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This study aimed to estimate the growth parameters of Muscovy ducks. The superiority of the study offers insightful information on the Muscovy duck growth curve, makes quantitative comparisons easier, allows for predictive capacities, and quickly finds problems. A total of 40 Muscovy ducks called “Rambon” were used in the study, consisting of 12 males and 28 females. Body weight was weighed periodically every two days from the day-old ducks (DOD) until 60 days of age. The data was analyzed by using Gompertz and Logistic models. The growth curves were analyzed, and parameters such as adult body weight (A), integral constant (B), and growth rate (K) were determined. Inflection points were also identified. Body weight (Wi) and age at the inflection (Ai) point using Gompertz were 1060.95 g and 46.34 d; 613.41 g and 30.52 d; 712.56 g and 36.81 d, respectively for males, females, and the unsexed. By using Logistic model, the Wi and Ai for males were 934.60 g and 41.46 d, females were 670.52 g and 32.96 d, and unsexed were 739.11 g and 36.56 d. Results showed that the Gompertz model generally outperformed the Logistic model, with lower AIC, BIC, MSE values and slightly higher R2 for all sex groups, indicating superior fit and predictive accuracy. These findings offer valuable insights into Rambon Muscovy duck growth dynamics, aiding in breeding and production strategies to enhance economic efficiency and sustainability. Farmers can utilize these models to optimize feeding schedules and make informed decisions about slaughtering, ultimately improving Muscovy duck production.

Children’s mental health symptoms’ development can be characterized by both continuity and discontinuity. However, existing studies ignore the potential discontinuity in children’s internalizing symptoms’ development. Hence, the current study examines continuous and discontinuous developmental trajectories using representative data from a sample of 2792 children (49.10% females) from the Growing Up in Australia cohort assessed seven times (ages 4, 6, 8, 10, 12, 14, 16). Longitudinal measurement invariance analyses revealed that internalizing symptoms were comparable over time. Linear, quadratic, and piecewise latent growth curve models were deployed to estimate the trajectory of internalizing symptoms from early childhood to late adolescence. The analyses showed that internalizing symptoms were characterized by a quadratic-quadratic piecewise growth curve comprising two distinct phases of upward concave growth. Internalizing scores reduced steadily between ages 4 and 8 years but exhibited a slight upward curvature between ages 8 and 10 years. By age 14 years, the trajectory remained relatively stable but spiked between age 14 and 16 years. The two phases of internalizing symptoms’ development were largely unrelated. Overall, the study adds to the knowledge about the development of internalizing mental health from early childhood to late adolescence and highlights the need for additional support in late adolescence.

The experiment explored the effects of supplementing different energy levels of concentrate feed on the serum biochemical indicators, growth performance, and ruminal fermentation parameters of Tianzhu white yak. The experiment was divided into two periods: The first period involved concentrate supplementation during the winter and spring grazing period, and the second period was the lush grass grazing period without supplementation. A total of 30 healthy male Tianzhu white yak calves, aged six months and weighing (46.62±4.37) kg, were selected and randomly divided into three groups with five replicates in each group and two yaks in each replicate according to a randomized block design. The control group was normally grazed without concentrate supplementation, while the experimental group I and group II were supplemented with concentrate feeds with metabolizable energy of 10.83 and 11.76 MJ/kg after grazing, respectively. The initial feeding amount of concentrate was 0.70 kg per head, with an increase of 0.05 kg every 15 days, and the final supplementation amount was 1.20 kg per head. The experimental period was 365 days, with a supplementation period of 150 days during the winter and spring, and a normal grazing period of 215 days. The results showed that cold-season supplementation increased the weight and weight gain of yaks at 11, 12, and 18 months of age, and during the periods of 6~11 months and 12~18 months of age (P<0.05), with group II having higher weight and weight gain at all ages compared to group I (P<0.05). The Gompertz model fit better than the Bertalantty model for all groups, with the experimental groups having higher breakpoint weights and breakpoint months than the control group, and group II having the highest breakpoint weight and month. The ruminal fluid acetic acid content, acetic acid/propionic acid ratio, and pH value in groups I and II were lower than in the control group (P<0.05), while the concentrations of propionic acid, isobutyric acid, butyric acid, isovaleric acid, valeric acid, and ammonia nitrogen were higher than in the control group (P<0.05), and the ammonia nitrogen concentration in the group II was higher than that in the experimental group I (P<0.05). The serum glucose, total cholesterol, triglycerides, and total protein concentration in groups I and II were higher than in the control group (P<0.05). The study indicates that cold-season supplementation with different energy levels of concentrate feed promoted the growth and development of yak calves, altered the ruminal fermentation patterns, and serum biochemical indicators, with the supplementation of concentrate feed with a metabolizable energy of 11.76 MJ/kg showing better results. [ABSTRACT FROM AUTHOR]

In order to understand the growth characteristics of Qingyuan yellow-feathered black bone chicken and select the best growth curve model, a total of 100 healthy Qingyuan yellow-feathered black bone chicken in the same batch number (half male and female) were selected in the experiment to measure the body weight weekly. Three models of Logistic, Von Bertalanffy and Gompertz were used to fit and analyze the body weight data of 0-22 week-old Qingyuan yellow-feathered black bone chicken. The results showed that the fitting degree (R² ) of the three growth curve models were more than 0. 990, which could be used to describe the growth and development laws of Qingyuan yellow-feathered black bone chicken. Among them, the fitting degree (R² ) of the body weight of cocks by Gompertz model was the highest, being 0. 999. The results showed that the inflection point body weight of cocks was 950. 49 g, the week-age of inflection point was 10. 28 w, and the maximum weekly weight gain was 133. 07 g. The fitting degree of the body weight of hens by Von Bertalanffy model was the highest(0. 999). The results showed that the inflection point body weight of the hens was 757. 62 g, the inflection point week-age was 10. 47 w, and the maximum weekly weight gain was 90. 91 g. The above results showed that the Gompertz model was more suitable for fitting the growth process of the cocks, and the Von Bertalanffy model was more suitable for fitting the growth process of the hens. The results preliminarily revealed the growth process of Qingyuan yellow-feathered black bone chicken, and provided references for breeding, feeding management and practical production of this breed. [ABSTRACT FROM AUTHOR]

This study aimed to estimate the growth parameters of Muscovy ducks. The superiority of the study offers insightful information on the Muscovy duck growth curve, makes quantitative comparisons easier, allows for predictive capacities, and quickly finds problems. A total of 40 Muscovy ducks called “Rambon” were used in the study, consisting of 12 males and 28 females. Body weight was weighed periodically every two days from the day-old ducks (DOD) until 60 days of age. The data was analyzed by using Gompertz and Logistic models. The growth curves were analyzed, and parameters such as adult body weight (A), integral constant (B), and growth rate (K) were determined. Inflection points were also identified. Body weight (Wi) and age at the inflection (Ai) point using Gompertz were 1060.95 g and 46.34 d; 613.41 g and 30.52 d; 712.56 g and 36.81 d, respectively for males, females, and the unsexed. By using Logistic model, the Wi and Ai for males were 934.60 g and 41.46 d, females were 670.52 g and 32.96 d, and unsexed were 739.11 g and 36.56 d. Results showed that the Gompertz model generally outperformed the Logistic model, with lower AIC, BIC, MSE values and slightly higher R2 for all sex groups, indicating superior fit and predictive accuracy. These findings offer valuable insights into Rambon Muscovy duck growth dynamics, aiding in breeding and production strategies to enhance economic efficiency and sustainability. Farmers can utilize these models to optimize feeding schedules and make informed decisions about slaughtering, ultimately improving Muscovy duck production. [ABSTRACT FROM AUTHOR]

Children's mental health symptoms' development can be characterized by both continuity and discontinuity. However, existing studies ignore the potential discontinuity in children's internalizing symptoms' development. Hence, the current study examines continuous and discontinuous developmental trajectories using representative data from a sample of 2792 children (49.10% females) from the Growing Up in Australia cohort assessed seven times (ages 4, 6, 8, 10, 12, 14, 16). Longitudinal measurement invariance analyses revealed that internalizing symptoms were comparable over time. Linear, quadratic, and piecewise latent growth curve models were deployed to estimate the trajectory of internalizing symptoms from early childhood to late adolescence. The analyses showed that internalizing symptoms were characterized by a quadratic-quadratic piecewise growth curve comprising two distinct phases of upward concave growth. Internalizing scores reduced steadily between ages 4 and 8 years but exhibited a slight upward curvature between ages 8 and 10 years. By age 14 years, the trajectory remained relatively stable but spiked between age 14 and 16 years. The two phases of internalizing symptoms' development were largely unrelated. Overall, the study adds to the knowledge about the development of internalizing mental health from early childhood to late adolescence and highlights the need for additional support in late adolescence. [ABSTRACT FROM AUTHOR]

Clustering longitudinal data for growth curve modelling is considered in this paper, where we aim to optimally estimate the underpinning unknown group partition matrix. Instead of following the conventional soft clustering approach, which assumes the columns of the partition matrix to have i.i.d. multinomial or categorical prior distributions and uses a regression model with the response following a finite mixture distribution to estimate the posterior distribution of the partition matrix, we propose an iterative partition and regression procedure to find the best partition matrix and the associated best growth curve regression model for each identified cluster. We show that the best partition matrix is the one minimizing a recently developed empirical Bayes information criterion (eBIC), which, due to the involved combinatorial explosion, is difficult to compute via enumerating all candidate partition matrices. Thus, we develop a Gibbs sampling method to generate a Markov chain of candidate partition matrices that has its equilibrium probability distribution equal the one induced from eBIC. We further show that the best partition matrix, given a priori the number of latent clusters, can be consistently estimated and is computationally scalable based on this Markov chain. The number of latent clusters is also best estimated by minimizing eBIC. The proposed iterative clustering and regression method is assessed by a comprehensive simulation study before being applied to two real-world growth curve modelling examples involving longitudinal data clustering. [ABSTRACT FROM AUTHOR]

In this paper, discrimination between two populations following the growth curve model is considered. A likelihood-based classification procedure is established, in the sense that we compare the two likelihoods given that the new observation belongs to respective population. The possibility to classify the new observation as belonging to an unknown population is discussed, which is shown to be natural when considering growth curves. Several examples and simulations are given to emphasize this possibility. [ABSTRACT FROM AUTHOR]

In this paper, we propose approximations for the misclassification probabilities in linear discriminant analysis when the group means have a bilinear regression structure. First, we give a unified location and scale mixture expression of the standard normal distribution for the linear discriminant function. Then, the estimated approximations of misclassification are obtained for the three cases: unweighted case, weighted known covariance matrix Σ , and weighted unknown Σ. It has to be pointed out that larger p is better for classification when Σ is known, also in unweighted case. In the case Σ is unknown, we gain more information if fewer repeated measurements are used compared to when many repeated measurements closer to the number of included sample size are used. Furthermore, the accuracies of the proposed approximations are checked numerically by conducting a Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach for approximating misclassification probabilities in Euclidean distance classifier when the group means exhibit a bilinear structure such as in the growth curve model first proposed by Potthoff and Roy (Biometrika 51:313–326, 1964). Initially, by leveraging certain statistical relationships, we establish two general results for the improved Euclidean discriminant function in both weighted and unweighted growth curve mean structures. We derive these approximations for the expected misclassification probabilities with respect to the distribution of the improved Euclidean discriminant function. Additionally, we compare the misclassification probabilities of the improved Euclidean discriminant function, the standard Euclidean discriminant function, and the linear discriminant function. It is important to note that in cases where the mean structure is weighted, a higher number of repeated measurements yields better classification results with the improved Euclidean discriminant function and the standard Euclidean discriminant function, allowing for more information to be acquired, as opposed to the linear discriminant function, which performs well with a smaller number of repeated measurements. Furthermore, we evaluate the accuracy of the suggested approximations by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Health disparity by race/ethnicity or gender has been well-documented. However, few researchers have examined health outcomes based on the intersection of individuals' race, ethnicity, and gender or investigated various health dimensions. Guided by an intersectionality framework, this study explores racial/ethnic/gender-based differences in trajectories of multiple health outcomes over a ten-year period among American older adults. Longitudinal data from the Health and Retirement Study (2004–2014) were used (N = 16,654). Older adults (65+) were stratified into six mutually-exclusive groups based on their race, ethnicity, and gender: Non-Hispanic (NH) White Men, NH White Women, NH Black Men, NH Black Women, Hispanic Men, and Hispanic Women. Growth curve models examined the trajectories of three health measures, including cognitive function, physical function limitations (i.e. activities of daily living and instrumental activities of daily living), and depressive symptoms. NH White men and women reported significantly better outcomes in cognition and physical function trajectories than racial/ethnic minority groups. Women in all racial/ethnic groups had more depressive symptoms but better cognition than men. Hispanic women reported the most depressive symptoms. Hispanic women and NH Black women had the worst physical function limitations. NH Black men/women were the most disadvantaged in cognition. Racial/ethnic/gender-based differences were stable over time in all health trajectories. Study findings highlight the utility of an intersectional framework in understanding how multiple social identities intersect to generate protective and/or risk effects on cognitive, mental, and physical health. Multilevel intervention strategies are warranted to reduce the persistent health inequity gap. [ABSTRACT FROM AUTHOR]

The classification of observations based on repeated measurements performed on the same subject over a given period of time or under different conditions is a common procedure in many disciplines such as medicine, psychology and environmental studies. In this article repeated measurements follow an extended growth curve model and are classified using linear discriminant analysis. The aim of this article is to propose approximation for the misclassification probabilities in the linear discriminant function when the population means follow an extended growth curve structure. Using specific statistic relations we derive the approximation of misclassification probabilities for known and unknown covariance matrices. Finally, we perform a Monte Carlo simulation study to assess the accuracy of the developed results. [ABSTRACT FROM AUTHOR]

The onset of the COVID-19 pandemic boosted political trust in many countries. This article tests the relevance of fear of infection as the micro-level mechanism behind this rally round the flag. This study employs three-wave panel data in the Netherlands, collected days before the first lockdown (early March 2020), during that lockdown (April/May 2020), and after that lockdown (October 2020). Growth curve models isolate the rally effect and its determinants. The article reaches three main conclusions. First, fear of infection is a constituting element of the rally effect: the rise in political trust is more pronounced among people who fear infection. Second, the rise occurs in response to the direct, external threat (health concerns), not in response to the secondary threats (social isolation, economic stagnation). Third, adherents of the radical right are particularly sensitive to the external threat, but only in the short run. [ABSTRACT FROM AUTHOR]

Diffusion-based item response theory models are measurement models that link parameters of the diffusion model (drift rate, boundary separation) to latent traits of test takers. Similar to standard latent trait models, they assume the invariance of the test takers' latent traits during a test. Previous research, however, suggests that traits change as test takers learn or decrease their effort. In this paper, we combine the diffusion-based item response theory model with a latent growth curve model. In the model, the latent traits of each test taker are allowed to change during the test until a stable level is reached. As different change processes are assumed for different traits, different aspects of change can be separated. We discuss different versions of the model that make different assumptions about the form (linear versus quadratic) and rate (fixed versus individual-specific) of change. In order to fit the model to data, we propose a Bayes estimator. Parameter recovery is investigated in a simulation study. The study suggests that parameter recovery is good under certain conditions. We illustrate the application of the model to data measuring visuo-spatial perspective-taking. [ABSTRACT FROM AUTHOR]

This study proposes a joint modeling approach to conduct causal mediation analysis that accommodates multivariate longitudinal data, dynamic latent mediator, and survival outcome. First, we introduce a confirmatory factor analysis model to characterize a time-varying latent mediator through multivariate longitudinal observable variables. Then, we establish a growth curve model to describe the linear trajectory of the dynamic latent mediator and simultaneously explore the relationship between the exposure and the mediating process. Finally, we link the mediating process to the survival outcome through a proportional hazards model. In addition, we use the mediation formula approach to assess the natural direct and indirect effects and prove the identifiability of the causal effects under sequential ignorability assumptions. A Bayesian approach incorporating the Markov chain Monte Carlo algorithm is developed to estimate the causal effects efficiently. Simulation studies are conducted to evaluate the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative study further confirms the utility of the proposed method. [ABSTRACT FROM AUTHOR]

The present research examined: (a) the co-development of chores and effortful control, and (b) the prospective impact of effortful control development (i.e., initial levels and the trajectory of effortful control from late childhood through adolescence) on work outcomes in young adulthood. We used data from a longitudinal study of 674 Mexican-origin youth assessed at ages 10, 12, 14, 16, and 19. We found no evidence of co-developmental associations between chores and effortful control, but we found that higher initial levels of effortful control (age 10) predicted working-student status, less job stress, and better job fit, and steeper increases in effortful control from age 10 to 16 predicted higher job satisfaction and job autonomy in young adulthood (age 19).

Abstract Background Bodily pain is a common presentation in several chronic diseases, yet the influence of sedentary behaviour, common in ageing adults, is unclear. Television-viewing (TV) time is a ubiquitous leisure-time sedentary behaviour, with a potential contribution to the development of bodily pain. We examined bodily pain trajectories and the longitudinal relationships of TV time with the bodily pain severity; and further, the potential moderation of the relationships by type 2 diabetes (T2D) status. Method Data were from 4099 participants (aged 35 to 65 years at baseline) in the Australian Diabetes, Obesity and Lifestyle Study (AusDiab), who took part in the follow-ups at 5 years, 12 years, or both. Bodily pain (from SF36 questionnaire: a 0 to 100 scale, where lower scores indicate more-severe pain), TV time, and T2D status [normal glucose metabolism (NGM), prediabetes, and T2D] were assessed at all three time points. Multilevel growth curve modelling used age (centred at 50 years) as the time metric, adjusting for potential confounders, including physical activity and waist circumference. Results Mean TV time increased, and bodily pain worsened (i.e., mean bodily pain score decreased) across the three time points. Those with T2D had higher TV time and more-severe bodily pain than those without T2D at all time points. In a fully adjusted model, the mean bodily pain score for those aged 50 years at baseline was 76.9(SE: 2.2) and worsened (i.e., bodily pain score decreased) significantly by 0.3(SE: 0.03) units every additional year (p

High-resolution circumference dendrometers measure the irreversible growth and the reversible shrinking and swelling due to the water content of a tree stem. We propose a novel statistical method to decompose these measurements into a permanent and a temporary component, while explaining differences between the trees and years by covariates. Our model embeds Gaussian processes with parametric mean and covariance functions as response structures in a distributional regression framework with structured additive predictors. We discuss different mean and covariance functions, connections with other model classes, Markov chain Monte Carlo inference, and the efficiency of our sampling scheme. [ABSTRACT FROM AUTHOR]

Abstract Background Missing data are ubiquitous in randomised controlled trials. Although sensitivity analyses for different missing data mechanisms (missing at random vs. missing not at random) are widely recommended, they are rarely conducted in practice. The aim of the present study was to demonstrate sensitivity analyses for different assumptions regarding the missing data mechanism for randomised controlled trials using latent growth modelling (LGM). Methods Data from a randomised controlled brief alcohol intervention trial was used. The sample included 1646 adults (56% female; mean age = 31.0 years) from the general population who had received up to three individualized alcohol feedback letters or assessment-only. Follow-up interviews were conducted after 12 and 36 months via telephone. The main outcome for the analysis was change in alcohol use over time. A three-step LGM approach was used. First, evidence about the process that generated the missing data was accumulated by analysing the extent of missing values in both study conditions, missing data patterns, and baseline variables that predicted participation in the two follow-up assessments using logistic regression. Second, growth models were calculated to analyse intervention effects over time. These models assumed that data were missing at random and applied full-information maximum likelihood estimation. Third, the findings were safeguarded by incorporating model components to account for the possibility that data were missing not at random. For that purpose, Diggle-Kenward selection, Wu-Carroll shared parameter and pattern mixture models were implemented. Results Although the true data generating process remained unknown, the evidence was unequivocal: both the intervention and control group reduced their alcohol use over time, but no significant group differences emerged. There was no clear evidence for intervention efficacy, neither in the growth models that assumed the missing data to be at random nor those that assumed the missing data to be not at random. Conclusion The illustrated approach allows the assessment of how sensitive conclusions about the efficacy of an intervention are to different assumptions regarding the missing data mechanism. For researchers familiar with LGM, it is a valuable statistical supplement to safeguard their findings against the possibility of nonignorable missingness. Trial registration The PRINT trial was prospectively registered at the German Clinical Trials Register (DRKS00014274, date of registration: 12th March 2018).

This study investigated the relationship between children's mathematics performance and physical health using data from the Early Childhood Longitudinal Study Kindergarten Class of 2010–2011 (ECLS-K 2011). A two-level hierarchical growth curve model was used to explore the relationships between childhood mathematics performance and childhood health taking moderator effects into consideration. The study results indicate that higher body mass index relates to higher kindergarten mathematics performance, holding all else constant. The results of this study have implications for educators, parents, and health providers in understanding the relationship between mathematics performance and health indicators. [ABSTRACT FROM AUTHOR]

I Research on child development considers it important to understand each childʼs developmental process as well as that of the entire population. Therefore, child development scholars must be proficient in two methodologies—longitudinal research and longitudinal analysis—with the latter based on drawing developmental trajectories. This study focuses on describing the populationʼs average developmental trajectory while capturing individual deviations from the average. To this end, this study introduces the growth curve model and latent class growth analysis, highlighting findings from the Hamamatsu Birth Cohort (HBC) Study. The growth curve model introduces the mixed-effects and latent class approaches using an example question of whether an individualʼs birth weight affects their expressive language development. Latent class growth analysis emphasizes the parallel-process approach, which processes multiple domains in parallel and the joint model, which can be used to examine links between the developmental trajectories of two outcomes. [ABSTRACT FROM AUTHOR]

The present study examined the effect of children's enrollment in U.S. dual-language immersion (DLI) programs in first grade on English development across five years, using the Early Childhood Longitudinal Study, Kindergarten Class of 2011 (ECLS-K:2011) database. Propensity score matching was used to create comparable groups of DLI and non-DLI students based on students' kindergarten reading performance and a series of student-, family-, and school-level characteristics. Growth curve models demonstrate that first-grade DLI enrollment had a positive effect on children's English reading growth from Grade 1 to 5. Children who enrolled in DLI experienced greater improvements by Grade 5. We also found that first-grade teacher judgment was related to children's initial reading performance but not their reading growth. Implications related to DLI programs, teacher practices, and bilingual educational policies are discussed. [ABSTRACT FROM AUTHOR]

How gender role attitudes develop during adolescence, and how biological, social, and cognitive factors predict this development, remains a matter of debate. This study examines the development of gender role attitudes from early adolescence to emerging adulthood and investigates how the developmental trajectory is affected by sex, socioeconomic status, and cognitive abilities (intelligence). Four waves of the large-scale longitudinal German dataset BIJU between 1991 (grade 7; N = 3828, Mage = 13, SD = 0.61, 53.1% female, 96.4% German nationality), 1995 (grade 10, Mage = 17), 1997 (grade 12, Mage = 19) and 2001/2002 (university/career entry, Mage = 24) were used. Measurement invariance was examined across waves and gender. Latent growth curve models showed that adolescents developed more egalitarian gender role attitudes. Differences between the sexes decreased over time but remained significant. Socioeconomic status seemed less relevant, while adolescents, especially those with lower intelligence scores, developed more egalitarian gender role attitudes during adolescence. The results showed that teenagers developed more open and egalitarian attitudes during adolescence, and that the development trajectories of female and male adolescents converge. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Missing data are ubiquitous in randomised controlled trials. Although sensitivity analyses for different missing data mechanisms (missing at random vs. missing not at random) are widely recommended, they are rarely conducted in practice. The aim of the present study was to demonstrate sensitivity analyses for different assumptions regarding the missing data mechanism for randomised controlled trials using latent growth modelling (LGM).Methods: Data from a randomised controlled brief alcohol intervention trial was used. The sample included 1646 adults (56% female; mean age = 31.0 years) from the general population who had received up to three individualized alcohol feedback letters or assessment-only. Follow-up interviews were conducted after 12 and 36 months via telephone. The main outcome for the analysis was change in alcohol use over time. A three-step LGM approach was used. First, evidence about the process that generated the missing data was accumulated by analysing the extent of missing values in both study conditions, missing data patterns, and baseline variables that predicted participation in the two follow-up assessments using logistic regression. Second, growth models were calculated to analyse intervention effects over time. These models assumed that data were missing at random and applied full-information maximum likelihood estimation. Third, the findings were safeguarded by incorporating model components to account for the possibility that data were missing not at random. For that purpose, Diggle-Kenward selection, Wu-Carroll shared parameter and pattern mixture models were implemented.Results: Although the true data generating process remained unknown, the evidence was unequivocal: both the intervention and control group reduced their alcohol use over time, but no significant group differences emerged. There was no clear evidence for intervention efficacy, neither in the growth models that assumed the missing data to be at random nor those that assumed the missing data to be not at random.Conclusion: The illustrated approach allows the assessment of how sensitive conclusions about the efficacy of an intervention are to different assumptions regarding the missing data mechanism. For researchers familiar with LGM, it is a valuable statistical supplement to safeguard their findings against the possibility of nonignorable missingness.Trial Registration: The PRINT trial was prospectively registered at the German Clinical Trials Register (DRKS00014274, date of registration: 12th March 2018). [ABSTRACT FROM AUTHOR]

In the present paper, we derive a new multivariate model to fit correlated data, representing a general model class. Our model is an extension of the Growth Curve model (also called generalized multivariate analysis of variance model) by additionally assuming randomness of regression coefficients like in linear mixed models. Each random coefficient has a linear or a bilinear form with respect to explanatory variables. In our model, the covariance matrices of the random coefficients is allowed to be singular. This yields flexible covariance structures of response data but the parameter space includes a boundary, and thus maximum likelihood estimators (MLEs) of the unknown parameters have more complicated forms than the ordinary Growth Curve model. We derive the MLEs in the proposed model by solving an optimization problem, and derive sufficient conditions for consistency of the MLEs. Through simulation studies, we confirmed performance of the MLEs when the sample size and the size of the response variable are large. [ABSTRACT FROM AUTHOR]

Residents in US cities are exposed to high levels of stress and violent crime. At the same time, a number of cities have put forward "greening" efforts which may promote nature's calming effects and reduce stressful stimuli. Previous research has shown that greening may lower aggressive behaviors and violent crime. In this study we examined, for the first time, the longitudinal effects over a 30-year period of average city greenness on homicide rates across 290 major cities in the US, using multilevel linear growth curve modeling. Overall, homicide rates in US cities decreased over this time-period (52.1–33.5 per 100,000 population) while the average greenness increased slightly (0.41–0.43 NDVI). Change in average city greenness was negatively associated with homicide, controlling for a range of variables (β = −.30, p -value =.02). The results of this study suggest that efforts to increase urban greenness may have small but significant violence-reduction benefits. [ABSTRACT FROM AUTHOR]

In the developing world, children are at high risk of growing up without one or both parents for extended periods of time during childhood, largely due to parental labor migration. Limited work has studied the potential impact of parental migration on early childhood development (ECD), and longitudinal data to address this question is particularly lacking. Using three waves of the China Family Panel Studies data collected in 2010, 2012 and 2014, the current study examines the association between parental migration and a number of ECD outcomes. We address the complexity and dynamic processes of family migration by categorizing patterns of parental migration during the first 5 years of children's lives, taking into account timing and sequencing of parental migration events, as well as children's cumulative experience with parental migration. We then associate various patterns of parental migration with the trajectories of childhood linear growth, childhood illness and home environment from age 1 to age 5, and with pre-primary school enrollment, social behavioral development, and cognitive stimulation measured at age 4 or 5. Our findings indicate that parental migration, regardless of the number of absent parents, was not associated with childhood illness, behavior, or preschool enrollment. We observe a negative association between parental migration and both cognitive stimulation and the quality of the home environment. The strength of the associations is stronger when migration involved two parents. Children of returned migrants exhibit a slower rate of linear growth, on average. The results are largely insensitive to the timing of parental migration. The implications of lower levels of cognitive stimulation and quality of the home environment on left-behind children's cognitive development deserve further investigation. [ABSTRACT FROM AUTHOR]

Research productivity has been a critical issue in terms of academic development in higher education. In this study, we adopt a life-course perspective to examine the personal factors, mostly age-related, affecting research productivity in a Taiwanese research-oriented university. Covering a time series of 20 years, our dataset includes individual research performance of faculty and other relevant covariates over their life course. The growth curve model designed for multilevel modeling of repeated measures is applied to capture the age effect. Our analysis contributes to the thread of this literature in several dimensions. First, the faculty's early academic achievement is positively associated with their later performance providing support for the cumulative advantage theory. Unlike the prediction of the utility maximizing theory, faculty with an administrative position leads to higher productivity. Finally, reinforcement still plays a critical role in regulating the productivity for non-early promising faculty. [ABSTRACT FROM AUTHOR]

Developing growth curve for forest and environmental management is a crucial activity in forestry planning. This paper describes a proposed technique for developing a growth curve based on the SPOT 6 satellite imageries. The most critical step in developing a model is on pre-processing the images, particularly during performing the radiometric correction such as reducing the thin cloud. The pre-processing includes geometric correction, radiometric correction with image regression, and index calculation, while the processing technique include training area selection, growth curve development, and selection. The study found that the image regression offered good correction to the haze-distorted digital number. The corrected digital number was successfully implemented to evaluate the most accurate growth-curve for predicting mangrove. Of the four growth curve models, i.e., Standard classical, Richards, Gompertz, and Weibull models, it was found that the Richards is the most accurate model in predicting the mean annual increment and current annual increment. The study concluded that the growth curve model developed using high-resolution satellite image provides comparable accuracy compared to the terrestrial method. The model derived using remote sensing has about 9.16% standard of error, better than those from terrestrial data with 15.45% standard of error.

This study examined the effect of maternal employment status during the first year of a child's life on the trajectory of fathers' engagement with preschool-aged children, using the Fragile Families and Child Wellbeing Study (N = 969). Further, the role of resources was examined regarding the relationship between first-year maternal employment and the fathers' engagement trajectory, guided by the conservation of resources (COR) theory. Analyses of the growth curve models found that during children's preschool years, the engagement trajectory of fathers whose wives were employed declined more rapidly than that of fathers whose wives were not employed. When resources are held constant, the engagement trajectory of fathers whose wives were employed declined less rapidly, resulting in an increased trajectory difference. These findings emphasize the importance of trajectories of father engagement associated with maternal employment when designing intervention programmes to increase fathers' engagement with their infants. [ABSTRACT FROM AUTHOR]

This study examined the gap between need and provision of community services in China and its association with older adults' life satisfaction over time. Longitudinal data from the Chinese Longitudinal Healthy Longevity Survey from 2008 to 2014 were used (3 waves, N = 16,199). Respondents reported if they needed nine types of community service and if their community provided such service. Growth curve models analyzed whether individual- and/or province-level characteristics predicted the initial level and/or changes of life satisfaction over time. Results indicated the presence of major unmet service needs in China. Available community services were mismatched with older adults' perceived needs. Unmet service needs were associated with decreased life satisfaction at baseline. However, unmet service needs were not associated with changes in life satisfaction over time. Study findings highlighted the urgent need to optimize service design in accordance with older adults' needs, which ultimately could promote older adults' well-being. [ABSTRACT FROM AUTHOR]

To confirm the effects of the development of economy and society and the utilization of fossil energy on the increasing of carbon emissions, the carbon emission of Chongqing city, a typical industrial city in the Yangtze River economic belt, was predicted. Based on the endogenous growth theory, the driving factors of carbon emission in Chongqing city by GDP, population and energy structure were analyzed and forecasted by the methods of data investigation and scenario analysis. Based on the production function theory, the comprehensive carbon emission model was built, and the carbon emission of Chongqing city from 2014 to 2035 was estimated. The results show that Chongqing' s GDP is expected to reach 494. 03 million yuan by 2035, and the added value of the secondary and tertiary industries accounts for 97. 72 % . The population will reach 34. 28 million, and the urban population accounts for 91. 17%. The proportion of fossil energy consumption will drop to 84. 53%, and the energy consumption intensity will drop to 4 400 tons of standard coal · ( 10 000 yuan) - I. When the growth of various driving factors is consistent with the endogenous growth trend, Chongqing' s carbon emissions will reach a peak of 175. 7 million tons around 2025. [ABSTRACT FROM AUTHOR]

We propose asymptotic approximations for the probabilities of misclassification in linear discriminant analysis when the group means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of several multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain asymptotic approximation of misclassification errors for the two group case. Finally, we perform Monte Carlo simulations to evaluate the reliability of the proposed results. [ABSTRACT FROM AUTHOR]

The global surge in childhood obesity is also evident in Indonesia. Parental body mass index (BMI) values were found to be one of the major determinants of the increasing prevalence of childhood obesity. It is uncertain if parental BMI during their offspring's childhood significantly affects their children's BMI trajectories into adulthood. We aimed to investigate the influence of parental BMI Z -scores on BMI trajectories of Indonesian school-aged children, with a focus on sex-specific effects. This study utilized data from the Indonesian Family Life Survey and tracked the same respondents over four time points, from wave 2 (1997-1998) to wave 5 (2014-2015). The sample of this study consisted of children aged 5-12 years in wave 2 for whom height and weight data were available. We utilized a two-level growth curve model to account for the hierarchical structure of the data, with time nested within individual children. Fathers' BMI Z-scores in wave 2 had a pronounced influence ( β = 0.31) on female children's BMI Z -scores compared to the influence of mothers' BMI Z-scores ( β = 0.17). Mothers' BMI Z -scores in wave 2 showed a stronger positive association with male children's BMI Z -scores ( β = 0.22) than did the father's BMI Z -scores ( β = 0.19). A significant interaction of fathers' BMI Z -scores and years of follow-up was found for male children. As male children's BMI Z -scores increased by year, this effect was stronger in those whose fathers' BMI Z -scores were at a higher level. In conclusion, we found that parental BMI values profoundly influenced their children's BMI trajectories.

Background The overall goal of this longitudinal study was to determine if the Black population has decreased myocardial function, which has the potential to lead to the early development of congestive heart failure, compared with the White population. Methods and Results A total of 673 subjects were evaluated over a period of 30 years including similar percentages of Black and White participants. Left ventricular systolic function was probed using the midwall fractional shortening (MFS). A longitudinal analysis of the MFS using a mixed effect growth curve model was performed. Black participants had greater body mass index, higher blood pressure readings, and greater left ventricular mass compared with White participants (all P

We analyze adolescent BMI and middle‐age systolic blood pressure (SBP) repeatedly measured on women enrolled in the Fels Longitudinal Study (FLS) between 1929 and 2010 to address three questions: Do adolescent‐specific growth rates in body mass index (BMI) and menarche affect middle‐age SBP? Do they moderate the aging effect on middle‐age SBP? Have the effects changed over historical time? To address the questions, we propose analyzing a growth curve model (GCM) that controls for age, birth‐year cohort, and historical time. However, several complications in the data make the GCM analysis nonstandard. First, the person‐specific adolescent BMI and middle‐age SBP trajectories are unobservable. Second, missing data are substantial on BMI, SBP, and menarche. Finally, modeling the latent trajectories for BMI and SBP, repeatedly measured on two distinct sets of unbalanced time points, are computationally intensive. We adopt a bivariate GCM for BMI and SBP with correlated random coefficients. To efficiently handle missing values of BMI, SBP, and menarche assumed missing at random, we estimate their joint distribution by maximum likelihood via the EM algorithm where the correlated random coefficients and menarche are multivariate normal. The estimated distribution will be transformed to the desired GCM for SBP that includes the random coefficients of BMI and menarche as covariates. We demonstrate unbiased estimation by simulation. We find that adolescent growth rates in BMI and menarche are positively associated with, and moderate, the aging effect on SBP in middle age, controlling for age, cohort, and historical time, but the effect sizes are at most modest. The aging effect is significant on SBP, controlling for cohort and historical time, but not vice versa. [ABSTRACT FROM AUTHOR]

This paper describes two tests in the growth curve model under multivariate normality. The first one is revisited test for intraclass structure of the covariance matrix, and the second one is the simultaneous test for intraclass covariance structure together with a specific mean value of the model. Both tests are likelihood ratio tests. [ABSTRACT FROM AUTHOR]

In the social sciences, applied researchers often face a statistical dilemma when multilevel data is structured such that lower-level units are not purely clustered within higher-level units. To aid applied researchers in appropriately analyzing such data structures, this study proposes a multiple membership growth curve model (MM-GCM). The MM-GCM offers some advantages to other similar modeling approaches, including greater flexibility in modeling the intercept at the time-point most desired for interpretation. A real longitudinal dataset from the field of education with a multiple membership structure, where some students changed schools over time, was used to demonstrate the application of the MM-GCM. Baseline and conditional MM-GCMs are presented, and parameter estimates were compared with two other common approaches to handling such data structures – the final school-GCM that ignores mobile students by only modeling the final school attended and the delete-GCM that deletes mobile students. Additionally, a simulation study was conducted to further assess the impact of ignoring mobility on parameter estimates. The results indicate that ignoring mobility results in substantial bias in model estimates, especially for cluster-level coefficients and variance components. [ABSTRACT FROM AUTHOR]

Small area estimation techniques have got a lot of attention during the last decades due to their important applications in survey studies. Mixed linear models and reduced rank regression analysis are jointly used when considering small area estimation. Estimates of parameters are presented as well as prediction of random effects and unobserved area measurements. [ABSTRACT FROM AUTHOR]

Background: Evidence suggests lack of understanding of the association of specific nutrients with different time points of linear growth trajectory.Objective: We investigated the role of dietary macro- and micronutrients on length-for-age z (LAZ) score trajectory of children across first 24 months of their life.Methods: The MAL-ED Bangladesh birth cohort study recruited 265 healthy newborn children after birth. The linear growth trajectory of those children was modeled using latent growth curve modeling (LGCM) technique.Results: Dietary magnesium intake at 9 to 11 months was positively associated (coefficient β = 0.006, P < .02) with LAZ at 12 months. Animal protein intake at 15 to 17 months, in turn, was positively associated (β = 0.03, P < .03) with LAZ at 18 months. However, vitamin D intake at 15 to 17 months was negatively associated (β = -0.06, P < .02) with LAZ at 18 months. Other micro- and macronutrients did not show any statistically significant association with the linear growth trajectory. We also found that birth weight (β = 0.91, P < .01), treating water (β = 0.35, P < 0.00), and maternal height (β = 3.4, P < .00) were positively associated with intercept. Gender had a significant negative association with the intercept, but a positive association with the slope (β = -0.39, P < .01; β = 0.08, P < .04), respectively. Conversely, birth weight had negative association with the slope (β = -0.12, P < .01).Conclusions: Dietary magnesium and animal protein were positively and vitamin D was negatively associated with the linear growth trajectory. Maternal height, birth weight, gender, and treatment of drinking water also played significant roles in directing the trajectory. [ABSTRACT FROM AUTHOR]

In this paper the growth curve model, with the data correlated according to uniform structure, is considered. It represents a useful statistical model for a variety of areas. Our aim is to present various estimators of unknown variance parameters and compare their statistical properties. In the first part the review of known results for different estimators of ρ and σ 2 and their properties is given. The aim is to compare and order these estimators based on biasedness and mean square error. [ABSTRACT FROM AUTHOR]

• Prospective longitudinal study of 600 adolescents followed from infancy. • Interpersonal conflict stress in infancy indirectly associated with later inflammation. • BMI mediates early life adversity and inflammation relationships. Early adversity, depression, and obesity are associated with increases in low-grade inflammation. However, there are few prospective and longitudinal studies to elucidate how these associations unfold in children. The present study used latent growth curve models to examine pathways between family adversity in infancy, depressive symptoms in childhood, body mass index (BMI) in childhood, and inflammation in adolescence (age = 16–18). The study is an adolescent follow-up of infants from working-class communities around Santiago, Chile, who participated in a preventive trial of iron supplementation at 6 months of age. Anthropometrics, stressful life events, maternal depression, socioeconomic status, and developmental assessments were measured at 12 months, 5 years, 10 years, and adolescence. In adolescence, participants provided blood samples for high-sensitivity C-reactive protein (hsCRP) assessment. Greater exposure to early adversity in the form of interpersonal conflict stress in infancy indirectly associated with increased hsCRP through its association to increased intercept and slope of childhood BMI. Depressive symptoms at any time were not directly or indirectly associated with increased hsCRP. These findings contribute to our understanding of how early family adversity and its associations with obesity and depressive symptoms across childhood are linked to low-grade, chronic inflammation in adolescence. The model identified as best capturing the data supported the pivotal role of childhood BMI in explaining how early-life adversity is associated with inflammation in adolescence. [ABSTRACT FROM AUTHOR]

Existing methods for estimating the parameters of the Growth Curve Model (GCM) rely on the assumption that the underlying distribution for the error terms is multivariate normal. However, we often come across skewed data in practical applications; and estimators developed under the normality assumption may not be valid in such situations. Simulation studies conducted in this paper, in fact, show that existing methods are sensitive to skewness, where normal based estimators are associated with increased bias and mean squared error (MSE), when the normality assumption is violated. Methods appropriate for skewed distributions are, therefore, required. In this paper, estimators for the mean and covariance matrices of the GCM under multivariate skew normal (MSN) distribution are proposed. An estimator for the additional skewness parameter of the MSN distribution is also provided. The estimators are derived using the expectation maximization (EM) algorithm and extensive simulations are performed to examine the performance of the estimators. Comparisons with existing estimators show that our estimators perform better than the existing estimators, when the underlying distribution is multivariate skew normal. Illustration using real data set is also provided. [ABSTRACT FROM AUTHOR]

This paper develops a new biased estimator—generalized ridge and principal correlation (GRPC) estimator of the regression coefficient in the growth curve model. The properties of the proposed estimator are shown to be superior to those of least squares (LS) estimator, principal correlation estimator, principal component estimator, and generalized ridge and principal component estimator in terms of both the mean squared error (MSE) and Pitman closeness (PMC). Moreover, a numerical study on synthetic data has been performed to demonstrate the optimality of the proposed estimator. [ABSTRACT FROM AUTHOR]