Multivariate Growth Curve Model Research Articles

THE BEST LINEAR UNBIASED ESTIMATORS OF REGRESSION COEFFICIENTS IN A MULTIVARIATE GROWTH-CURVE MODEL. A COORDINATE-FREE APPROACH

The problems of the existence of the best linear unbiased estimators (BLUE) and of their equality to the ordinary least squares estimators (OLSE) of the expected value of the observations are treated in a coordinate-free approach using a multivariate growth-curve model. It will be proved that the alternative forms of the necessary and sufficient conditions used in solving these problems are independent of the between-individuals design matrix of the model.

Antecedents of geographical expansion: The case of federally qualified health centers.

Federally qualified health centers (FQHCs) are pivotal safety net primary care providers for the medically underserved. FQHCs have complex organizational designs, with many FQHCs providing care at multiple physical locations ("sites"). The number of sites, however, varies considerably between FQHCs, which can have important implications for differential access that may perpetuate disparities in quality of care. The objective of this study is to explore the organizational and environmental antecedents of the number of sites operated by each FQHC. The findings of this study contribute to a better understanding of FQHCs' expansion that has vital implications for cost and access outcomes. The study is based on data between the years 2012 and 2018. Using multivariate growth curve modeling, we analyzed the final sample, consisting of 5,482 FQHC-years. The level of competition, measured as the number of FQHC sites in the Primary Care Service Area (PCSA) and the number of primary care physicians per 1,000 PCSA residents, was positively associated with the number of FQHC sites. The number of patients, the level of federal grant, and the year were also positively associated with the number of FQHC sites, whereas percentage of Medicaid patients; workforce supply, measured as primary care physician assistants per 1,000 PCSA residents; Medicaid expansion; and state/local funding available for FQHCs were not. Findings of this study indicate that competition, especially between peer FQHCs, is significantly associated with FQHC expansion. This result suggests that FQHC managers and policymakers may closely monitor cost, access, and quality implications of competition and FQHC expansion.

Growth Modeling in a Diagnostic Classification Model (DCM) Framework-A Multivariate Longitudinal Diagnostic Classification Model.

A multivariate longitudinal DCM is developed that is the composite of two components, the log-linear cognitive diagnostic model (LCDM) as the measurement model component that evaluates the mastery status of attributes at each measurement occasion, and a generalized multivariate growth curve model that describes the growth of each attribute over time. The proposed model represents an improvement in the current longitudinal DCMs given its ability to incorporate both balanced and unbalanced data and to measure the growth of a single attribute directly without assuming that attributes grow in the same pattern. One simulation study was conducted to evaluate the proposed model in terms of the convergence rates, the accuracy of classification, and parameter recoveries under different combinations of four design factors: the sample size, the growth patterns, the G matrix design, and the number of measurement occasions. The results revealed the following: (1) In general, the proposed model provided good convergence rates under different conditions. (2) Regarding the classification accuracy, the proposed model achieved good recoveries on the probabilities of attribute mastery. However, the correct classification rates depended on the cut point that was used to classify individuals. For individuals who truly mastered the attributes, the correct classification rates increased as the measurement occasions increased; however, for individuals who truly did not master the attributes, the correct classification rates decreased slightly as the numbers of measurement occasions increased. Cohen's kappa increased as the number of measurement occasions increased. (3) Both the intercept and main effect parameters in the LCDM were recovered well. The interaction effect parameters had a relatively large bias under the condition with a small sample size and fewer measurement occasions; however, the recoveries were improved as the sample size and the number of measurement occasions increased. (4) Overall, the proposed model achieved acceptable recoveries on both the fixed and random effects in the generalized growth curve model.

Graphical analysis of residuals in multivariate growth curve models and applications in the analysis of longitudinal data

Statistical models often rely on several assumptions including distributional assumptions on outcome variables as well as relational assumptions representing the relationship between outcomes and independent variables. Model diagnostics is, therefore, a crucial component of any model fitting problem. Residuals play important roles in model diagnostics and checking assumptions. In multivariate models, residuals are not commonly used in practice, although approaches have been proposed to check multivariate normality and other model assumptions. When done, ordinary residuals are often used. Nevertheless, it has been shown that ordinary residuals in the analysis of longitudinal data are correlated and are not normally distributed. Under sufficiently large sample size, a transformation of residuals were previously proposed to check the normality assumption. The transformation solely focuses on removing the correlation. In this paper, we show that the ordinary residuals in the analysis of longitudinal data are not normally distributed and should not be used for checking the normality assumption. Via extensive simulations, we also show that the transformed (de-correlated) residuals fail to provide accurate model validation, in particular in the presence of model misspecification. We consider decomposed residuals from the multivariate growth curve model, provide practical interpretations, examine their property analytically as well as via simulations, and show how the different components can be used to examine model misspecification and distributional assumptions. Extensive simulations are performed to evaluate and compare performances for normal and non-normal data. Analysis of real data sets are presented as illustrations.

Retinal microvascular features and cognitive change in the Lothian-Birth Cohort 1936

IntroductionWe test whether measures of the retinal vasculature are associated with cognitive functioning and cognitive change. MethodsRetinal images from a narrow-age cohort were analyzed using Vessel Assessment and Measurement Platform for Images of the Retina, producing a comprehensive range of quantitative measurements of the retinal vasculature, at mean age 72.5 years (SD = 0.7). Cognitive ability and change were measured using a battery of multiple measures of memory, visuospatial, processing speed, and crystallized cognitive abilities at mean ages 73, 76, and 79 years. We applied multivariate growth curve models to test the association between retinal vascular measurements with cognitive abilities and their changes. ResultsAlmost all associations were nonsignificant. In our most parsimonious model, venular asymmetry factor was associated with speed at age 73. DiscussionOur null findings suggest that the quantitative retinal parameters applied in this study are not significantly associated with cognitive functioning or cognitive change.

Effects of Initiating Abstinence from Alcohol on Daily Craving and Negative Affect: Results from a Pharmacotherapy Clinical Trial.

Craving and negative affect are distressing and commonly experienced during alcohol use disorder (AUD) treatment. Patients may assume that initiating abstinence will intensify their cravings and negative affect despite limited empirical data to support this assumption. This study extends and replicates, under improved methodological conditions, previous work that found reductions in daily craving associated with initiating abstinence. Seventy-eight adults (80.8% male, 57.1% Caucasian) in a clinical trial testing prazosin for AUD provided daily reports of drinking, craving, and negative affect for up to 12weeks (mean=64.77 daily reports). Participants were classified into 3 subgroups based on whether and when they initiated 14days of continuous abstinence, including (i) "abstinence initiators" who quit drinking during treatment (n=17), (ii) "already abstainers" who were abstinent at the start of treatment (n=20), and (iii) "continued drinkers" who never initiated abstinence (n=41). The timing and degree of change in craving and negative affect were compared across these groups using multivariate growth curve modeling. All participant subgroups reported gradual reductions in craving over the course of treatment, with "abstinence initiators" reporting additional sudden reductions in craving upon initiating abstinence from alcohol. "Continued drinkers" reported higher levels of craving than "already abstainers" throughout the full course of treatment. Negative affect followed a different pattern of change, with "abstinence initiators" experiencing gradual reductions in negative affect after initiating abstinence but no changes prior to or immediately upon initiating abstinence, and with "already abstainers" and "continued drinkers" experiencing no changes in negative affect over time. Initiating abstinence is associated with immediate reductions in craving, followed by gradual reductions in both craving and negative affect. Results provide insight into the timing and magnitude of changes in theoretically and clinically important variables and may help patients anticipate when to expect improvement in craving and negative effect.

Longitudinal assessment of daily activity patterns on weight change after involuntary job loss: the ADAPT study protocol

BackgroundThe World Health Organization has identified obesity as one of the most visible and neglected public health problems worldwide. Meta-analytic studies suggest that insufficient sleep increases the risk of developing obesity and related serious medical conditions. Unfortunately, the nationwide average sleep duration has steadily declined over the last two decades with 25% of U.S. adults reporting insufficient sleep. Stress is also an important indirect factor in obesity, and chronic stress and laboratory-induced stress negatively impact sleep. Despite what we know from basic sciences about (a) stress and sleep and (b) sleep and obesity, we know very little about how these factors actually manifest in a natural environment. The Assessing Daily Activity Patterns Through Occupational Transitions (ADAPT) study tests whether sleep disruption plays a key role in the development of obesity for individuals exposed to involuntary job loss, a life event that is often stressful and disrupting to an individual’s daily routine.MethodsThis is an 18-month closed, cohort research design examining social rhythms, sleep, dietary intake, energy expenditure, waist circumference, and weight gain over 18 months in individuals who have sustained involuntary job loss. Approximately 332 participants who lost their job within the last 3 months are recruited from flyers within the Arizona Department of Economic Security (AZDES) Unemployment Insurance Administration application packets and other related postings. Multivariate growth curve modeling will be used to investigate the temporal precedence of changes in social rhythms, sleep, and weight gain.DiscussionIt is hypothesized that: (1) unemployed individuals with less consistent social rhythms and worse sleep will have steeper weight gain trajectories over 18 months than unemployed individuals with stable social rhythms and better sleep; (2) disrupted sleep will mediate the relationship between social rhythm disruption and weight gain; and (3) reemployment will be associated with a reversal in the negative trajectories outlined above. Positive findings will provide support for the development of obesity prevention campaigns targeting sleep and social rhythms in an accessible subgroup of vulnerable individuals.

Influence diagnostics for multivariate growth curve models

Research has shown that in mixed effect longitudinal models, influential observations can have a large effect on the estimates of subject-specific parameters. Furthermore, they cannot always be detected by the classical Cook’s distance due to potentially large between subject variation. Thus, influential observations should be approached by conditioning on the subjects. However, no rigorous approach has been developed for influential observation detection for multivariate longitudinal mixed models where more than one response is measured for each subject at each time point. We propose a multivariate conditional Cook’s distance for this more general situation. Examples are given to illustrate how the influential observation in one characteristic changes the effects of both characteristics.

Temperamental Anger and Effortful Control, Teacher-Child Conflict, and Externalizing Behavior Across the Elementary School Years.

This study examined teacher-child conflict as a possible mediator of the effects of temperamental anger and effortful control on subsequent externalizing behavior. Reciprocal influences between teacher-child conflict and externalizing behavior were also examined. Participants were 1,152 children (49% female; 81.6% non-Hispanic White) from the Study of Early Child Care and Youth Development. Multivariate growth curve modeling revealed that greater effortful control at age 54months indirectly predicted lower levels of, and subsequent changes in, externalizing behavior from kindergarten to Grade 6 through reduced teacher-child conflict. An alternative model, in which greater effortful control predicted lower teacher-child conflict through lower externalizing behavior, received less support. Within persons, greater-than-expected teacher-child conflict predicted greater-than-expected teacher-reported externalizing behavior concurrently and over time.

Multiple-response repeated measurement or multivariate growth curve model with distribution-free errors

ABSTRACTIn this article, we propose a new modeling approach for the multivariate growth curve model with distribution-free errors, which is a useful tool for analyzing multiple-response repeated measurements. We first use the outer product least-squares technique to directly estimate covariance and then explore the feasible generalized least-squares technique to derive the estimator of regression coefficients. Large-sample properties are investigated for these estimators. Moreover, the above estimations for covariance and regression coefficients are extended to the situation under certain null hypothesis tests and the best subset BIC is used for variable selection. A real dataset is analyzed to demonstrate the usefulness and competency of the proposed methodology for model specification (identification) and model fitting (parameter estimation) in multiple-response repeated measurements.

Predictors of ageing-related decline across multiple cognitive functions

It is critical to discover why some people's cognitive abilities age better than others'. We applied multivariate growth curve models to data from a narrow-age cohort measured on a multi-domain IQ measure at age 11years and a comprehensive battery of thirteen measures of visuospatial, memory, crystallized, and processing speed abilities at ages 70, 73, and 76years (n=1091 at age 70). We found that 48% of the variance in change in performance on the thirteen cognitive measures was shared across all measures, an additional 26% was specific to the four ability domains, and 26% was test-specific. We tested the association of a wide variety of sociodemographic, fitness, health, and genetic variables with each of these cognitive change factors. Models that simultaneously included all covariates accounted for appreciable proportions of variance in the cognitive change factors (e.g. approximately one third of the variance in general cognitive change). However, beyond physical fitness and possession of the APOE e4 allele, very few predictors were incrementally associated with cognitive change at statistically significant levels. The results highlight a small number of factors that predict differences in cognitive ageing, and underscore that correlates of cognitive level are not necessarily predictors of decline. Even larger samples will likely be required to identify additional variables with more modest associations with normal-range heterogeneity in aging-related cognitive declines.

Do Cognitive and Physical Functions Age in Concert from Age 70 to 76? Evidence from the Lothian Birth Cohort 1936.

The present study concerns the relation of mental and bodily characteristics to one another during ageing. The 'common cause' theory of ageing proposes that declines are shared across multiple, seemingly-disparate functions, including both physical and intellectual abilities. The concept of 'reserve' suggests that healthier cognitive (and perhaps bodily) functions from early in life are protective against the effects of senescence across multiple domains. In three waves of physical and cognitive testing data from the longitudinal Lothian Birth Cohort 1936 (n = 1,091 at age 70 years; n = 866 at 73; n = 697 at 76), we used multivariate growth curve modeling to test the 'common cause' and 'reserve' hypotheses. Support for both concepts was mixed: although levels of physical functions and cognitive functions were correlated with one another, physical functions did not decline together, and there was little evidence for shared declines in physical and mental functions. Early-life intelligence, a potential marker of system integrity, made a significant prediction of the levels, but not the slopes, of later life physical functions. These data suggest that common causes, which are likely present within cognitive functions, are not as far-reaching beyond the cognitive arena as has previously been suggested. They also imply that bodily reserve may be similar to cognitive reserve in that it affects the level, but not the slope, of ageing-related declines.

Shared and unique genetic and environmental influences on aging-related changes in multiple cognitive abilities.

Aging-related declines occur in many different domains of cognitive function during middle and late adulthood. However, whether a global dimension underlies individual differences in changes in different domains of cognition and whether global genetic influences on cognitive changes exist is less clear. We addressed these issues by applying multivariate growth curve models to longitudinal data from 857 individuals from the Swedish Adoption/Twin Study of Aging, who had been measured on 11 cognitive variables representative of verbal, spatial, memory, and processing speed abilities up to 5 times over up to 16 years between ages 50 and 96 years. Between ages 50 and 65 years scores on different tests changed relatively independently of one another, and there was little evidence for strong underlying dimensions of change. In contrast, over the period between 65 and 96 years of age, there were strong interrelations among rates of change both within and across domains. During this age period, variability in rates of change were, on average, 52% domain-general, 8% domain-specific, and 39% test-specific. Quantitative genetic decomposition indicated that 29% of individual differences in a global domain-general dimension of cognitive changes during this age period were attributable to genetic influences, but some domain-specific genetic influences were also evident, even after accounting for domain-general contributions. These findings are consistent with a balanced global and domain-specific account of the genetics of cognitive aging.

Risk factors for children's receptive vocabulary development from four to eight years in the longitudinal study of Australian children.

Receptive vocabulary develops rapidly in early childhood and builds the foundation for language acquisition and literacy. Variation in receptive vocabulary ability is associated with variation in children's school achievement, and low receptive vocabulary ability is a risk factor for under-achievement at school. In this study, bivariate and multivariate growth curve modelling was used to estimate trajectories of receptive vocabulary development in relation to a wide range of candidate child, maternal and family level influences on receptive vocabulary development from 4–8 years. The study sample comprised 4332 children from the first nationally representative Longitudinal Study of Australian Children (LSAC). Predictors were modeled as risk variables with the lowest level of risk as the reference category. In the multivariate model, risks for receptive vocabulary delay at 4 years, in order of magnitude, were: Maternal Non- English Speaking Background (NESB), low school readiness, child not read to at home, four or more siblings, low family income, low birthweight, low maternal education, maternal mental health distress, low maternal parenting consistency, and high child temperament reactivity. None of these risks were associated with a lower rate of growth from 4–8 years. Instead, maternal NESB, low school readiness and maternal mental health distress were associated with a higher rate of growth, although not sufficient to close the receptive vocabulary gap for children with and without these risks at 8 years. Socio-economic area disadvantage, was not a risk for low receptive vocabulary ability at 4 years but was the only risk associated with a lower rate of growth in receptive vocabulary ability. At 8 years, the gap between children with and without socio-economic area disadvantage was equivalent to eight months of receptive vocabulary growth. These results are consistent with other studies that have shown that social gradients in children's developmental outcomes increase over time.

Characterizing the Self-System over Time in Adolescence: Internal Structure and Associations with Internalizing Symptoms

The longitudinal effects among self and identity processes, and between these processes and internalizing symptoms, are not well understood. As a result, the present study was designed to ascertain the over-time effects among identity commitment, reconsideration of commitments, and self-concept clarity, as well as to map the interplay of these self and identity processes with anxiety and depressive symptoms in early adolescence. A sample of 923 Dutch adolescents (mean age 12.4 years at Time 1; 49.3% female) participated at each of five annual assessments. Multivariate growth curve and cross-lagged panel models indicated that the association between self-concept clarity and commitment was bidirectional, that reconsideration occurs based on problems or dissatisfaction with self-concept clarity and with identity commitments, and that self-concept clarity (but not commitment or reconsideration) temporally precedes depressive and anxiety symptoms. Results are discussed in terms of the structure of the self-system and its associations with internalizing symptoms.

Relations between informational sources, self-efficacy and academic achievement: a developmental approach

As a cognitive-motivational construct, self-efficacy has been researched extensively and has involved two important lines of inquiries, namely the impact of sources of information on self-efficacy and the predictive effect of self-efficacy on learning outcomes. We proposed and tested the relations between the four major sources of information (enactive performance accomplishments, vicarious experiences, verbal persuasion and emotional and physiological states), self-efficacy and academic achievement for mathematics and science within one conceptual model. Our model was tested with the conjunctive use of longitudinal data and latent growth curve modelling (LGM) procedures. Two hundred and fifty-two (110 girls, 142 boys) upper elementary school children from three government schools participated in this longitudinal study. Likert-scale inventories were administered over four occasions within a one-year period. We measured the four sources of information at T 1, whereas self-efficacy for mathematics and science was measured at T 2–T 4, and academic achievement was measured at T 4 only. SPSS AMOS v18 was used to test a number of a priori multivariate growth curve models. LGM analyses provided moderate evidence in support of our conceptual model, noting different patterns of trajectories for both mathematics and science.

Correlated longitudinal changes across linguistic, achievement, and psychomotor domains in early childhood: evidence for a global dimension of development

An important question within developmental psychology concerns the extent to which the maturational gains that children make across multiple diverse domains of functioning can be attributed to global (domain-general) developmental processes. The present study investigated this question by examining the extent to which individual differences in change across children's development in five different domains are correlated. Multivariate growth-curve models were fit to longitudinal data on linguistic, mathematics, reading, gross motor, and fine motor skills in 8950 children ranging in age from 44 to 86 months (3.7 years to 7.2 years). All five rates of change were positively intercorrelated. A common factor accounted for 42% of the individual differences in change. These results suggest that a global dimension underlies substantial proportions of cognitive and psychomotor development.

Global and domain-specific changes in cognition throughout adulthood.

Normative adult age-related decrements are well documented for many diverse forms of effortful cognitive processing. However, it is currently unclear whether each of these decrements reflects a distinct and independent developmental phenomenon, or, in part, a more global phenomenon. A number of studies have recently been published that show moderate to large magnitudes of positive relations among individual differences in rates of changes in different cognitive variables during adulthood. This suggests that a small number of common dimensions or even a single common dimension may underlie substantial proportions of individual differences in aging-related cognitive declines. This possibility was directly examined using data from 1,281 adults 18-95 years of age who were followed longitudinally over up to 7 years on 12 different measures of effortful processing. Multivariate growth curve models were applied to examine the dimensionality of individual differences in longitudinal changes. Results supported a hierarchical structure of aging-related changes, with an average of 39% of individual differences in change in a given variable attributable to global (domain-general) developmental processes, 33% attributable to domain-specific developmental processes (abstract reasoning, spatial visualization, episodic memory, and processing speed), and 28% attributable to test-specific developmental processes. Although it is often assumed that systematic and pervasive sources of cognitive decline only emerge in later adulthood, domain-general influences on change were apparent for younger (18-49 years), middle aged (50-69 years), and older (70-95 years) adults.

The longitudinal relationship between behavior and emotional disturbance in young people with intellectual disability and maternal mental health

Although elevated rates of parent psychosocial distress have been associated with child behavior and emotional problems, little is known about the nature of this relationship over time. This study followed an epidemiological cohort of children and adolescents over 11 years with 4 waves of data collection. Within this cohort, complete data were available on 238 mothers and their children. Behavior and emotional problems were assessed using the DBC, maternal mental health with the GHQ. Multivariate growth curve modelling was used to evaluate the commonality of individual change patterns. High levels of mental health problems were reported, which were stable over time. Higher scores on the DBC were associated with higher rates of mental health problems. Increases in child social relating problems were associated with increases mental health symptoms, particularly depression and anxiety.

A novel trace test for the mean parameters in a multivariate growth curve model

A trace test for the mean parameters of the growth curve model is proposed. It is constructed using the restricted maximum likelihood followed by an estimated likelihood ratio approach. The statistic reduces to the Lawley–Hotelling trace test for the Multivariate Analysis of Variance (MANOVA) models. Our test statistic is, therefore, a natural extension of the classical trace test to GMANOVA models. We show that the distribution of the test under the null hypothesis does not depend on the unknown covariance matrix Σ . We also show that the distributions under the null and alternative hypotheses can be represented as sums of weighted central and non-central chi-square random variables, respectively. Under the null hypothesis, the Satterthwaite approximation is used to get an approximate critical point. A novel Satterthwaite type approximation is proposed to obtain an approximate power. A simulation study is performed to evaluate the performance of our proposed test and numerical examples are provided as illustrations.