A Linear-Linear Growth Model with Individual Change Point and its Application to ECLS-K Data

The latent growth curve model with piecewise functions is a useful analytics tool to investigate the growth trajectory consisted of distinct phases of development in observed variables. An interesting feature of the growth trajectory is the time point that the trajectory changes from one phase to another one. In this thesis, we propose a simple computational pipeline to locate the change point under the linear-linear piecewise model and apply it to the longitudinal study of reading and math ability in early childhood (from kindergarten to eighth grade). In the first step, we conduct the hypothesis testing to filter out the samples that do not exhibit a change point. For samples with significant change point, we use the maximum likelihood estimation(MLE) to determine the location of a change point. However, a small portion of samples contains abnormal observations, which makes the MLE method fail to identify the change point. To overcome this difficulty, we apply a Bayesian approach to locate the change point for these samples. By comparison of the change point distributions in math and reading, as well as students with different overall performance, we conclude that: (a) most students have change points between Spring-first grade and Spring-third grade; (b) students with overall better performance have change point at earlier stage; (c) compared with math, the change point distribution for reading is more concentrated between Spring-first grade and Spring-third grade

Witnessing Community Violence and its Consequences: Changes Across Middle School

Community violence exposure is prevalent among youth residing in economically marginalized communities that have high rates of violence. Witnessing community violence has been concurrently associated with persistent adverse consequences. However, few studies have applied a developmental psychopathology framework and examined dynamic developmental processes between witnessing community violence and outcomes over time. Moreover, most prior studies have used analyses that assume that associations between witnessing violence and outcomes are the same for all adolescents, which is inconsistent with both developmental theories and theories specific to community violence exposure. The goal of this study was to apply a developmental psychopathological framework to (a) examine heterogeneity in changes in witnessing community violence across middle school, and (b) examine their associations with distress symptoms and aggression. I used three analyses that made different assumptions about the heterogeneity and functional form of change within a subgroup of adolescents residing in an economically marginalized community with high rates of violence. Participants were 1,323 youth (54.3% female, 17.5% Latine, 88.3% African American/Black) attending middle schools in neighborhoods with high percentages of residents below the federal poverty line and high rates of violence. I used latent curve models to identify trajectories of witnessing community violence, distress symptoms, and physical aggression for the overall sample. For witnessing community violence, a piecewise model fit the data best and indicated that witnessing community violence decreased across middle school with the steepest decrease during the 6th grade. Additionally, there were significant drops in witnessing violence during the summer. For distress symptoms, a quadratic model fit the data best such that symptoms decreased across middle school and the rate of change decreased (i.e., decelerated) over time. For aggression, a piecewise model fit the data best and indicated that the frequency of physical aggression was stable during each school year and decreased significantly during the summer. Results of a growth mixture model (GMM) analysis using the parameters of the witnessing violence trajectory as latent class indicators suggested that there was heterogeneity in trajectories of witnessing violence that could be modeled by three distinct subgroups. Latent profile analysis, which allowed the functional form of change in witnessing violence to vary over time by examining patterns in frequency, produced similar subgroups to the GMM. Thus, the GMM, which constrained the functional form to be the same across subgroups and allowed within-group variability in parameters, was further evaluated for subgroup differences in distress symptoms and physical aggression. Overall, frequencies of witnessing violence differed across subgroups, and subgroups with higher overall frequencies had greater decreases (i.e., slopes) in witnessing over time. The subgroups also differed in their overall levels of distress and aggression, but not in their rates of change (i.e., slopes) in these constructs. A rarely witnessing subgroup (22%) had the lowest levels of distress symptoms and frequencies of aggression across middle school. The frequent witnessing subgroup (33%) had the highest levels of distress symptoms and frequencies of physical aggression across middle school. Additionally, this subgroup had the largest decreases in witnessing violence and physical aggression frequencies during the summer. Finally, the moderate witnessing subgroup (45%) consistently reported levels of distress symptoms and frequency of physical aggression in between those reported by the other two subgroups. These findings suggest that there is heterogeneity in adolescents’ experiences of witnessing community violence exposure across time that can be modeled with the same functional form. These findings have implications for interventions and highlight the importance of early intervention

Dynamic Relations Within and Between Early Communication Proficiencies and Key Skill Elements' Growth Trajectories of Infants and Toddlers

Preliteracy experiences inform language learning outcomes in early childhood, of which proficiency in expressive communication is requisite to children’s cognitive and social development. Identification of communication and language delays must be made as early as possible to inform appropriate intervention services targeting prevention of childhood disabilities. The Early Communication Indicator (ECI)—designed to monitor individual progress through brief repeated measurement of early expressive communication—is one of a growing class of general outcome measures emerging in early education and early childhood special education. Comparable to K–12 curriculum–based measures, the ECI is a resource for accountability as well as response to intervention (RTI) efforts. Current implementation applies differential scaling of four key skill elements into a total communication indicator sensitive to increasing proficiency over time. The literature describing observed developmental trajectories of the constituent key skill elements of the total communication indicator provides theoretical and empirical bases for establishing their utility for earlier identification of language delays among infants and toddlers and informing sensitive ages for targeted intervention. The present study applied latent growth curve modeling (LGCM) in order to examine predictive relations within and between ECI key skill elements’ proficiencies and growth, extending previous research limited to the study of early expressive communication development measured by the total communication indicator. Findings support the hypothesis that dynamic relations exist within and between ECI proficiencies and key skill elements’ growth trajectories that may inform benchmarks and decision making related to early intervention in the development of symbolic communication and language. Future directions are discussed

Anxiety and Depression During Childhood and Adolescence: Testing Theoretical Models of Continuity and Discontinuity

The present study sought to clarify the trajectory (i.e., continuous vs. discontinuous) and expression (i.e., homotypic vs. heterotypic) of anxiety and depressive symptoms across childhood and adolescence. We utilized a state-of-the-science analytic approach to simultaneously test theoretical models that describe the development of internalizing symptoms in youth. In a sample of 636 children (53% female; M age = 7.04; SD age = 0.35) self-report measures of anxiety and depression were completed annually by youth through their freshman year of high school. For both anxiety and depression, a piecewise growth curve model provided the best fit for the data, with symptoms decreasing until age 12 (the “developmental knot”) and then increasing into early adolescence. The trajectory of anxiety symptoms was best described by a discontinuous homotypic pattern in which childhood anxiety predicted adolescent anxiety. For depression, two distinct pathways were discovered: A discontinuous homotypic pathway in which childhood depression predicted adolescent depression and a discontinuous heterotypic pathway in which childhood anxiety predicted adolescent depression. Analytical, methodological, and clinical implications of these findings are discussed

Substance use and exercise participation among young adults: parallel trajectories in a national cohort‐sequential study

Aims  This study examined the extent to which the trajectory of participation in sports, athletics or exercising (PSAE) covaried with substance use in early adulthood controlling for team sports participation using parallel process latent growth curve modeling. Design, setting and participants  Analysis of data collected from a series of panel studies using a cohort‐sequential design. Specifically, the analyses used longitudinal data from 11 741 individuals from the graduating classes of 1986–2001, first surveyed as seniors in American high schools. Up to four additional follow‐up surveys were administered to age 26 years. Data were collected using in‐school and mailed self‐administered questionnaires. Measurements  Level of PSAE, past‐30‐day alcohol, cigarette and marijuana use frequency and any past‐30‐day use of illicit drugs other than marijuana (IOTM) were the main processes of interest. Self‐reported race/ethnicity, college status at age 19/20 years, parental education, gender and team sports participation during high school were included as covariates. Findings  Results indicate that higher initial levels of PSAE related to lower initial substance use prevalence rates other than alcohol, and lower initial prevalence rates of substance use then corresponded with lower substance use rates throughout early adulthood. Further, as individuals increased PSAE levels throughout early adulthood, the frequency of their use of cigarettes, marijuana and IOTM correspondingly decreased. Conclusions  Increased participation in sports, athletics or exercising (PSAE) is related to significantly lower substance use frequency at modal age 18 and through significantly and negatively correlated growth trajectories through early adulthood. Encouraging PSAE among adolescents and early adults may relate to lower substance use levels throughout early adulthood.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86876/1/j.1360-0443.2011.03489.x.pd

Applying Bayesian Growth Modeling In Machine Learning For Longitudinal Data

There has been increasing interest in the use of Bayesian growth modeling in machine learning environment to answer the questions relating to the patterns of change in trends of social and human behavior in longitudinal data. It is well understood that machine learning works properly with “big data,” because large sample sizes offer machines the better opportunity to “learn” the pattern/structure of data from a training data set to predict the performance in an unseen testing data set. Unfortunately, not all researchers have access to large samples and there is a lack of methodological research addressing the utility of using machine learning with longitudinal data based on small sample size. Additionally, there is limited methodological research conducted around moderation effect that priors have on other data conditions. Therefore, the purpose of the current study was to understand: (a) the interactive relationship between priors and sample sizes in longitudinal predictive modeling, (b) the interactive relationship between priors and number of waves of data, and (c) the interactive relationship between priors and the proportion of cases in the two levels of a dichotomous time-invariant predictor for Bayesian growth modeling in a machine learning environment. Monte Carlo simulation was adopted to answer assess the above aspects and data were generated based on alumni donation data from a university in the mid-Atlantic region where model parameters were set to mimic “real life” data as closely as possible. Results from the study show that although all main and interaction effects are statistically significant, only main effect of sample size, wave of data, and interaction between waves of data and sample sizes show meaningful effect size. Additionally, given the condition of prior of the study, informative priors did not show any higher prediction accuracy compared to non-informative priors. The reason behind indifferent between choices of informative and non-informative prior associated with model complexity, competition between strong informative and weakly informative prior. This study was one of the first known study to examine Bayesian estimation in the context of machine learning. Results of the current study suggest that capitalizing on the advantages offered jointly by these two modeling approaches shows promise. Although much is still unknown and in need of investigation regarding the conditions under which a combination of Bayesian modeling and machine learning affects prediction accuracy, the current dissertation provides a first step in that direction

ESTIMATING UNKNOWN KNOTS IN PIECEWISE LINEAR-LINEAR LATENT GROWTH MIXTURE MODELS

A piecewise linear-linear latent growth mixture model (LGMM) combines features of a piecewise linear-linear latent growth curve (LGC) model with the ideas of latent class methods all within a structural equation modeling (SEM) context. A piecewise linear-linear LGMM is an appropriate framework for analyzing longitudinal data that come from a mixture of two or more subpopulations (i.e., latent classes) where each latent class incorporates a separate growth trajectory corresponding to multiple growth phases from which repeated measurements arise. The benefit of the model is that it allows the specification of each growth phase to conform to a particular form of overall change process within each latent class thereby making these models flexible and useful for substantive researchers. There are two main objectives of this current study. The first objective is to demonstrate how the parameters of a piecewise linear-linear LGMM, including the unknown knot, can be estimated using standard SEM software. A series of Monte Carlo simulations empirically investigated the ability of piecewise linear-linear LGMMs to recover true (known) growth parameters of distinct populations. Specifically, the current research compared the performance of the piecewise linear-linear LGMM under different manipulated conditions of 1) sample size, 2) class mixing proportions, 3) class separation of location of knot, 4) the mean of the slope growth factor of the second phase, 5) the variance of the slope growth factor of the second phase, and 6) residual variance of the observed variables. The second objective is to address the issue of model mis-specification. It is important to analyze this issue because applied researchers have to make model selection decisions. Therefore, the current research examined the possibility of extracting spurious latent classes. To achieve this objective 1-, 2-, and 3-class piecewise linear-linear LGMMs were fit to data sets generated under different manipulated conditions using a 2-class piecewise linear-linear LGMM as a population model. The number of times the correct model (i.e., 2-class piecewise linear-linear LGMM) was preferred over incorrect models (i.e., 1- and 3-class piecewise linear-linear LGMMs) using the Bayesian Information Criterion (BIC) was examined. Results suggested that the recovery of model parameters, specifically, the variances of growth factors were generally poor. In addition, none of the manipulated conditions were systematically related to the outcome measures, parameter bias and variability index of parameter bias. Furthermore, among all the manipulated conditions, the residual variance of observed variable had the strongest statistically significant effect on both the model convergence rate and the model selection rate. Other manipulated conditions that had an impact on the model convergence rate and/or the model selection rate were the growth factor mean of slope of the second phase, the growth factor variance of slope of the second phase, and the class mixing proportion. The manipulated conditions whose levels had no influence on either the model convergence rate or the model selection rate were sample size and the class separation of location of knot

Pathways from maternal depression to young adult offspring depression: an exploratory longitudinal mediation analysis.

Maternal depression in the peri-natal period is associated with increased risk for young adult depression in offspring. This study explored mediation of these links via trajectories of child conduct and emotional problems (Strengths and Difficulties Questionnaire) from ages 4-16 years old in data from the Avon Longitudinal Study of Parents and Children cohort (n = 13373). Through gender-specific structural equation models, a composite measure of exposure to early maternal depression (Edinburgh Postnatal Depression Scale), predicted young adult depression at age 18 (Revised Clinical Interview Schedule - distal outcome). Mediational effects were then estimated by testing which parts of joint piecewise latent trajectory models for child/adolescent conduct and emotional problems were associated with both exposure and distal outcome. For girls, only conduct problems in early childhood were consistently indicated to mediate effects of early maternal depression on risk of young adulthood depression. Some evidence for a pathway via changing levels of childhood and adolescent emotional difficulties was also suggested. For boys, by contrast, the differing models gave less consistent findings providing some evidence for a small time-specific indirect effect via early childhood conduct problems. In addition to its practice implications the current methodological application offers considerable potential in exploratory longitudinal developmental mediation studies. © 2016 The Authors International Journal of Methods in Psychiatric Research Published by John Wiley & Sons Ltd

Modelling vocabulary development among multilingual children prior to and following the transition to school entry

Differences between monolingual and multilingual vocabulary development have been observed but few studies provide a longitudinal perspective on vocabulary development before and following school entry. This study compares vocabulary growth profiles of 106 multilingual children to 211 monolingual peers before and after school entry to examine whether: (1) school entry coincides with different rates of vocabulary growth compared to prior to school entry, (2) compared to monolingual peers, multilingual children show different vocabulary sizes or rates of vocabulary growth, (3) the age of onset of second-language acquisition for multilingual children is associated with vocabulary size or rate of vocabulary growth, and (4) the sociolinguistic context of the languages spoken by multilingual children is associated with vocabulary size or rate of vocabulary growth. Results showed increases in vocabulary size across time for all children, with a steeper increase prior to school entry. A significant difference between monolingual and multilingual children who speak a minority language was observed with regards to vocabulary size at school entry and vocabulary growth prior to school entry, but growth rate differences were no longer present following school entry. Taken together, results suggest that which languages children speak may matter more than being multilingual per se