Estimated Growth Curve Research Articles

Estimating long-term multivariate progression from short-term data

MotivationDiseases that progress slowly are often studied by observing cohorts at different stages of disease for short periods of time. The Alzheimer's Disease Neuroimaging Initiative (ADNI) follows elders with various degrees of cognitive impairment, from normal to impaired. The study includes a rich panel of novel cognitive tests, biomarkers, and brain images collected every 6 months for as long as 6 years. The relative timing of the observations with respect to disease pathology is unknown. We propose a general semiparametric model and iterative estimation procedure to estimate simultaneously the pathological timing and long-term growth curves. The resulting estimates of long-term progression are fine-tuned using cognitive trajectories derived from the long-term “Personnes Agées Quid” study. ResultsWe demonstrate with simulations that the method can recover long-term disease trends from short-term observations. The method also estimates temporal ordering of individuals with respect to disease pathology, providing subject-specific prognostic estimates of the time until onset of symptoms. When the method is applied to ADNI data, the estimated growth curves are in general agreement with prevailing theories of the Alzheimer's disease cascade. Other data sets with common outcome measures can be combined using the proposed algorithm. AvailabilitySoftware to fit the model and reproduce results with the statistical software R is available as the grace package. ADNI data can be downloaded from the Laboratory of NeuroImaging.

Empirical growth curve estimation considering multiple seasonal compensatory growths of body weights in Japanese Thoroughbred colts and fillies1

Thoroughbred horses are seasonal mating animals, and their foals are born yearly in spring seasons. In northern regions or countries, the foals generally show a typical seasonal compensatory growth pattern, where their growth rate declines in winter and increases in the next spring. In this study, a new empirical approach is proposed to adjust for this compensatory growth when growth curve equations are estimated, by using BW of Japanese Thoroughbred colts and fillies raised in Hidaka, Hokkaido. Based on the traditional Richards growth curve equation, new growth curve equations were developed and fit to the weight-age data. The foals generally experience 2 major winter seasons before their debut in horseracing. The new equations had sigmoid subfunctions that can empirically adjust the first and second year compensatory growths, combined with the Richards biological parameter responsible for the maturity of animals. The unknown parameters included in the equations were estimated by SAS NLMIXED procedure. The goodness-of-fit was examined by using several indices of goodness-of-fit (i.e., Akaike's information criterion, Bayesian information criterion, -2 log likelihood, and residual sum of squares) for the multiple applications of the subfunctions. The indices indicated the best fit of the new equations including both subfunctions for the first and second compensatory growths to the weight-age data. The shapes of the growth curves were improved during the periods of compensatory growth. The proposed method is one of the useful approaches for adjusting multiple seasonal compensatory growths in growth curve estimations of Thoroughbreds and for the management of young horses during the compensatory periods.

The nature and correlates of self-esteem trajectories in late life.

Is it possible to maintain a positive perspective on the self into very old age? Empirical research so far is rather inconclusive, with some studies reporting substantial declines in self-esteem late in life, whereas others report relative stability into old age. In this article, we examine long-term change trajectories in self-esteem in old age and very old age and link them to key correlates in the health, cognitive, self-regulatory, and social domains. To do so, we estimated growth curve models over chronological age and time-to-death using 18-year longitudinal data from the Australian Longitudinal Study of Ageing (N = 1,215; age 65-103 years at first occasion; M = 78.8 years, SD = 5.9; women: 45% of sample). Results revealed that self-esteem was, on average, fairly stable with minor declines only emerging in advanced ages and at the very end of life. Examination of the vast between-person differences revealed that lower cognitive abilities and lower perceived control independently related to lower self-esteem. Also, lower cognitive abilities were associated with steeper age-related and mortality-related self-esteem decrements. In our discussion, we consider a variety of challenges that potentially shape self-esteem late in life and highlight the need for more mechanism-oriented research to better understand the pathways underlying stability and change in self-esteem.

Possible stock structure of dolphinfish (Coryphaena hippurus) in Taiwan coastal waters and globally based on reviews of growth parameters

Dolphinfish (Coryphaena hippurus) is used by many coastal countries. Sustaining harvest of this resource will require cooperation among fishing countries in each region, and determining population structure is paramount to ensuring effective management. Examining life-history parameters (such as growth rate) is a useful and relatively inexpensive method for identifying possible stock units, which can be subsequently confirmed by other methods. The purpose of this study is two-fold. First, we examine the two-stock assumption for Taiwanese dolphinfish and the reliability of estimated growth curves based on seasonally-stratified growth performance indices. The von Bertalanffy growth functions (VBGF) were firstly estimated from 2005 to 2009 length frequency sample data of eastern and southern coasts of Taiwan. New growth performance indices were then calculated from the log-transformed parameters of the VBGF and examined by a simultaneous confidence region (SCR) under the assumption of bivariate normal distribution. Second, we summarize VBGF parameter estimates from all regions worldwide and based on the growth parameters and performance indices, review the possible stock structures and the reliability of growth estimations for dolphinfish. The results support a single-stock hypothesis for dolphinfish in the Kuroshio Current off Taiwan with new estimated VBGF parameters of L∞=149.4cm and K=0.72year−1. Some potentially biased estimates of dolphinfish growth parameters are identified in the worldwide VBGF dataset and are suggested for further investigations. Excluding these estimates, the results indicate at least a five-stock structure in the Pacific and the Atlantic oceans.

Hypothesized, Directly-Coded Curve Shapes in Growth Curve Analysis: An Example

Growth curve analysis provides important informational benefits regarding intervention outcomes over time. Rarely, however, should outcome trajectories be assumed to be linear. Instead, both the shape and the slope of the growth curve can be estimated. Non-linear growth curves are usually modeled by including either higher-order time variables or orthogonal polynomial contrast codes. Each has limitations (multicollinearity with the first, a lack of coefficient interpretability with the second, and a loss of degrees of freedom with both) and neither encourages direct testing of alternative hypothesized curve shapes. Especially in studies with relatively small samples it is likely to be useful to preserve as much information as possible at the individual level. This article presents a step-by-step example of the use and testing of hypothesized curve shapes in the estimation of growth curves using hierarchical linear modeling for a small intervention study. DOI:10.2458/azu_jmmss_v3i2_herman

Hypothesized, Directly-Coded Curve Shapes in Growth Curve Analysis: An Example

Growth curve analysis provides important informational benefits regarding intervention outcomes over time. Rarely, however, should outcome trajectories be assumed to be linear. Instead, both the shape and the slope of the growth curve can be estimated. Non-linear growth curves are usually modeled by including either higher-order time variables or orthogonal polynomial contrast codes. Each has limitations (multicollinearity with the first, a lack of coefficient interpretability with the second, and a loss of degrees of freedom with both) and neither encourages direct testing of alternative hypothesized curve shapes. Especially in studies with relatively small samples it is likely to be useful to preserve as much information as possible at the individual level. This article presents a step-by-step example of the use and testing of hypothesized curve shapes in the estimation of growth curves using hierarchical linear modeling for a small intervention study.

Hypothesized, Directly-Coded Curve Shapes in Growth Curve Analysis: An Example

Growth curve analysis provides important informational benefits regarding intervention outcomes over time. Rarely, however, should outcome trajectories be assumed to be linear. Instead, both the shape and the slope of the growth curve can be estimated. Non-linear growth curves are usually modeled by including either higher-order time variables or orthogonal polynomial contrast codes. Each has limitations (multicollinearity with the first, a lack of coefficient interpretability with the second, and a loss of degrees of freedom with both) and neither encourages direct testing of alternative hypothesized curve shapes. Especially in studies with relatively small samples it is likely to be useful to preserve as much information as possible at the individual level. This article presents a step-by-step example of the use and testing of hypothesized curve shapes in the estimation of growth curves using hierarchical linear modeling for a small intervention study. DOI:10.2458/azu_jmmss_v3i2_herman

Estimation of children growth curve based on kernel smoothing in multi-response nonparametric regression

Physical children growth is measured by using anthropometric measures i.e. weight, height and head circumference. The children around two years old grow rapidly, and than decrease slowly along with increasing of children age. It means that locally model approach is more appropriate to the data. Kernel smoothing is one of estimation methods in nonparametric regression. In this paper, we study about Kernel smoothing in multi-response nonparametric regression model and apply it for estimating children up to five years old growth. The model consists of three response variables i.e. weight, height and head circumference, and age as a predictor variable. For determining optimal bandwidth for each response variable, we use cross-validation method. Based on children data in Surabaya 2010, and the 50 th percentiles estimation of weight, height and head circumference versus age, we obtain the mean squared error value is 0.05583 and coefficient of determination is 99.99%. The estimation model of children growth curve based on multi-respon kernel smoothing shows fluctuation of the curve and gives mean squared error value tends to zero and coefficient of determination tends to one. These facts mean that the estimation has satisfied goodness of fit criterion.

Estimation of Growth Curve Parameters for Body Weight and Length in Miniature Pigs

This study was conducted to estimate the growth curve parameters for the body weight (BW) and body length (BL) of miniature pigs in Korea. Growth curve parameters were estimated through a nonlinear regression model using Gompertz, Logistic, and von Bertalanffy methods. A total of 25 piglets were measured monthly from birth up to 15 months of age to estimate both body weight and length. Results showed that the estimated average values for the body weight (body length) were 31.83 kg (58.77 cm) for the mature weight (A), 3.06 (1.74) for the growth ratio (), and 0.28 (0.52) for the maturing rate (). Average inflection points showing maximum growth rate estimated each month for body weight were 3.97 kg and 11.70 cm, while for the body length were 1.06 kg and 21.61 cm. Moreover, the estimated maturation rates of the body weight and length for the group of Sire 1 were 0.22 and 0.40 respectively, whereas for the group of Sire 2 these values were 0.34 and 0.39. On the other hand, for the groups of Dam 1, Dam 2, and Dam 3, maturation rates for their body weights were 0.26, 0.28 and 0.33 respectively, while for their body lengths these values were 0.43, 0.37, and 0.38, respectively. The study also indicated a negative relationship between the values of mature weight and maturity rate for the body weight will result to a higher inflection point which is in contrast for the body length where results show that a positive relationship between the values of mature length and the maturity rate will result to a higher inflection point. Furthermore, the growth performance of miniature pig varies across stages but using these estimated growth curve parameters could improve the genetic traits of miniature pig.

Growth and maturity of a terrestrial ectotherm near its northern distributional limit: does latitude matter?

High-latitude environments are challenging for terrestrial ectotherms because short and cool active seasons generally limit the time available for foraging and growth, thereby negatively influencing life-history variables such as growth rate and age at maturity and ultimately, via fitness differences, their evolution. Many species show latitudinal clines in life-history traits, including growth rate and body size. We estimated growth curves of Plains Garter Snakes ( Thamnophis radix (Baird and Girard, 1853)) near the northern limit of the species’ range in central Alberta and compared our findings to similar estimates for more southerly populations. Despite a short growing season, female T. radix at Miquelon Lake grew rapidly, reaching maturity in 1 or 2 years, similar to southern populations, and attained greater maximum sizes than snakes in southern populations. Overall, growth in this high-latitude population is comparable with what is seen in other conspecific populations. Possible reasons for lack of marked latitudinal effect include longer days at high latitudes, highly productive aquatic habitats for foraging, effective thermoregulation, reduced competition, and (or) countergradient variation in growth rate.

Growth curve estimation in pure goat breeds and crosses of first and second generation in Tunisian oases

Five non-linear statistical models were tested to fit the growth curve parameters of the kids of indigenous, Alpine and Damascus goats and their crosses. Data from 16 years’ periodical weight study was used to adjust the growth curve of 1,687 suckling kids before they attained the age of five months. Among the tested models, the iterative procedure made it possible for the Gompertz model to be identified as the best for use to adjust kids’ growth evolution. Brody, Richards, Logistic and Polynomial models showed some convergence problems of accuracy. Curve parameters were fitted by Gompertz model after about 16 iterations with a coefficient of determination (CD) value of 71%. Growth parameters were established by genetic groups and the shape of the curve changed with kids’ genotypes. Crossbreeding allowed for a better growth kinetic in indigenous kids. After birth, kids’ weights increased rapidly to an asymptotic weight at an early age. The best growth performances were obtained in the first generation of crossbreeding due to heterosis. The growth curve adjustment helped in better flock management and in the fattening of kids according to the potentialities of each genotype. Key words: Goat, kids’ growth, curve model, Gompertz, crossbreeding, Tunisian oases.

Development of a new standardised method for sustainable monitoring of the vulnerable pink sea fan Eunicella verrucosa

The aim of this survey was to test a standardised method to follow the demographic evolution of a dense aggregative ‘forest’ population of the temperate gorgonian Eunicella verrucosa (Octocorallia, Gorgoniidae) using in situ photographic recordings. Distribution, density, growth and demographic evolution of the colonies was compared along two parallel transects. Computer treatment allowed the estimation of the total branch fan surface area, and the individual growth of tagged colonies was determined by measuring the increase in this surface area, using consecutive photographs taken at two-year intervals. To integrate the potential bias of branch overlapping, we proposed a correction factor between the in situ photographic surface area and the surface area of the gorgonian calculated from ex situ photographic surface area with all branches deployed. The surface-frequency distribution of colonies was converted to estimated-age-frequency distribution using an estimated growth curve based on the net growth rate. The technique used revealed significant differences in population structure and the dynamics of gorgonian colonies, as the two transects appeared to be influenced by different environmental conditions. The recruitment also seemed to vary according to year and transect, resulting in different densities. Our work showed clear results in characterising the variations of gorgonian demographic evolution at a small spatial scale; thus, it is assumed that this method could be a sustainable tool for coastal environmental managers.

Process based model sheds light on climate sensitivity of Mediterranean tree-ring width

Abstract. We use the process-based VS (Vaganov-Shashkin) model to investigate whether a regional Pinus halepensis tree-ring chronology from Tunisia can be simulated as a function of climate alone by employing a biological model linking day length and daily temperature and precipitation (AD 1959–2004) from a climate station to ring-width variations. We check performance of the model on independent data by a validation exercise in which the model's parameters are tuned using data for 1982–2004 and the model is applied to generate tree-ring indices for 1959–1981. The validation exercise yields a highly significant positive correlation between the residual chronology and estimated growth curve (r=0.76 p<0.0001, n=23). The model shows that the average duration of the growing season is 191 days, with considerable variation from year to year. On average, soil moisture limits tree-ring growth for 128 days and temperature for 63 days. Model results depend on chosen values of parameters, in particular a parameter specifying a balance ratio between soil moisture and precipitation. Future work in the Mediterranean region should include multi-year natural experiments to verify patterns of cambial-growth variation suggested by the VS model.

Growth modeling of dairy heifers in Québec based on random regression

Cue, R. I., Pietersma, D., Lefebvre, D., Lacroix, R., Wade, K., Pellerin, D., de Passillé, A-M. and Rushen, J. 2012. Growth modeling of dairy heifers in Québec based on random regression. Can. J. Anim. Sci. 92: 33–47. A total of 144 006 weight (calculated from tape girth measurements) and height data records from Québec dairy heifers were analyzed using random regression to estimate growth curve parameters of Ayrshires, Brown Swiss and Holstein animals to permit prediction of individual heifer growth from 0 to 32 mo. There were, on average, 5.15 records per heifer (minimum 3 records, maximum 25 records). The body weight data were analyzed using linear and quadratic fixed and random regressions, with a power-of-the-mean (POM) function to model the residual variance. The POM was 1.2 for Holstein and Ayrshire and slightly less than 1 for Brown Swiss. Estimated body weight at 24 mo was 507, 564, 624 kg, for Ayrshires, Brown Swiss and Holstein, respectively. The height data were analyzed with a Brody, monomolecular non-linear growth curve model. Mature height was estimated to be 148 cm in both Holstein and Ayrshires, and 150 cm in Brown Swiss. Random regression models were shown to be able to predict individual growth, and can be incorporated in decision-support tools to help producers reducing the average age at first calving.

THE ESTIMATION OF GROWTH CURVE OF BALI CATTLE AT BONE AND BARRU DISTRICTS, SOUTH SULAWESI, INDONESIA USING TEN BODY MEASUREMENTS

The estimation of growth curves and mature size of ten body measurements, namely withers height,hip height, body length, chest girth, chest depth, chest width, rump length, hip width, thurl width, andpin bone width, were studied in Bali bulls and heifers at the age of 12, 15, 18, 21 and 24 months. 108bulls and 146 heifers at Bone district and 152 bulls and 110 heifers at Barru district, South Sulawesi,Indonesia were measured. The Brody growth function was fitted to each animal’s records and leastsquaresanalysis were used to investigate the effects of place, sex, and age to growth curve and maturesize of body measurements of Bali bulls and heifers. The result showed that the growth of bodymeasurements of Bali cattle until 24 months of age were still increasing and not reaching the mature sizeyet. The place, sex and age factors were significantly affected to the growth of body measurements ofBali cattle.

Estimation of growth curve parameters in Beetal goats

Abstract. Growth data from birth to one year of age on 120 Beetal goats, 30 animals on each farm, including Livestock Experiment Station (LES) Rakh Kheirewala, LES Rakh Ghulaman, LES Alladad and LPRI Bahadurnagar, Okara, Pakistan, were recorded and analysed for estimating growth curve parameters: predicted live weight, »a«, turning point of growth, »b« and rate of growth »k« by using Brody and Gompertz mathematical functions employing non-linear regression models. Estimates of the growth curve parameters »a«, »b« and »k« were 29.1, 0.916 and 0.108 for Brody and 23.4, 1.984 and 0.258 for Gompertz functions, respectively. The corresponding values of determination coefficient and mean absolute deviation for these models were 99.8 and 99.8 percent and 0.0061 and 0.0050, respectively. Flock significantly affected parameter »b« of Brody and Gompertz models. Sex did not affect any of the parameters in both models. Type of birth was a significant source of variation for parameter »b« in the Brody model. The determination coefficient showed that both the models efficiently explained the growth of Beetal kids.

Long-Term Influences of Intergenerational Ambivalence on Midlife Parents' Psychological Well-being

We investigated changes in midlife parents' intergenerational ambivalence toward a focal child and its influence on their psychological well-being over 14 years, as the focal child moved from adolescence into young adulthood. We estimated growth curve models using three waves of data from the National Survey of Families and Households (N = 1,510 parents aged 35–54 years at Time 1). Parental ambivalence declined over time, equally among mothers and fathers. The prediction from ambivalence theory that children's attainment of adult statuses reduces parental ambivalence received only modest support. Only the focal child's marriage reduced parental ambivalence. The focal child's lifestyle–behavioral problems during adolescence still elevated ambivalence 14 years later, albeit less so. For its part, intergenerational ambivalence counteracted trends toward declining depressive symptoms and greater happiness for mothers and fathers alike, and its effects remained constant over time.

Empirical Growth Curve Estimation Using Sigmoid Sub-functions that Adjust Seasonal Compensatory Growth for Male Body Weight of Thoroughbred Horses.

Thoroughbred horses are seasonal mating animals, raised in northern regions or countries. Foals born yearly in spring generally show a typical seasonal compensatory growth pattern, in which their growth rate declines in the first winter and increases in the next spring. In this study, a new empirical adjustment approach is proposed to adjust for this compensatory growth when growth curve equations are estimated, by using 1,633 male body weights of Thoroughbreds as an illustrating example. Based on general Richards growth curve equation, a new growth curve equation was developed and fit to the weight-age data. The new growth curve equation had a sigmoid sub-function that can adjust the compensatory growth, combined with the Richards biological parameter responsible for the maturity of animals. The unknown parameters included in the equations were estimated by SAS NLMIXED procedure. The goodness of fit was examined by using Akaike’s Information Criterion (AIC). The AIC values decreased from 13,053 (general Richards equation) to 12,794 (the newly developed equation), indicating the better fit of the new equation to the weight-age data. The shape of the growth curve was improved during the period of compensatory growth. The proposed method is one of the useful approaches for adjusting seasonal compensatory growth in growth curve estimations for Thoroughbreds, and for their management during the compensatory period. Based on this approach, the optimal growth curve equations can be estimated also for female body weight of Thoroughbreds or other growth traits affected by seasonal compensatory growth.

Military service and men's health trajectories in later life.

This study examines differences in the relationship between veteran status and men's trajectories of health conditions, activities of daily living limitations, and self-rated health. We use data on 12,631 men drawn from the 1992-2006 waves of the Health and Retirement Study to estimate growth curve models that examine differences in health trajectories between nonveterans and veterans, veterans with and without wartime service, and war service veterans who served during World War II, Korea, Vietnam, and multiple wars. The results indicate that veterans have better health at the mean age of 66.2 years, but experience greater age-related changes in health than nonveterans. Similarly, men who served during wartime have better health at the mean age, but more age-related changes in health than men who did not serve during wartime. Among war veterans, Vietnam veterans are in poorer health at the mean age, but they experience less substantial age-related health changes than men who served during previous wars. Although veterans experience better health relative to nonveterans around retirement age, they have poorer health than nonveterans among the oldest old. These findings inform our understanding of the veteran-nonveteran health-mortality paradox found in previous research and suggest a health crossover among veterans and nonveterans in later life.

Co‐occurring problems of early onset persistent, childhood limited, and adolescent onset conduct problem youth

It is increasingly recognized that youth who follow early onset persistent (EOP), childhood limited (CL) and adolescent onset (AO) trajectories of conduct problems show somewhat varying patterns of risk (in childhood) and adjustment problems (in adolescence and adulthood). Little, however, is known about how other adjustment problems differentially co-develop with the EOP, CL and AO trajectories across the childhood and adolescent years. Using data from the Avon Longitudinal Study of Parents and Children, an epidemiological, longitudinal cohort of boys and girls, we estimated growth curves for parent-reported hyperactivity, emotional difficulties, peer relational problems, and prosocial behaviors conditional on trajectories of conduct problems (i.e., EOP, CL and AO) from ages 4 to 13 years. At ages 7-8 years, DSM-IV-based diagnoses of conduct disorder, oppositional-defiant disorder, attention deficit/hyperactivity disorder (ADHD), anxiety, depression were examined by conduct problems trajectory. Overall, the development of hyperactivity, emotional difficulties, peer relational problems, and prosocial behaviors mirrored the development of conduct problems, showing similar trajectories. Results indicated that the problems of EOP youth were persistent across domains, CL youth showed decreased behavior problems while increasing in prosocial behaviors, and AO youth increased in adjustment problems after 10 years of age.