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Multivariate functional data often present theoretical and practical complications which are not found in their univariate functional counterparts. One of these is a situation where the component functions of multivariate functional data are subject to mutual time warping. That is, the component processes exhibit a similar shape but are subject to systematic phase variation across their time domains. This dissertation addresses this previously unconsidered mode of warping with the introduction of multivariate time warping models which rely on either time-shifting or nonlinear time-distortion frameworks.In the first chapter, we introduce a shift-warping model for multivariate time relations. This model is motivated by the Zürich longitudinal growth dataset, in which the growth trajectories for multiple body parts were observed from birth to adulthood for a sample of children. The proposed method differs from existing registration methods for functional data in a fundamental way. Namely, instead of focusing on the traditional approach to warping, where one aims to recover individual-specific registration, this technique focuses on shift registration across the components of a multivariate functional data vector on a population-wide level. After applying the method to the Zürich data, we find that there exists an archetypal ordering of pubertal growth spurts across modalities: on average, legs tend to experience peak growth velocity approximately a half a year before standing height and arms, which themselves tend to precede the growth spurt of the spine by half a year. Our proposed estimates for these shifts are identifiable, enjoy parametric rates of convergence, and often have intuitive physical interpretations, all in contrast to traditional curve-specific registration approaches.Finite sample properties of these estimators were also investigated in simulation studies. The second chapter of this dissertation introduces the Latent Transport Model for multivariate functional data. This model widens the class of possible cross-component warps from simple shifts to flexible and nonlinear transport functions. The proposed approach combines a random amplitude factor for each component with population-based registration across the components of a multivariate functional data vector. It also includes a latent population function, which corresponds to a common underlying trajectory as well as a subject-specific warping component. This model allows for meaningful interpretation and is well suited to represent functional vector data. We also propose estimators for all components of the model, which not only lead to a novel representation for multivariate functional data, but can also be used in downstream analyses like Fréchet regression. Rates of convergence are established when curves are fully observed or observed with measurement error. The usefulness of the model, interpretations, and practical aspects are illustrated in simulations and with application to multivariate human growth curves as well as multivariate environmental pollution data.

A novel parametric regression model is proposed to fit incidence data typically collected during epidemics. The proposal is motivated by real-time monitoring and short-term forecasting of the main epidemiological indicators within the first outbreak of COVID-19 in Italy. Accurate short-term predictions, including the potential effect of exogenous or external variables are provided. This ensures to accurately predict important characteristics of the epidemic (e.g., peak time and height), allowing for a better allocation of health resources over time. Parameter estimation is carried out in a maximum likelihood framework. All computational details required to reproduce the approach and replicate the results are provided. publishedVersion

Brazil is the world’s largest sugarcane producer (Saccharum spp.), followed by India and China. In 2019, Brazil produced 642.7 million tons of sugarcane, having collected 1.44 billion and 983.52 million dollars from sugar and ethanol exports, respectively. For crop management, it is important to monitor plant growth, duration of growth phases and point of physiological maturation. The aim of this study was to evaluate the fit of nonlinear Logistic, Gompertz, Brody and von Bertalanffy models to the height and diameter growth of ratoon cane stalk RB92579 variety, considering age in days. The parameters of models were estimated using R software routines, applying the least squares method and the iterative Gauss-Newton process. The adjustment of models was compared using the following evaluators: determination coefficient (R2), residual standard deviation (RSD) and corrected Akaike information criterion (AICc). In all models, parameters were significant by the t test at 1% level, except for the Brody model. When using the Shapiro-Wilk, Durbin-Watson and Breusch-Pagan tests, it was found that residues were normal, homoscedastic and independent at 1% significance level. All models fitted well to data, except for the Brody model for stalk height. Based on results, the Gompertz and Logistic models presented higher R2 values and lower RSD and AICc values; thus, it could be concluded that these models are suitable to describe the height and diameter of sugarcane RB92579 cultivar, respectively.

The aim of the present study was to determine the best non-linear growth function to describe the growth of Kajli sheep. For this aim, the Brody, von Bertalanffy, Logistic, and Gompertz models were used to describe the sigmoidal relationship between bodyweight and age of the Kajli sheep. The records obtained from the Livestock Experiment Station, Khushab, were collected between 2007 and 2018. The records comprised 9864 age-weight observations (300 for male, 9564 for female, 7392 for single, 2388 for twin, and 84 for triplet lambs), which extended from birth to 12 months old. Candidate non-linear functions were fitted and the curve parameters were estimated by nlsfit (fit non-linear models) function in R statistical package, version 3.6.1. Goodness of fit criteria that were used to evaluate predictive performances of candidate models were adjusted coefficient of determination (R2adj), Akaike’s information criterion (AIC), Bayesian information criterion (BIC) and root means square error (RMSE). The Brody model was the best non-linear function that described the biological growth pattern of all, male, female, single, twin, and triplet lambs. Differences in curve parameter estimates between male and female suggested a definite pattern of sexual dimorphism. Moreover, a higher estimate of rate of maturity in female lambs reflects their early maturity compared with male Kajli lambs. Similarly, the single-born Kajli animals with highest maturity rate were maturing at an earlier age than twins and triplets. This is the first report on the non-linear pattern of visible changes in bodyweight of Kajli sheep from birth to 12 months old.Key words: age, bodyweight, growth curves, regression, sheep

We propose analyzing our data with a model that exhibits errors-in-variables (EIV) in auxiliary information and which has an autoregressive covariance structure using a Bayesian methodology. The incorporation of these components into a model is often necessary and realistic in the study of many statistical problems. However, such an analysis usually mandates many simplifying and restrictive assumptions, especially when using a traditional probabilistic approach. Much research has been accumulated in this area. We will show that by taking a Bayesian approach, we can effectively deal with the complexity of these types of models. Such an approach cannot be found in the literature. In fitting statistical models for the analysis of growth data, many curves and/or models have been proposed. We have collected an exhaustive list of the most important and frequently used growth curves, some of which are used in our model analysis. A motivating example is presented to show the applicability of our general approach. In addition, auxiliary covariates, both qualitative and quantitative, can be added into our model as an extension. These EIV growth curves with auxiliary covariates provide a very general framework for practical application. We give several illustrative examples demonstrating how a Bayesian approach using MCMC (Metropolis Hastings in Gibbs sampler) techniques and goodness of fit statistics for model selections can be utilized in our analysis. Highest Density Regions (HDR's) are also used to facilitate Bayesian estimation and inference in these examples. Multivariate growth curve models are presented and detailed to study the relationship of the variables in models.In the final chapter, we present growth curve models with auxiliary variables containing uncertain data distributions (i.e. mixtures of standard components, such as normal distributions) using Dirichlet Process Priors (DPP, which are composed of discrete and continuous components). We show that DPPs are appropriate in determining the number of components and in estimating the parameters simultaneously, and are especially useful and advantageous in the aforementioned multimodal scenario with respect to the goodness of fit of the model.

Background: Genomic growth curves are generally defined only in terms of population mean; an alternative approach that has not yet been exploited in genomic analyses of growth curves is the Quantile Regression (QR). This methodology allows for the estimation of marker effects at different levels of the variable of interest. We aimed to propose and evaluate a regularized quantile regression for SNP marker effect estimation of pig growth curves, as well as to identify the chromosome regions of the most relevant markers and to estimate the genetic individual weight trajectory over time (genomic growth curve) under different quantiles (levels). Results: The regularized quantile regression (RQR) enabled the discovery, at different levels of interest (quantiles), of the most relevant markers allowing for the identification of QTL regions. We found the same relevant markers simultaneously affecting different growth curve parameters (mature weight and maturity rate): two (ALGA0096701 and ALGA0029483) for RQR(0.2), one (ALGA0096701) for RQR(0.5), and one (ALGA0003761) for RQR(0.8). Three average genomic growth curves were obtained and the behavior was explained by the curve in quantile 0.2, which differed from the others. Conclusions: RQR allowed for the construction of genomic growth curves, which is the key to identifying and selecting the most desirable animals for breeding purposes. Furthermore, the proposed model enabled us to find, at different levels of interest (quantiles), the most relevant markers for each trait (growth curve parameter estimates) and their respective chromosomal positions (identification of new QTL regions for growth curves in pigs). These markers can be exploited under the context of marker assisted selection while aiming to change the shape of pig growth curves. Made available in DSpace on 2018-01-03T23:20:13Z (GMT). No. of bitstreams: 1 2017M.DeonJASBRegularized.pdf: 529201 bytes, checksum: f7a0a79c7f5c710e225da410f3ac2a5b (MD5) Previous issue date: 2018-01-03

A normal semiparametric mixture regression model is proposed for longitudinal data. The proposed model contains one smooth term and a set of possible linear predictors. Model terms are estimated using the penalized likelihood method with the EM algorithm. A computationally feasible alternative method that provides an approximate solution is also introduced. Simulation experiments and a real data example are used to illustrate the methods.

Bu çalışmada Şanlıurfa'da yetiştiriciliği yapılan Şarole ve Esmer erkek sığırlarda Bertalanffy modeli kullanılarak büyüme ve gelişme özelliklerinin tahminlenmesi ve elde edilen parametreler ile iki ırkın Şanlıurfa koşullarında besi performanslarının karşılaştırılma olanakları araştırılmıştır. Çalışmada Şanlıurfa'da bulunan özel bir besi işletmesinde 2008-2009 yılları arasında tutulmuş hiçbir sağlık problemi olmadığı gözlenen 30 Şarole ve 32 adet Esmer sığıra ait periyodik tartım kayıtları kullanılmıştır. Her iki ırka mensup hayvan guruplarında tartım günleri ve tartım sonucu kaydedilen ağırlıkların Bertalanffy modeline direk uyumu yapılmış ve model parametreleri her iki ırk grubu için ayrı ayrı tahminlenmiştir. Bundan sonraki aşamada ise ilgili modelde 30 günlük aralıklarla 270. güne kadar canlı ağırlık, erginleşme oranı ve mutlak büyüme hızı değerleri her iki ırk grubu içinde ayrı olarak tekrar tahmin edilmiştir. Araştırma sonucunda her iki ırk için tüm tahmin edilen özelliklere ilişkin ortalamalar arasındaki farkların istatistiksel olarak önemsiz olduğu görülmüştür (P > 0.01).Bu araştırma ile büyüme eğrisi modelleri kullanılarak besi sığırlarında besi performanslarının karşılaştırılabileceği gösterilmiştir. In this study, growth and growing characteristics of Charolais and Brown Swiss beef cattle, bred in Sanliurfa province, was predicted the using Bertalanffy growth model and searched the possibilities of comparing of fattening performance of Charolais and Brown Swiss beef cattle using these obtained parameters from the model. Periodical live weight records of healthy 30 Charolais and 32 Brown Swiss beef cattle which were recorded between 2008-2009 years were used in this research and these records obtained from a commercial farm placed in Sanliurfa. Using Bertalanffy growth model test days and live weights were fitted for the different two cattle breeds groups and parameters of model were predicted for the breed groups. The next step, live weight, maturing rate and absolute growth rate were predicted using model parameters throughout 270 days with 30 days periods for two cattle breed groups separately. At the end of research, considering the predicted characteristics for the cattle breeds, difference of between the means of groups were not statistically significant (P > 0.01).With this research it was shown that able to comparison of the fattening performances of beef cattle using growth curve models. 42

SUMMARYThe objective of the current study was to assess the use of nonlinear mixed model methodology to fit the growth curves (weightv.time) of two dairy goat genotypes (Alpine, +A and Saanen, +S). The nonlinear functions evaluated included Brody, Von Bertalanffy, Richards, Logistic and Gompertz. The growth curve adjustment was performed using two steps. First, random effectsu1,u2andu3were linked to the asymptotic body weight (β1), constant of integration (β2) and rate constant of growth (β3) parameters, respectively. In addition to a traditional fixed-effects model, four combinations of models were evaluated using random variables: all parameters associated with random effects (u1,u2andu3), onlyβ1andβ2(u1andu2), onlyβ1andβ3(u1andu3) and onlyβ1(u1). Second, the fit of the best adjusted model was refined by using the power variance and modelling the error structure. Residual variance ($\sigma _e^2 $) and the Akaike information criterion were used to evaluate the models. After the best fitting model was chosen, the genotype curve parameters were compared. The residual variance was reduced in all scenarios for which random effects were considered. The Richards (u1andu3) function had the best fit to the data. This model was reparameterized using two isotropic error structures for unequally spaced data, and the structure known in the literature as SP(MATERN) proved to be a better fit. The growth curve parameters differed between the two genotypes, with the exception of the constant that determines the proportion of the final size at which the inflection point occurs (β4). The nonlinear mixed model methodology is an efficient tool for evaluating growth curve features, and it is advisable to assign biologically significant parameters with random effects. Moreover, evaluating error structure modelling is recommended to account for possible correlated errors that may be present even when using random effects. Different Richard growth curve parameters should be used for the predominantly Alpine and Saanen genotypes because there are differences in their growth patterns.

14 páginas, 3 figuras, 2 tablas.

We develop a Bayesian nonparametric framework for modeling ordinal regression relationships, which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length, and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut-off points relating the latent continuous and ordinal responses. A novel-dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along th...

Motivation: Diseases 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. Results: We 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 todisease 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. Availability: Software 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. © 2014 The Alzheimer's Association.

Microtubules are part of the structural network within a cell's cytoplasm, providing structural support as well as taking part in many of the cellular processes. A large body of data provide evidence that dynamics of microtubules in a cell is reponsible for the performance of many critical cellular functions such as cell division. In this article, we study the effect of four different isoforms of a protein tau on microtubule dynamics using growth curve models. The results show that a linear growth curve model is sufficient to explain the data. Moreover, we find that a mutated version of a 3-repeat tau protein has a similar effect as a 4-repeat tau protein on microtubule dynamics. The latter findings conform with the biological understanding of the effect of the protein tau on microtubule dynamics. © 2009 Taylor & Francis.

Infant size at birth is a useful indicator to evaluate fetal growth in relation to gestational age. There is no standard model to create anthropometric reference curves in neonates, but the method chosen could determine the reference values estimated. We describe the methods used to construct population-based reference curves of birth weight for gestational age in Catalonia, Spain. These methods included detection of implausible values of birth weight for gestational age by a probabilistic cluster model, utilization of the Generalized Additive Model for Location and Scale method to obtain smoothed percentiles and z-scores, and calculation of 95% confidence intervals by bootstrapping. To our knowledge, these are the first reference curves in neonates constructed through a method allowing asymmetric distributions with kurtosis to be modelled. Estimation of confidence intervals is useful to determine which reference intervals can be employed to assess newborn size. (c) 2007 SESPAS. Published by Elsevier Espana, S.L. All rights reserved.

Reference growth curves estimate the distribution of a measurement as it changes according to some covariate, often age. We present a new methodology to estimate growth curves based on mixture models and splines. We model the distribution of the measurement with a mixture of normal distributions with an unknown number of components, and model dependence on the covariate through the weights, using smooth functions based on B-splines. In this way the growth curves respect the continuity of the covariate and there is no need for arbitrary grouping of the observations. The method is illustrated with data on triceps skinfold in Gambian girls and women.

International audience; A heteroskedastic random coefficients model was described for analyzing weight performances between the 100th and the 650th days of age of Maine-Anjou beef cattle. This model contained both fixed effects, random linear regression and heterogeneous variance components. The objective of this study was to analyze the difference of growth curves between animals born as twin and single bull calves. The method was based on log-linear models for residual and individual variances expressed as functions of explanatory variables. An expectation-maximization (EM) algorithm was proposed for calculating restricted maximum likelihood (REML) estimates of the residual and individual components of variances and covariances. Likelihood ratio tests were used to assess hypotheses about parameters of this model. Growth of Maine-Anjou cattle was described by a third order regression on age for a mean growth curve, two correlated random effects for the individual variability and independent errors. Three sources of heterogeneity of residual variances were detected. The difference of weight performance between bulls born as single and twin bull calves was estimated to be equal to about 15 kg for the growth period considered.

Between 1982 and 1988 a growth study was carried out at the Division of Pediatric Oncology of the University Hospital of Groningen. A special feature of the project was that sample sizes are small and that ages at entry may be very different. In addition the intended design was not fully complied with. This paper highlights some aspects of the statistical analysis which is based on (1) reference scores, (2) statistical procedures allowing for an irregular pattern of measurement times caused by missing data and shifted measurement times.

Four topics, selected from the range of statistical subjects with current relevance for agricultural research are considered. The first is concerned with the need and usefulness of efficient incomplete block designs for any number of treatments, either equireplicate or with different number of replicates. The second one is a presentation of linear prediction procedures for phenomena with spatially random behaviour and its generalization towards kriging. Next, a reparametrization of a general four–parameter family of growth curves is recommended, leading to numerically stable parameter estimation for RICHARDS' functions and additional special cases. Finally, the modelling of factorials with continuous response and of log–linear relationships for frequencies is proposed to be handled on the same footing, with preference for an alternative criteria of model deviance over test critera or Cp–like measures.

In recent years, nonparametric curve estimates have been extensively explored in theoretical work. There has, however, been a certain lack of convincing applications, in particular involving comparisons with parametric techniques. The present investigation deals with the analysis of human height growth, where longitudinal measurements were collected for a sample of boys and a sample of girls. Evidence is presented that kernel estimates of acceleration and velocity of height, and of height itself, might offer advantages over a parametric fitting via functional models recently introduced. For the specific problem considered, both approaches are biased, but the parametric one shows qualitative and quantitative distortion which both are not easily predictable. Data-analytic problems involved with kernel estimation concern the choice of kernels, the choice of the smoothing parameter, and also whether the smoothing parameter should be chosen uniformly for all subjects or individually.

Let $M \in M(m, p)$ be the matrix of means of interest in the GMANOVA problem. Our main results characterize all confidence sets for $M$ in a given class (invariant plus a weak additional restriction) that are exact for the families of parametric functions $a'Mb$ for all $a \in \mathbb{R}^m, b \in \mathbb{R}^p$ and $\operatorname{tr} N'M$ for all $N \in M(m, p)$. The corresponding families of smallest exact simultaneous confidence intervals are also given. Similar results are obtained for the MANOVA problem under triangular group reduction.