The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Monitoring the covariance matrix with the VMAX chart

In this article, we propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample vat-lances of the two quality characteristics, shortly VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar are faster detection of process changes and better diagnostic feature, that is, with the VMAX statistic It is easier to identify the out-of-control variable.

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimates of genetic parameters and eigenvector indices for milk production of Holstein cows

The objectives of the present study were to estimate genetic parameters of monthly test-day milk yield (TDMY) of the first lactation of Brazilian Holstein cows using random regression (RR), and to compare the genetic gains for milk production and persistency, derived from RR models, using eigenvector indices and selection indices that did not consider eigenvectors. The data set contained monthly TDMY of 3,543 first lactations of Brazilian Holstein cows calving between 1994 and 2011. The RR model included the fixed effect of the contemporary group (herd-month-year of test days), the covariate calving age (linear and quadratic effects), and a fourth-order regression on Legendre orthogonal polynomials of days in milk (DIM) to model the population-based mean curve. Additive genetic and nongenetic animal effects were fit as RR with 4 classes of residual variance random effect. Eigenvector indices based on the additive genetic RR covariance matrix were used to evaluate the genetic gains of milk yield and persistency compared with the traditional selection index (selection index based on breeding values of milk yield until 305 DIM). The heritability estimates for monthly TDMY ranged from 0.12 ± 0.04 to 0.31 ± 0.04. The estimates of additive genetic and nongenetic animal effects correlation were close to 1 at adjacent monthly TDMY, with a tendency to diminish as the time between DIM classes increased. The first eigenvector was related to the increase of the genetic response of the milk yield and the second eigenvector was related to the increase of the genetic gains of the persistency but it contributed to decrease the genetic gains for total milk yield. Therefore, using this eigenvector to improve persistency will not contribute to change the shape of genetic curve pattern. If the breeding goal is to improve milk production and persistency, complete sequential eigenvector indices (selection indices composite with all eigenvectors) could be used with higher economic values for persistency. However, if the breeding goal is to improve only milk yield, the traditional selection index is indicated. © 2013 American Dairy Science Association.

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

The genetic basis of academic achievement on the Queensland Core Skills Test and its shared genetic variance with IQ

First, this study examined genetic and environmental sources of variation in performance on a standardised test of academic achievement, the Queensland Core Skills Test (QCST) (Queensland Studies Authority, 2003a). Second, it assessed the genetic correlation among the QCST score and Verbal and Performance IQ measures using the Multidimensional Aptitude Battery (MAB), [Jackson, D. N. (1984) Multidimensional Aptitude Battery manual. Port Huron, MI:Research Psychologist Press, Inc.]. Participants were 256 monozygotic twin pairs and 326 dizygotic twin pairs aged from 15 to 18 years (mean 17 years +/- 0.4 [SD]) when achievement tested, and from 15 to 22 years (mean 16 years +/- 0.4 [SD]) when IQ tested. Univariate analysis indicated a heritability for the QCST of 0.72. Adjustment to this estimate due to truncate selection (downward adjustment) and positive phenotypic assortative mating (upward adjustment) suggested a heritability of 0.76 The phenotypic (0.81) and genetic (0.91) correlations between the QCST and Verbal IQ (VIQ) were significantly stronger than the phenotypic (0.57) and genetic (0.64) correlations between the QCST and Performance IQ (PIQ). The findings suggest that individual variation in QCST performance is largely due to genetic factors and that common environmental effects may be substantially accounted for by phenotypic assortative mating. Covariance between academic achievement on the QCST and psychometric IQ (particularly VIQ) is to a large extent due to common genetic influences.

Dissecting the complex genetic basis of mate choice

The genetic analysis of mate choice is fraught with difficulties. Males produce complex signals and displays that can consist of a combination of acoustic, visual, chemical and behavioural phenotypes. Furthermore, female preferences for these male traits are notoriously difficult to quantify. During mate choice, genes not only affect the phenotypes of the individual they are in, but can influence the expression of traits in other individuals. How can genetic analyses be conducted to encompass this complexity? Tighter integration of classical quantitative genetic approaches with modern genomic technologies promises to advance our understanding of the complex genetic basis of mate choice.

Large body size in an island-dwelling bird : a microevolutionary analysis

Island races of passerine birds display repeated evolution towards larger body size compared with their continental ancestors. The Capricorn silvereye (Zosterops lateralis chlorocephalus) has become up to six phenotypic standard deviations bigger in several morphological measures since colonization of an island approximately 4000 years ago. We estimated the genetic variance-covariance (G) matrix using full-sib and 'animal model' analyses, and selection gradients, for six morphological traits under field conditions in three consecutive cohorts of nestlings. Significant levels of genetic variance were found for all traits. Significant directional selection was detected for wing and tail lengths in one year and quadratic selection on culmen depth in another year. Although selection gradients on many traits were negative, the predicted evolutionary response to selection of these traits for all cohorts was uniformly positive. These results indicate that the G matrix and predicted evolutionary responses are consistent with those of a population evolving in the manner observed in the island passerine trend, that is, towards larger body size.

Yellow perch strain evaluation I: Genetic variance of six broodstock populations

As a prelude to strain selection for domestication and future marker assisted selection, genetic variation revealed by microsatellite DNA was evaluated in yellow perch, Perca flavescens, from four wild North American populations collected in 2003-2004 (Maine, New York, North Carolina, and Pennsylvania,), and two captive populations (Michigan and Ohio). For the loci examined, levels of heterozygosity ranged from H-e=0.04 to 0.88, genetic differentiation was highly significant among all population pairs, and effective migration ranged from low (N(e)m=0.3) to high (N(e)m=4.5). Deviation from Hardy-Weinberg equilibrium was regularly observed indicating significant departures from random mating. Instantaneous measures of inbreeding within these populations ranged from near zero to moderate (median F=0.16) and overall inbreeding levels averaged F-IS=0.18. Estimates of genetic diversity, Phi(ST), and genetic distance were highest between Michigan and all other broodstock groups and lowest between New York and Ohio. Genetic differentiation among groups did not correlate with geographic distance. Overall, the patterns of variation exhibited by the captive (Michigan and Ohio) populations were similar to patterns exhibited by the other wild populations, indicating that spawning and management practices to date have not significantly reduced levels of genetic variation. (C) 2007 Elsevier B.V. All rights reserved.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

Background: Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike’s information criterion using h-likelihood to select the best fitting model. Methods: We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike’s information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters. Results: Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike’s information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed. Conclusion: The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

Variance-covariance based weighing for neural network ensembles

Neural network (NN) is a popular artificial intelligence technique for solving complicated problems due to their inherent capabilities. However generalization in NN can be harmed by a number of factors including parameter's initialization, inappropriate network topology and setting parameters of the training process itself. Forecast combinations of NN models have the potential for improved generalization and lower training time. A weighted averaging based on Variance-Covariance method that assigns greater weight to the forecasts producing lower error, instead of equal weights is practiced in this paper. While implementing the method, combination of forecasts is done with all candidate models in one experiment and with the best selected models in another experiment. It is observed during the empirical analysis that forecasting accuracy is improved by combining the best individual NN models. Another finding of this study is that reducing the number of NN models increases the diversity and, hence, accuracy.