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## Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

BIGNARDI, A. B.; FARO, L. El; CARDOSO, V. L.; MACHADO, P. F.; ALBUQUERQUE, L. G.
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.04%
The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.; State of Sao Paulo Research Foundation (Fapesp); National Council of Technological and Scientific Development (CNPq)

## Covariance structure in the skull of Catarrhini: a case of pattern stasis and magnitude evolution

OLIVEIRA, Felipe Bandoni de; PORTO, Arthur; MARROIG, Gabriel
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.24%
The study of the genetic variance/covariance matrix (G-matrix) is a recent and fruitful approach in evolutionary biology, providing a window of investigating for the evolution of complex characters. Although G-matrix studies were originally conducted for microevolutionary timescales, they could be extrapolated to macroevolution as long as the G-matrix remains relatively constant, or proportional, along the period of interest. A promising approach to investigating the constancy of G-matrices is to compare their phenotypic counterparts (P-matrices) in a large group of related species; if significant similarity is found among several taxa, it is very likely that the underlying G-matrices are also equivalent. Here we study the similarity of covariance and correlation structure in a broad sample of Old World monkeys and apes (Catarrhini). We made phylogenetically structured comparisons of correlation and covariance matrices derived from 39 skull traits, ranging from between species to the superfamily level. We also compared the overall magnitude of integration between skull traits (r(2)) for all Catarrhim genera. Our results show that P-matrices were not strictly constant among catarrhines, but the amount of divergence observed among taxa was generally low. There was significant and positive correlation between the amount of divergence in correlation and covariance patterns among the 30 genera and their phylogenetic distances derived from a recently proposed phylogenetic hypothesis. Our data demonstrate that the P-matrices remained relatively similar along the evolutionary history of catarrhines...

## Análise de modelos lineares mistos com um fator longitudinal quantitativo e um qualitativo ordinal; Analysis of linear mixed models with one quantitative and one ordinal qualitative longitudinal factor

Maestre, Marina Rodrigues
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
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Os experimentos agronômicos que envolvem somente um fator longitudinal são bastante comuns. No entanto, existem casos em que as observações são tomadas considerando dois ou mais desses fatores, como nos casos em que são feitas medidas de uma variável resposta em profundidades diferentes ao longo do tempo, por exemplo. Admite-se que essas observações, tomadas de modo sistemático em cada unidade experimental, sejam correlacionadas e as variâncias nos diferentes níveis do fator longitudinal sejam heterogêneas. Com o uso de modelos mistos, essa correlação entre medidas repetidas e a heterogeneidade de variâncias podem ser modeladas convenientemente. Para que esses modelos sejam ajustados a um conjunto de dados envolvendo presença de dois fatores longitudinais, existe a necessidade de se adaptarem algumas estruturas de variâncias e covariâncias que são comuns em experimentos com somente um fator longitudinal. O objetivo do presente trabalho é utilizar a classe dos modelos lineares mistos para estudar a massa seca de raiz no solo de uma plantação de cana-de-açúcar. O experimento foi casualizado em blocos e as parcelas receberam quatro doses de nitrogênio. Foram feitas medidas repetidas ao longo de dois fatores longitudinais...

## Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures and Instrumental Variables

Ramalho, Joaquim
Tipo: Trabalho em Andamento
ENG
Relevância na Pesquisa
56.07%
It is now widely recognized that the most commonly used efficient two-step GMM estimator may have large bias in small samples. This problem has motivated the search for alternative estimators with better finite sample properties. Two classes of alternatives are considered in this paper. The first includes estimators which are asymptotically first-order equivalent to the GMM estimator, namely the continuous-updating, exponential tilting, and empirical likelihood estimators. Analytical and bootstrap bias-adjusted GMM estimators form the second class of alternatives. Two extensive Monte Carlo simulation studies are conducted in this paper for covariance structure and instrumental variable models. We conclude that all alternative estimators offer much reduced bias as compared to the GMM estimator, particularly the empirical likelihood and some of the bias-corrected GMM estimators analyzed.

## A simulation study of the effects of assignment of prior identity-by-descent probabilities to unselected sib pairs, in covariance-structure modeling of a quantitative-trait locus.

Dolan, C V; Boomsma, D I; Neale, M C
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.11%
Sib pair-selection strategies, designed to identify the most informative sib pairs in order to detect a quantitative-trait locus (QTL), give rise to a missing-data problem in genetic covariance-structure modeling of QTL effects. After selection, phenotypic data are available for all sibs, but marker data-and, consequently, the identity-by-descent (IBD) probabilities-are available only in selected sib pairs. One possible solution to this missing-data problem is to assign prior IBD probabilities (i.e., expected values) to the unselected sib pairs. The effect of this assignment in genetic covariance-structure modeling is investigated in the present paper. Two maximum-likelihood approaches to estimation are considered, the pi-hat approach and the IBD-mixture approach. In the simulations, sample size, selection criteria, QTL-increaser allele frequency, and gene action are manipulated. The results indicate that the assignment of prior IBD probabilities results in serious estimation bias in the pi-hat approach. Bias is also present in the IBD-mixture approach, although here the bias is generally much smaller. The null distribution of the log-likelihood ratio (i.e., in absence of any QTL effect) does not follow the expected null distribution in the pi-hat approach after selection. In the IBD-mixture approach...

## A Covariance Structure Model for the Admixture of Binary Genetic Variation

Grote, Mark N.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.01%
I derive a covariance structure model for pairwise linkage disequilibrium (LD) between binary markers in a recently admixed population and use a generalized least-squares method to fit the model to two different data sets. Both linked and unlinked marker pairs are incorporated in the model. Under the model, a pairwise LD matrix is decomposed into two component matrices, one containing LD attributable to admixture, and another containing, in an aggregate form, LD specific to the populations forming the mixture. I use population genetics theory to show that the latter matrix has block-diagonal structure. For the data sets considered here, I show that the number of source populations can be determined by statistical inference on the canonical correlations of the sample LD matrix.

## Use of the score test as a goodness-of-fit measure of the covariance structure in genetic analysis of longitudinal data

Jaffrézic, Florence; White, Ian MS; Thompson, Robin
Fonte: BioMed Central Publicador: BioMed Central
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.11%
Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.

## Nonparametric Modeling of Longitudinal Covariance Structure in Functional Mapping of Quantitative Trait Loci

Yap, John Stephen; Fan, Jianqing; Wu, Rongling
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.17%
Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points. Specifically, we adopt Huang et al.’s (2006a) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an L2 penalty. This approach, embedded within a mixture likelihood framework, leads to enhanced accuracy, precision and flexibility of functional mapping while preserving its biological relevance. Simulation studies are performed to reveal the statistical properties and advantages of the proposed method. A real example from a mouse genome project is analyzed to illustrate the utilization of the methodology. The new method will provide a useful tool for genome-wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture...

## Developmental plasticity in covariance structure of the skull: effects of prenatal stress

Gonzalez, Paula N; Hallgrímsson, Benedikt; Oyhenart, Evelia E
Fonte: Blackwell Science Inc Publicador: Blackwell Science Inc
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.28%
Environmental perturbations of many kinds influence growth and development. Little is known, however, about the influence of environmental factors on the patterns of phenotypic integration observed in complex morphological traits. We analyze the changes in phenotypic variance–covariance structure of the rat skull throughout the early postnatal ontogeny (from birth to weaning) and evaluate the effect of intrauterine growth retardation (IUGR) on this structure. Using 2D coordinates taken from lateral radiographs obtained every 4 days, from birth to 21 days old, we show that the pattern of covariance is temporally dynamic from birth to 21 days. The environmental perturbation provoked during pregnancy altered the skull growth, and reduced the mean size of the IUGR group. These environmental effects persisted throughout lactancy, when the mothers of both groups received a standard diet. More strikingly, the effect grew larger beyond this point. Altering environmental conditions did not affect all traits equally, as revealed by the low correlations between covariance matrices of treatments at the same age. Finally, we found that the IUGR treatment increased morphological integration as measured by the scaled variance of eigenvalues. This increase coincided and is likely related to an increase in morphological variance in this group. This result is expected if somatic growth is a major determinant of covariance structure of the skull. In summary...

## Constrained Maximum Likelihood Estimation for Two-level Mean and Covariance Structure Models2

Bentler, Peter M.; Liang, Jiajuan; Tang, Man-Lai; Yuan, Ke-Hai
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.97%
Maximum likelihood is commonly used for estimation of model parameters in analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in maximum likelihood analysis. Nonlinear constraints could be encountered in complicated applications. In this paper we develop an EM-type algorithm for estimating model parameters with both linear and nonlinear constraints. The empirical performance of the algorithm is demonstrated by a Monte Carlo study. Application of the algorithm for linear constraints is illustrated by setting up a two-level mean and covariance structure model for a real two-level data set and running an EQS program.

## Modelling marginal covariance structures in linear mixed models

MacKenzie, Gilbert; Pan, Jianxin
Tipo: info:eu-repo/semantics/conferenceObject; all_ul_research; ul_published_reviewed
ENG
Relevância na Pesquisa
46.17%
peer-reviewed; Pourahmadi (1999) provided a convenient reparameterisation of the marginal covariance matrix arising in longitudinal studies. We exploit his work to model the dependence of this covariance structure on baseline covariates, time and their interaction. The rationale for this approach is the realisation that in linear mixed models (LMMs) the assumption of a homogeneous covariance structure with respect to the covariate space is a testable model choice. Accordingly, we provide methods for testing this assumption and re-analyse Kenward’s (1987) cattle data set using our new model.

## Modelling of covariance structure in constrained marginal models for longitudinal data

Xu, Jing; MacKenzie, Gilbert
Tipo: info:eu-repo/semantics/conferenceObject; all_ul_research; ul_published_reviewed
ENG
Relevância na Pesquisa
45.98%
peer-reviewed; A data-driven method for modelling intra-subject covariance matrix is introduced to constrained marginal models with longitudinal data. A constrained iteratively re-weighted least squares algorithm is presented consequently. Asymptotic properties of the constrained ML estimates, including strong consistency, approximate representation and asymptotic distribution, are given. Real data analysis and simulations are conducted to compare our new approach with classical menu-selection-based modelling technique.

## Modelling covariance structure in bivariate marginal models for longitudinal data

Xu, Jing; MacKenzie, Gilbert
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: info:eu-repo/semantics/article; all_ul_research; ul_published_reviewed
ENG
Relevância na Pesquisa
46.11%
peer-reviewed; It can be more challenging and demanding to efficiently model the covariance matrices for multivariate longitudinal data than for univariate case because of the correlations between responses arising from multiple variables and repeated measurements over time. In addition to the more complicated covariance structures, the positive-definiteness constraint is still the major obstacle in modelling covariance matrices as in univariate case. In this paper, we develop a data-based method to model the covariance structures. Using this method, the constrained and hard-to-model parameters of ∑i are traded in for uncon- strained and interpretable parameters. Estimates of these parameters, together with the parameters in the mean, are obtained by maximum likelihood approach, and the large- sample asymptotic properties are derived when the observations are normally distributed. A simulation is carried out to illustrate the asymptotics. Application to a set of bivariate visual data shows that our method performs very well even when modelling bivariate nonstationary dependence structures.

## The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure

Davies, C.E.; Glonek, G.F.; Giles, L.C.
Fonte: SAGE Publications Publicador: SAGE Publications
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.2%
One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost; Christopher E Davies...

## Some remarks on estimating a covariance structure model from a sample correlation matrix

Tipo: Trabalho em Andamento Formato: application/octet-stream; application/octet-stream; application/pdf
Relevância na Pesquisa
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A popular model in structural equation modeling involves a multivariate normal density with a structured covariance matrix that has been categorized according to a set of thresholds. In this setup one may estimate the covariance structure parameters from the sample tetrachoricl polychoric correlations but only if the covariance structure is scale invariant. Doing so when the covariance structure is not scale invariant results in estimating a more restricted covariance structure than the one intended. When the covariance structure is not scale invariant, then the model parameters must be estimated jointly from the sample thresholds and tetrachoricl polychoric correlations. In general, when fitting a covariance structure from a sample correlation matrix one should consider the population correlation structure under the null hypothesis. This is obtained by pre and post-multiplying the covariance structure by a diagonal matrix consisting of the inverse of the square root of the diagonal of the covariance structure under consideration. We provide computer algebra code for assessing whether a covariance structure is scale invariant and for assessing the identification of threshold and correlation structures.

MacKenzie, Gilbert
Tipo: info:eu-repo/semantics/conferenceObject; all_ul_research; ul_published_reviewed
ENG
Relevância na Pesquisa
46.2%
peer-reviewed; Conventionally, in longitudinal studies, the mean structure has been thought to be more important than the covariance structure between the repeated measures on the same individual. Often, it has been argued that, with re- spect to the mean, the covariance was merely a nuisance parameter' and, consequently, was not of scientific interest'. Today, however, one can see that from a formal statistical standpoint, the inferential problem is entirely symmetric in both parameters. In recent years there has been a steady stream of new results and we pause to review some key advances in the expanding field of covariance modelling, In particular, developments since the seminal work by Pourahmadi (1999, 2000) are traced. While the main focus is on longitudinal data with continuous responses, emerging approaches to joint mean-covariance modelling in the GEE, and GLMM arenas are also considered briefly.

## The beak of the other finch: coevolution of genetic covariance structure and developmental modularity during adaptive evolution

Fonte: The Royal Society Publicador: The Royal Society
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.11%
The link between adaptation and evolutionary change remains the most central and least understood evolutionary problem. Rapid evolution and diversification of avian beaks is a textbook example of such a link, yet the mechanisms that enable beak's precise adaptation and extensive adaptability are poorly understood. Often observed rapid evolutionary change in beaks is particularly puzzling in light of the neo-Darwinian model that necessitates coordinated changes in developmentally distinct precursors and correspondence between functional and genetic modularity, which should preclude evolutionary diversification. I show that during first 19 generations after colonization of a novel environment, house finches (Carpodacus mexicanus) express an array of distinct, but adaptively equivalent beak morphologies—a result of compensatory developmental interactions between beak length and width in accommodating microevolutionary change in beak depth. Directional selection was largely confined to the elimination of extremes formed by these developmental interactions, while long-term stabilizing selection along a single axis—beak depth—was mirrored in the structure of beak's additive genetic covariance. These results emphasize three principal points. First...

## Tests for Large Dimensional Covariance Structure Based on Rao's Score Test

Jiang, Dandan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.17%

## Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure

Choi, Myung Jin; Chandrasekaran, Venkat