On the Probability of a Negative Estimator of Heteroscedasticity in the Random Coefficient Model

In the estimation of a linear regression model with random coefficients, sometimes negative estimates of variances of random coefficients are obtained–an undesirable feature. In this paper we have obtained the asymptotic bounds of the probability of obtaining negative estimators. A simple illustration is also provided for the purpose.     

Population genetics of the population in the European north of the RSFSR. V. An evaluation of the virtual size of the population by computer simulation of marriage and migration processes

The paper deals with the effect of assortative matings on some parameters of population structure. To solve this problem, two rural populations near Archangelsk (river Peosa region) were used. Some genetic and demographic characteristics of these populations were described in previous publications. A comparison between random matches through a random number generator and true marriages was made by computer estimation of the spouses kinship coefficients. Significant avoidance of first and second cousins marriages in real populations was discovered. As a consequence of this avoidance of consanguinity, the effective breeding size of villages is increased twofold. Similar results were obtained by estimation os isonymy.     

On Testing for Equicorrelation in Random Coefficient Models

Recently BHATTI (1993) considered an efficient estimation of random coefficient model based on survey data. The main objective of this paper is to construct one sided test for testing equicorrelation coefficient in presence of random coefficients using optimal testing procedure. The test statistic is a ratio of quadratic forms in normal variables which is most powerful and point optimal invariant.     

Modelling animal growth in random environments: An application using nonparametric estimation

We study a stochastic differential equation growth model to describe individual growth in random environments. In particular, in this paper, we discuss the estimation of the drift and the diffusion coefficients using nonparametric methods for the case of nonequidistant data for several trajectories. We illustrate the methodology by using bovine growth data. Our goal is to assess: (i) if the parametric models (with specific functional forms for the drift and the diffusion coefficients) previously used by us to describe the evolution of bovine weight were adequate choices; (ii) whether some alternative specific parameterized functional forms of these coefficients might be suggested for further parametric analysis of this data.     

Minimum Hellinger distance estimation for k-component poisson mixture with random effects

Summary .   The k-component Poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations. However, the residual maximum likelihood estimation (REML) of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination. In the literature, the minimum Hellinger distance (MHD) estimation has been investigated to obtain robust estimation for finite Poisson mixtures. This article aims to develop a robust MHD estimation approach for k-component Poisson mixtures with normally distributed random effects. By applying the Gaussian quadrature technique to approximate the integrals involved in the marginal distribution, the marginal probability function of the k-component Poisson mixture with random effects can be approximated by the summation of a set of finite Poisson mixtures. Simulation study shows that the MHD estimates perform satisfactorily for data without outlying observation(s), and outperform the REML estimates when data are contaminated. Application to a data set of recurrent urinary tract infections (UTI) with random institution effects demonstrates the practical use of the robust MHD estimation method.     

Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.     

Potential bias in inbreeding depression estimates when using pedigree relationships to assess the degree of homozygosity for loci under selection

A potential bias in estimation of inbreeding depression when using pedigree relationships to assess the degree of homozygosity for loci under selection is indicated. A comparison of inbreeding coefficients based on either pedigree or genotypic frequencies indicated that, as a result of selection, the inbreeding coefficient based on pedigree might not correspond with the random drift of allelic frequencies. Apparent differences in average levels of both inbreeding coefficients were obtained depending on the genetic model (additive versus dominance, initial allelic frequencies, heritability) and the selection system assumed (no versus mass selection). In the absence of selection, allelic frequencies within a small population change over generations due to random drift, and the pedigree-based inbreeding coefficient gives a proper assessment of the accompanying probability of increased homozygosity within a replicate by indicating the variance of allelic frequencies over replicates. With selection, in addition to random drift, directional change in allelic frequencies is not accounted for by the pedigree-based inbreeding coefficient. This result implies that estimation of inbreeding depression for traits under either direct or indirect selection, estimated by a regression of performance on pedigree-based coefficients, should be carefully interpreted.Deceased     

Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period

Abstract

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.     

A penalized spline approach to functional mixed effects model analysis

In this article, we propose penalized spline (P-spline)-based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects, and residual measurement error processes. Using P-splines, we propose nonparametric estimation of the population mean function, varying coefficient, random subject-specific curves, and the associated covariance function that represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Proposed methods offer flexible estimation of both the population- and subject-level curves. In addition, decomposing variability of the outcomes as a between- and within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood-based method to select multiple smoothing parameters. Furthermore, we study the asymptotics of the baseline P-spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between- and within-subject covariance decomposition is illustrated through an analysis of Berkeley growth data, where we identified clearly distinct patterns of the between- and within-subject covariance functions of children's heights. We also apply the proposed methods to estimate the effect of antihypertensive treatment from the Framingham Heart Study data.     

The Treatment of Missing Values in Logistic Regression

The efficiencies of the estimators in the linear logistic regression model are examined using simulations under six missing value treatments. These treatments use either the maximum likelihood or the discriminant function approach in the estimation of the regression coefficients. Missing values are assumed to occur at random. The cases of multivariate normal and dichotomous independent variables are both considered. We found that in general, there is no uniformly best method. However, mean substitution and discriminant function estimation using existing pairs of values for correlations turn out to be favourable for the cases considered.     

Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models

Factor analysis models are widely used in health research to summarize hard-to-measure predictor or outcome variable constructs. For example, in the ELEMENT study, factor models are used to summarize lead exposure biomarkers which are thought to indirectly measure prenatal exposure to lead. Classic latent factor models are fitted assuming that factor loadings are constant across all covariate levels (e.g., maternal age in ELEMENT); that is, measurement invariance (MI) is assumed. When the MI is not met, measurement bias is introduced. Traditionally, MI is examined by defining subgroups of the data based on covariates, fitting multi-group factor analysis, and testing differences in factor loadings across covariate groups. In this paper, we develop novel tests of measurement invariance by modeling the factor loadings as varying coefficients, i.e., letting the factor loading vary across continuous covariate values instead of groups. These varying coefficients are estimated using penalized splines, where spline coefficients are penalized by treating them as random coefficients. The test of MI is then carried out by conducting a likelihood ratio test for the null hypothesis that the variance of the random spline coefficients equals zero. We use a Monte Carlo EM algorithm for estimation, and obtain the likelihood using Monte Carlo integration. Using simulations, we compare the Type I error and power of our testing approach and the multi-group testing method. We apply the proposed methods to summarize data on prenatal biomarkers of lead exposure from the ELEMENT study and find violations of MI due to maternal age.     

Random-effects models for serial observations with binary response

This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore (1979, Biometrics 35, 795-804), using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.     

Artificial neural networks for blur identification and restoration of nonlinearly degraded images.

In this paper, an image restoration algorithm is proposed to identify noncausal blur function. Image degradation processes include both linear and nonlinear phenomena. A neural network model combining an adaptive auto-associative network with a random Gaussian process is proposed to restore the blurred image and blur function simultaneously. The noisy and blurred images are modeled as continuous associative networks, whereas auto-associative part determines the image model coefficients and the hetero-associative part determines the blur function of the system. The self-organization like structure provides the potential solution of the blind image restoration problem. The estimation and restoration are implemented by using an iterative gradient based algorithm to minimize the error function.     

When Should Epidemiologic Regressions Use Random Coefficients?

Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed-effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable-selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer.     

One‐Sided Test to Assess Correlation in Linear Logistic Models using Estimating Equations

A score‐type test is proposed for testing the hypothesis of independent binary random variables against positive correlation in linear logistic models with sparse data and cluster specific covariates. The test is developed for univariate and multivariate one‐sided alternatives. The main advantage of using score test is that it requires estimation of the model only under the null hypothesis, that in this case corresponds to the binomial maximum likelihood fit. The score‐type test is developed from a class of estimating equations with block‐diagonal structure in which the coefficients of the linear logistic model are estimated simultaneously with the correlation. The simplicity of the score test is illustrated in two particular examples.     

Unbalanced Repeated Measures with Random Coefficients

In a random coefficient repeated measures model, the regression coefficients relating the observations to some underlying variable, such as time, are themselves taken to be random distributed over experimental units. In this paper, a general approach to repeated measures analysis is extended to this wider model. In the model three specific error structures for the random regression coefficients have been studied, viz, the random coefficients variance matrix is considered to be (i) diagonal, (ii) proportional to the identity matrix and (iii) completely general. An example will be analyzed to illustrate the procedure.     

乌兰布和沙漠天然白刺适应性群团抽样技术的研究

以乌兰布和沙漠地区天然白刺为具体研究对象,对不同抽样方法获取的数据进行了分析.研究结果表明,当适应性标准大于等于占位单元平均数时,适应性群团抽样比简单随机抽样更有效,并且可以保证估计精度;初始抽样比例越大,总体均值估计值和抽样相对效率越稳定.在该研究区域采用二阶适应性群团抽样,可以达到估计精度,但与简单随机抽样和适应性群团抽样相比效率偏低.     

Combining yield coefficients and exit-gas analysis for monitoring of the baker's yeast fed-batch fermentation

Baker's yeast is one of the micro-organisms that is studied most in literature. Therefore, a lot of knowledge on the biochemical pathways and corresponding yield coefficients is available. This knowledge is combined with measurements of oxygen and carbon dioxide in the exit-gas to determine the coefficients appearing in the stoichiometric equations. In this manner, two measurements are sufficient to yield on-line estimates for biomass, glucose, ethanol and the specific growth rate, and information about the (ill-defined) nitrogen source NH_q. This is not possible if the yield coefficients are not included in the estimation procedure. A sensitivity analysis illustrates that this estimation scheme is rather insensitive to uncertainties on the yield coefficients.     

Impact of adolescent obesity on middle-age health of women given data MAR

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.     

Biased random walk models for chemotaxis and related diffusion approximations

Summary Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distributions are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.