Restricted BLUP for Mixed Linear Models

A new estimation procedure for mixed regression models is introduced. It is a development of Henderson's best linear unbiased prediction procedure which uses the joint distribution of the observed dependent random variables and the unknown realisations of the random components of the model. It is proposed to replace the likelihood of the observations given the random components by the asymptotic likelihood of the maximum likelihood estimators and the prior distribution of the random components by a restricted prior distribution which is consistent with the usual restrictions placed on the random components when they are considered conditionally fixed.     

广义岭回归在家禽育种值估计中的应用

讨论了岭回归方法应用于混合线性模型方程组中估计家禽育种值的方法,其实质是将传统的混合线性模型方程组理解为一种广义岭回归估计,为确定遗传参数的估计提供了一种途径;同时,以番鸭为例,考虑了一个性状和两个固定效应,采用广义岭回归法对公番鸭育种值进行了估计,并与最佳线性无偏预测法(BLUP 法)进行了比较,结果表明,广义岭回归方法和BLUP 法估计的育种值及其排序非常接近,其相关系数和秩相关系数分别达到了0.998~(**)和0.986~(**),且采用广义岭回归法预测的误差率低(在±10%以内);表明在混合线性模型方程组中使用广义岭回归估计动物育种值的方法具有可行性,并可省去估计遗传参数的过程,使BLUP 法在动物选育中的应用更具实用性.     

A Dynamic Logistic Regression Model for Multiple Spell Failure Time Data

The paper deals with discrete-time regression models to analyze multistate-multiepisode failure time data. The covariate process may include fixed and external as well as internal time dependent covariates. The effects of the covariates may differ among different kinds of failures and among successive episodes. A dynamic form of the logistic regression model is investigated and maximum likelihood estimation of the regression coefficients is discussed. In the last section we give an application of the model to the analysis of survival time after breast cancer operation.     

Stein‐Rule Estimation in Mixed Regression Models

This paper considers a Stein‐rule mixed regression estimator for estimating a normal linear regression model in the presence of stochastic linear constraints. We derive the small disturbance asymptotic bias and risk of the proposed estimator, and analytically compare its risk with other related estimators. A Monte‐Carlo experiment investigates the empirical risk performance of the proposed estimator.     

Misclassification in Logistic Regression with Discrete Covariates

We study the effect of misclassification of a binary covariate on the parameters of a logistic regression model. In particular we consider 2 × 2 × 2 tables. We assume that a binary covariate is subject to misclassification that may depend on the observed outcome. This type of misclassification is known as (outcome dependent) differential misclassification. We examine the resulting asymptotic bias on the parameters of the model and derive formulas for the biases and their approximations as a function of the odds and misclassification probabilities. Conditions for unbiased estimation are also discussed. The implications are illustrated numerically using a case control study. For completeness we briefly examine the effect of covariate dependent misclassification of exposures and of outcomes.     

Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non-Negativity of Variance Estimators

For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones.     

On the Estimation of Intra-Sire Regression Heritability Subject to Linear Constraint

The derivation of the restricted intra-sire regression heritability estimator is provided. Procedures for obtaining a stable estimate of residual error variance σ² are outlined. A small illustration based on live data is given.     

Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in confidence intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used. As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑ a_qθ_q, where a₁…,a_Q are known constants, U_q = n_qS/θ_q is a chi-squared random variable with n_q degrees of freedom, for each q = 1,…, Q, and X,U₁,…, U_Q are mutually independent. In this paper, we consider the case where Q = 3 and a₃ ≤0.     

Parameterizing Potential Exposure to Sulfur Mustard (HD) Using Mixed Model Regression

The possible threat posed by terrorists using chemical warfare agents (CWAs) against civilian targets is a major concern, reflecting the fact that CWAs are highly toxic to unprotected populations, with releases as vapors or aerosols likely to produce mass casualties on a highly localized basis within minutes or hours after an incident. A conceptual site model is developed and mixed model regression is used to estimate concentration values for the vesicant sulfur mustard (HD) based on the output from computational fluid dynamics (CFD) simulation following wind tunnel experimentation. The analysis provides a first-approximation of the spatial and temporal distribution of potential exposures within a set of 50 m × 50 m × 2 m grids across a 1000 m width by 300 m height by 2250 m length domain in a geographic information system (GIS) environment. The HD concentration values are calculated as log-averaged mean and the 95% confidence intervals for each grid at 1.9 d and 6.0 d after initial release. The technique offers a statistically valid means for rapidly generating unbiased first-approximations of concentration values subsequent to an initial release as an alternative to extensive monitoring or multiple runs of CFD models to parameterize potential exposure to HD spatially and temporally.     

A Primer on Interpreting Regression Models

Abstract: We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x₁, x₂) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models     

Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models

Summary This article introduces new methods for performing classification of complex, high‐dimensional functional data using the functional mixed model (FMM) framework. The FMM relates a functional response to a set of predictors through functional fixed and random effects, which allows it to account for various factors and between‐function correlations. The methods include training and prediction steps. In the training steps we train the FMM model by treating class designation as one of the fixed effects, and in the prediction steps we classify the new objects using posterior predictive probabilities of class. Through a Bayesian scheme, we are able to adjust for factors affecting both the functions and the class designations. While the methods can be used in any FMM framework, we provide details for two specific Bayesian approaches: the Gaussian, wavelet‐based FMM (G‐WFMM) and the robust, wavelet‐based FMM (R‐WFMM). Both methods perform modeling in the wavelet space, which yields parsimonious representations for the functions, and can naturally adapt to local features and complex nonstationarities in the functions. The R‐WFMM allows potentially heavier tails for features of the functions indexed by particular wavelet coefficients, leading to a down‐weighting of outliers that makes the method robust to outlying functions or regions of functions. The models are applied to a pancreatic cancer mass spectroscopy data set and compared with other recently developed functional classification methods.     

Improved Estimation of Coefficients in Regression Models with Incomplete Prior Information

The method of mixed regression is considered for the estimation of coefficients in a linear regression model when incomplete prior information is available, and two families of improved estimators stemming from Stein-rule are proposed. Their properties are studied when disturbances are normal but small.     

Bayesian Methods for Regression Using Surrogate Variables

If a dependent variable in a regression analysis is exceptionally expensive or hard to obtain the overall sample size used to fit the model may be limited. To avoid this one may use a cheaper or more easily collected “surrogate” variable to supplement the expensive variable. The regression analysis will be enhanced to the degree the surrogate is associated with the costly dependent variable. We develop a Bayesian approach incorporating surrogate variables in regression based on a two‐stage experiment. Illustrative examples are given, along with comparisons to an existing frequentist method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

可交换条件下多维结构回归模型总体平均处理效应的估计

在可交换条件下，当响应变量为多维时，利用结构回归模型研究总体平均处理效应的估计。     

离散型单种群扩散模型的全局渐近稳定性

本文研究离散单种扩散模型全局渐近稳定性,利用单调算子和凹算子的理论讨论了其全局渐近稳定性,并得到了正平衡点全局渐的稳定和物种绝灭的充分条件。     

A Two-Level Regression Model for Growth Curves with Correlated Outcomes

We propose a mixed-effect linear model, as a particular case of the two-level regression model, for analyzing repeated measures made at completely irregular time points. The model allows for subject-level covariates, so as to study the trend and the variability of the individual growth curves. Application of this model is illustrated on a published data set.     

Zero‐Inflated Negative Binomial Mixed Regression Modeling of Over‐Dispersed Count Data with Extra Zeros

In many biometrical applications, the count data encountered often contain extra zeros relative to the Poisson distribution. Zero‐inflated Poisson regression models are useful for analyzing such data, but parameter estimates may be seriously biased if the nonzero observations are over‐dispersed and simultaneously correlated due to the sampling design or the data collection procedure. In this paper, a zero‐inflated negative binomial mixed regression model is presented to analyze a set of pancreas disorder length of stay (LOS) data that comprised mainly same‐day separations. Random effects are introduced to account for inter‐hospital variations and the dependency of clustered LOS observations. Parameter estimation is achieved by maximizing an appropriate log‐likelihood function using an EM algorithm. Alternative modeling strategies, namely the finite mixture of Poisson distributions and the non‐parametric maximum likelihood approach, are also considered. The determination of pertinent covariates would assist hospital administrators and clinicians to manage LOS and expenditures efficiently.     

On Characterizing Some Discrete Distributions by a Conditional Distribution and a Regression Function

In this paper we consider characterizations of the binomial, negative binomial, hypergeometric, negative hypergeometric, multinomial and multivariate hypergeometric distributions, by linear regression of one random variable (vector) on the other and the conditional distribution of the other random variable (vector) given the first. It is also indicated how these results can be used in genetics.     

Analysis of Multiply Matched Retrospective Studies When Risk Factor Under Study is Discrete,With Two or More Levels

The odds ratio is known to closely approximate the relative risk when the disease is rare. Logistic regression models are often used to estimate such odds ratios, but here a different model is used which avoids the assumptions implicit in logistic modelling; it also has the advantage of providing a test of homogeneity for odds rat os in situations where the logistic model cannot.