 2006-2014) to fit generalized linear and linear latent growth curve models for: 1) global cognition (Modified Telephone Interview for Cognitive Status; TICS-M); 2) memory and attention subdomains of TICS-M; and 3) cognitive dysfunction. We also tested for sex modifications. In age and sex adjusted models, all Latino subgroups, independent of nativity and age of migration, had lower global and domain-specific cognitive scores and higher propensity of cognitive impairment classification compared to USB-NLWs. Differences between USB Latinos, but not other Latino subgroups, and USB-NLWs remained after full covariate adjustment. Latinas, independent of nativity or age of migration, had poorer cognitive scores relative to NLW females. Differences between all Latinos and USB-NLWs were principally expressed at baseline. Racial/ethnic, nativity, and age of migration grouping was not associated with slope (nor explained variance) of cognitive decline. Older US-born Latinos, regardless of sex exhibit poorer cognitive function than older USB-NLWs and foreign-born Latinos. Social determinants that differentially affect cognitive function, particularly those that compensate for education and sex differences among US-born Latinos and foreign-born Latinos, require further exploration.

Optimal planned missing data design for linear latent growth curve models

Longitudinal data collection is a time-consuming and cost-intensive part of developmental research. Wu et al. (2016) discussed planned missing (PM) designs that are similar in efficiency to complete designs but require fewer observations per person. The authors reported optimal PM designs for linear latent growth curve models based on extensive Monte Carlo simulations. They called for further formal investigation of the question as to how much the proposed PM mechanisms influence study design efficiency to arrive at a better understanding of PM designs. Here, we propose an approximate solution to the design problem by comparing the asymptotic effective errors of PM designs. Effective error was previously used to find optimal longitudinal study designs for complete data designs; here, we extend the approach to planned missing designs. We show how effective error is a metric for comparing the efficiency of study designs with both planned and unplanned missing data, and how earlier simulation-based results for PM designs can be explained by an asymptotic solution. Our approach is computationally more efficient than Wu et al.’s approach and leads to a better understanding of how various design factors, such as the number of measurement occasions, their temporal arrangement, attrition rates, and PM design patterns interact and how they conjointly determine design efficiency. We provide R scripts to calculate effective errors in various scenarios of PM designs.

How do educational reforms change the share of students in special education? Trends in special education in Finland

Recent European and global trends in education have been to promote inclusive education and expand education, resulting in the increased provision of special education. In promoting inclusive education, recent special education reforms have also aimed to curtail the rise in identification rates for students in special education, for example, by focusing more on early support and discontinuing fiscal incentives to identify students with special educational needs. Using official special education statistics, we studied how Finland’s special education system reforms changed the share of students in special education. In addition, we examined variations in special education provisions among municipalities before and after the reforms, and identified municipal-level predictors of variations. This study utilised piecewise linear latent growth curve modelling to analyse changes, thereby providing an example of how this method can be applied in policy reform studies. The results indicated, in particular, that the funding reform has incentivised municipalities to decrease identification rates for students in special education and to diminish special education provision. However, different municipalities have different special education provisions and have changed these provisions in varied ways. In particular, we found that small and large municipalities differ in special education practices and reform implementation.

Sequential treatment of ADHD in mother and child (AIMAC study): importance of the treatment phases for intervention success in a randomized trial

BackgroundThe efficacy of parent-child training (PCT) regarding child symptoms may be reduced if the mother has attention-deficit/hyperactivity disorder (ADHD). The AIMAC study (ADHD in Mothers and Children) aimed to compensate for the deteriorating effect of parental psychopathology by treating the mother (Step 1) before the beginning of PCT (Step 2). This secondary analysis was particularly concerned with the additional effect of the Step 2 PCT on child symptoms after the Step 1 treatment.MethodsThe analysis included 143 mothers and children (aged 6–12 years) both diagnosed with ADHD. The study design was a two-stage, two-arm parallel group trial (Step 1 treatment group [TG]: intensive treatment of the mother including psychotherapy and pharmacotherapy; Step 1 control group [CG]: supportive counseling only for mother; Step 2 TG and CG: PCT). Single- and multi-group analyses with piecewise linear latent growth curve models were applied to test for the effects of group and phase. Child symptoms (e.g., ADHD symptoms, disruptive behavior) were rated by three informants (blinded clinician, mother, teacher).ResultsChildren in the TG showed a stronger improvement of their disruptive behavior as rated by mothers than those in the CG during Step 1 (Step 1: TG vs. CG). In the CG, according to reports of the blinded clinician and the mother, the reduction of children’s disruptive behavior was stronger during Step 2 than during Step 1 (CG: Step 1 vs. Step 2). In the TG, improvement of child outcome did not differ across treatment steps (TG: Step 1 vs. Step 2).ConclusionsIntensive treatment of the mother including pharmacotherapy and psychotherapy may have small positive effects on the child’s disruptive behavior. PCT may be a valid treatment option for children with ADHD regarding disruptive behavior, even if mothers are not intensively treated beforehand.Trial registrationISRCTN registry ISRCTN73911400. Registered 29 March 2007.

Development of hot and cool executive functions in middle childhood: Three-year growth curves of decision making and working memory updating

Although middle childhood is an important period for the development of hot and cool executive functions (EFs), longitudinal studies investigating trajectories of childhood EF development are still limited and little is known about predictors for individual developmental trajectories. The current study examined the development of two typical facets of cool and hot EFs over a 3-year period during middle childhood, comparing a younger cohort (6- and 7-year-olds at the first wave [T1]; n = 621) and an older cohort (8- and 9-year-olds at T1; n = 975) of children. “Cool” working memory updating (WM) was assessed using a backward digit span task, and “hot” decision making (DM) was assessed using a child variant of the Iowa Gambling Task. Linear latent growth curve analyses revealed evidence for developmental growth as well as interindividual variance in the initial level and rate of change in both EF facets. Initial level of WM was positively associated with age (both between and within cohorts), socioeconomic status, verbal ability, and processing speed, whereas initial levels of DM were, in addition to a (potentially age-related) cohort effect, exclusively predicted by gender, with boys outperforming girls. None of the variables predicted the rate of change, that is, the developmental trajectories. However, younger children, as compared with older children, had slightly steeper WM growth curves over time, hinting at a leveling off in the development of WM during middle childhood. In sum, these data add important evidence to the understanding of hot and cool EF development during middle childhood.

Like a bridge over troubled water? A longitudinal study of general social support, colleague support, and leader support as recovery factors after a traumatic event

ABSTRACTBackground: Whereas the association between social support and psychological distress has been well-established through both cross-sectional and longitudinal studies, less is known about whether social support influences rate of change in psychological distress over time. Nor is it clear whether social support predicts baseline psychological distress, or, more importantly, whether social support may contribute to more rapid recovery following trauma exposure.Objective: This study aimed to determine the extent to which social support contributed to the recovery process among individuals with psychological distress after being exposed to trauma.Methods: Prospective survey data from ministry employees were collected 10, 22, and 34 months after the 2011 Oslo bombing that targeted the governmental quarters. We explored recovery in a clinical subsample (N = 238) of individuals with elevated levels of psychological distress (defined as mean 10-item Hopkins symptom checklist score > 1.85) one year after the event. A linear latent growth curve of psychological distress with general social support from friends and family, colleague support, and leader support as predictors was examined.Results: High levels of general social support and leader support were independently associated with a more rapid decline in psychological distress over time.Conclusions: General social support, as well as support from a leader in one’s working life, may facilitate recovery from psychological distress after exposure to a traumatic event. Enhancing social support from family and friends, as well as in work settings, may benefit those with psychological distress following a traumatic workplace event.

Regime Switching Modeling of Substance Use: Time-Varying and Second-Order Markov Models and Individual Probability Plots

A linear latent growth curve mixture model with regime switching is extended in 2 ways. Previously, the matrix of first-order Markov switching probabilities was specified to be time-invariant, regardless of the pair of occasions being considered. The first extension, time-varying transitions, specifies different Markov transition matrices between each pair of occasions. The second extension is second-order time-invariant Markov transition probabilities, such that the probability of switching depends on the states at the 2 previous occasions. The models are implemented using the R package OpenMx, which facilitates data handling, parallel computation, and further model development. It also enables the extraction and display of relative likelihoods for every individual in the sample. The models are illustrated with previously published data on alcohol use observed on 4 occasions as part of the National Longitudinal Survey of Youth, and demonstrate improved fit to the data.

LIFESPAN: A tool for the computer-aided design of longitudinal studies.

Researchers planning a longitudinal study typically search, more or less informally, a multivariate space of possible study designs that include dimensions such as the hypothesized true variance in change, indicator reliability, the number and spacing of measurement occasions, total study time, and sample size. The main search goal is to select a research design that best addresses the guiding questions and hypotheses of the planned study while heeding applicable external conditions and constraints, including time, money, feasibility, and ethical considerations. Because longitudinal study selection ultimately requires optimization under constraints, it is amenable to the general operating principles of optimization in computer-aided design. Based on power equivalence theory (MacCallum et al., 2010; von Oertzen, 2010), we propose a computational framework to promote more systematic searches within the study design space. Starting with an initial design, the proposed framework generates a set of alternative models with equal statistical power to detect hypothesized effects, and delineates trade-off relations among relevant parameters, such as total study time and the number of measurement occasions. We present LIFESPAN (Longitudinal Interactive Front End Study Planner), which implements this framework. LIFESPAN boosts the efficiency, breadth, and precision of the search for optimal longitudinal designs. Its initial version, which is freely available at http://www.brandmaier.de/lifespan, is geared toward the power to detect variance in change as specified in a linear latent growth curve model.

A longitudinal twin study of physical aggression during early childhood: evidence for a developmentally dynamic genome

Physical aggression (PA) tends to have its onset in infancy and to increase rapidly in frequency. Very little is known about the genetic and environmental etiology of PA development during early childhood. We investigated the temporal pattern of genetic and environmental etiology of PA during this crucial developmental period. Participants were 667 twin pairs, including 254 monozygotic and 413 dizygotic pairs, from the ongoing longitudinal Quebec Newborn Twin Study. Maternal reports of PA were obtained from three waves of data at 20, 32 and 50 months. These reports were analysed using a biometric Cholesky decomposition and linear latent growth curve model. The best-fitting Cholesky model revealed developmentally dynamic effects, mostly genetic attenuation and innovation. The contribution of genetic factors at 20 months substantially decreased over time, while new genetic effects appeared later on. The linear latent growth curve model revealed a significant moderate increase in PA from 20 to 50 months. Two separate sets of uncorrelated genetic factors accounted for the variation in initial level and growth rate. Non-shared and shared environments had no effect on the stability, initial status and growth rate in PA. Genetic factors underlie PA frequency and stability during early childhood; they are also responsible for initial status and growth rate in PA. The contribution of shared environment is modest, and perhaps limited, as it appears only at 50 months. Future research should investigate the complex nature of these dynamic genetic factors through genetic-environment correlation (r GE) and interaction (G×E) analyses.

Some Trends in the Prestige of U.S. Ph.D. Programs in Sociology, 1976–2011

The prestige ranks of 110 U.S. Ph.D. programs in Sociology are examined at seven times between 1976 and 2011. Linear latent growth curve models are fitted to test differences between public and private institutions, institutions located in the four major census regions, and between three historically strong communities (the Ivy League, Big-10, and Pac-10) and others. The relative prestige ranks display considerable stability, totaling 90 % of the variance between, and 10 % of the variance within programs. Differences between the three historically high-prestige communities and others are more important than geographic or public/private distinctions. The Big-10 institutions have declined markedly in relative prestige, as has the mean prestige rank of institutions in the Midwest generally. Ivy and other Eastern schools have gained modestly; Western, but not Pac-10, schools have also gained, while schools in the South are little changed. Overall, public institutions have shown gains relative to private during the period.

The Interplay Between Interpersonal Stress and Psychological Intimate Partner Violence Over Time for Young At-Risk Couples

The substantial number of young people in romantic relationships that involve intimate partner violence, a situation deleterious to physical and mental health, has resulted in increased attention to understanding the links between risk factors and course of violence. The current study examined couples' interpersonal stress related to not liking partners' friends and not getting along with parents as contextual factors associated with couples' psychological partner violence and determined whether and when couples' friend and parent stress increased the likelihood of couples' psychological partner violence. A linear latent growth curve modeling approach was used with multiwave measures of psychological partner violence, friend stress, parent stress, and relationship satisfaction obtained from 196 men at risk for delinquency and their women partners over a 12-year period. At the initial assessment, on average, the men were age 21.5 years and the women were age 21 years. Findings indicated that couples experiencing high levels of friend and parent stress were more likely to engage in high levels of psychological partner violence and that increases in couples' friend stress predicted increases in couples' partner violence over time, even when accounting for the couples' relationship satisfaction, marital status, children in the home, and financial strain. Interactive effects were at play when the couples were in their early 20s, with couples being most at risk for increases in psychological partner violence if they experienced both high friend stress and low relationship satisfaction. Couples' friend stress had the greatest effect on psychological partner violence when the couples were in their early to mid 20s when levels of friend stress were high. As the couples reached their 30s, low relationship satisfaction became the leading predictor of couples' psychological partner violence.

The effect of multiple indicators on the power to detect inter‐individual differences in change

Hertzog et al. evaluated the statistical power of linear latent growth curve models (LGCMs) to detect individual differences in change, i.e., variances of latent slopes, as a function of sample size, number of longitudinal measurement occasions, and growth curve reliability. We extend this work by investigating the effect of the number of indicators per measurement occasion on power. We analytically demonstrate that the positive effect of multiple indicators on statistical power is inversely related to the relative magnitude of occasion-specific latent residual variance and is independent of the specific model that constitutes the observed variables, in particular of other parameters in the LGCM. When designing a study, researchers have to consider trade-offs of costs and benefits of different design features. We demonstrate how knowledge about power equivalent transformations between indicator measurement designs allows researchers to identify the most cost-efficient research design for detecting parameters of interest. Finally, we integrate different formal results to exhibit the trade-off between the number of measurement occasions and number of indicators per occasion for constant power in LGCMs.

Regime Switching in the Latent Growth Curve Mixture Model

A linear latent growth curve mixture model is presented which includes switching between growth curves. Switching is accommodated by means of a Markov transition model. The model is formulated with switching as a highly constrained multivariate mixture model and is fitted using the freely available Mx program. The model is illustrated by analyzing data from the National Longitudinal Survey of Youth (NLSY97). The data concern alcohol use in a sample of 737 White youths who were assessed on 4 occasions.

Multilevel models for censored and latent responses.

Multilevel models were originally developed to allow linear regression or ANOVA models to be applied to observations that are not mutually independent. This lack of independence commonly arises due to clustering of the units of observations into 'higher level units' such as patients in hospitals. In linear mixed models, the within-cluster correlations are modelled by including random effects in a linear model. In this paper, we discuss generalizations of linear mixed models suitable for responses subject to systematic and random measurement error and interval censoring. The first example uses data from two cross-sectional surveys of schoolchildren to investigate risk factors for early first experimentation with cigarettes. Here the recalled times of the children's first cigarette are likely to be subject to both systematic and random measurement errors as well as being interval censored. We describe multilevel models for interval censored survival times as special cases of generalized linear mixed models and discuss methods of estimating systematic recall bias. The second example is a longitudinal study of mental health problems of patients nested in clinics. Here the outcome is measured by multiple questionnaires allowing the measurement errors to be modelled within a linear latent growth curve model. The resulting model is a multilevel structural equation model. We briefly discuss such models both as extensions of linear mixed models and as extensions of structural equation models. Several different model structures are examined. An important goal of the paper is to place a number of methods that readers may have considered as being distinct within a single overall modelling framework.

A Structural Modeling Approach to a Multilevel Random Coefficients Model

A method for estimating the random coefficients model using covariance structure modeling is presented. This method allows one to estimate both fixed and random effects. A way of translating the general linear mixed model into a structural equation modeling (SEM) format is presented. In particular, a LISREL setup for the multiple group linear latent growth curve model is illustrated with suggestions on ways to parameterize more complex models. To illustrate the procedure, we apply the method to both simulated and real data. The method is shown to recover the simulated parameter values. Results and interpretation for the Belsky and Rovine (1990) marriage data are presented. Other applications of the more general model are suggested.