Boosted regression trees with errors in variables

In this article, we consider nonparametric regression when covariates are measured with error. Estimation is performed using boosted regression trees, with the sum of the trees forming the estimate of the conditional expectation of the response. Both binary and continuous response regression are investigated. An approach to fitting regression trees when covariates are measured with error is described, and the boosting algorithms consist of its repeated application. The main feature of the approach is that it handles situations where multiple covariates are measured with error. Some simulation results are given as well as its application to data from the Framingham Heart Study.     

The significance for breeding of linear regression analysis of genotype-environment interactions.

Methods of regression analysis of genotype-environment interaction are considered in relation to existing theory dealing with the relative efficiencies of selection for general or specific adaptation to the environment, and the choice of environments for assessment. The two alternative models is involving regression on to environmental effects (model 2) or genotypic effects (model 3) are equivalent when regression lines are concurrent, but are shown to be mutually exclusive when concurrence is absent...     

Estimation in regression models with externally estimated parameters

In many regression applications, some of the model parameters are estimated from separate data sources. Typically, these estimates are plugged into the regression model and the remainder of the parameters is estimated from the primary data source. This situation arises frequently in compartment modeling when there is an external input function to the system. This paper provides asymptotic and bootstrap-based approaches for accounting for all sources of variability when computing standard errors for estimated regression model parameters. Examples and simulations are provided to motivate and illustrate the ideas.     

Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements

We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.     

Improved Predictions in Linear Regression Models with Stochastic Linear Constraints

In this article, we have considered two families of predictors for the simultaneous prediction of actual and average values of study variable in a linear regression model when a set of stochastic linear constraints binding the regression coefficients is available. These families arise from the method of mixed regression estimation. Performance properties of these families are analyzed when the objective is to predict values outside the sample and within the sample.     

Estimation of Relative Risk in Case Control Studies Through Logistic Regression Analysis

Multiple logistic regression analysis is used to estimate the relative risk in case control studies. The estimators obtained are valid when disease is rare. In this paper an estimator of relative risk in a case control study has been proposed using logistic regression results when the incidence of disease is not small. The bias of the usual estimator through logistic regression as compared to the new estimator has been worked out. The expression of Mean Square Error of proposed estimator has been derived in situations when the incidence of disease is known exactly as well as when estimated through an independent survey. It has been observed that there is a significant bias using the conventional estimator of relative risk when incidence of disease is high. In such situations the proposed estimator can be used with advantage.     

Estimation of heritability by offspring-parent regression when observations do not have a common mean

Summary Offspring-parent regression is a simple method for estimating heritability. This method yields unbiased estimates even when parents are selected. The usual model in offspring-parent regression assumes that observations have the same mean. This assumption, however, is not met in many situations. A method for estimating heritability by offspring-parent regression when observations do not have a common mean is presented. The estimator is distributed as a multiple of a t random variable centered at its parametric value and is unbiased even when the parents are selected. When observations have a common mean, the method reduces to the usual regression estimator.     

Mixed Model Discrete Regression

Models and estimention procedures are given for linear regression models in discrete distributions when the regression contains both fixed and random effects. The methods are developed for discrete variables with typically a small number of possible outcomes such as occurs in ordinal regression. The method is applied to a problem arising in the comparison of microbiological test methods.     

Independent contrasts and regression through the origin

Following the pioneering work of Felsenstein and Garland, phylogeneticists have been using regression through the origin to analyze comparative data using independent contrasts. The reason why regression through the origin must be used with such data was revisited. The demonstration led to the formulation of a permutation test for the coefficient of determination and the regression coefficient estimates in regression through the origin. Simulations were carried out to measure type I error and power of the parametric and permutation tests under two models of data generation: regression models I and II (correlation model). Although regression through the origin assumes model I data, in independent contrast data error is present in the explanatory as well as the response variables. Two forms of permutations were investigated to test the regression coefficients: permutation of the values of the response variable y, and permutation of the residuals of the regression model. The simulations showed that the parametric tests or any of the permutation tests can be used when the error is normal, which is the usual assumption in independent contrast studies; only the test by permutation of y should be used when the error is highly asymmetric; and the parametric tests should be used when extreme values are present in covariables. Two examples are presented. The first one concerns non-specificity in fish parasites of the genus Lamellodiscus, the second the richness in parasites in 78 species of mammals.     

生态学研究中常见的统计学问题分析

在当代生态学研究中统计学方法的应用日益广泛,对于生态科学的发展和研究水平的提高起到了积极的作用。但是不容忽视的是在生态学研究应用统计学方法的过程中存在若干问题,主要表现在:1)回归分析方面的问题。直线回归方程用相关指数R²来描述直线回归的显著性;曲线回归方程往往用相关系数r来表示显著性;多元线性回归方程只对方程进行显著性检验,没有对每一个回归系数进行显著性检验。2)方差分析方面的问题。当处理数超过2时,不恰当地使用t_检验比较平均数的差异显著性。该文分析了产生这些问题的原因,提出了改进的对策。     

Fitting curves to data using nonlinear regression: a practical and nonmathematical review

Many types of data are best analyzed by fitting a curve using nonlinear regression, and computer programs that perform these calculations are readily available. Like every scientific technique, however, a nonlinear regression program can produce misleading results when used inappropriately. This article reviews the use of nonlinear regression in a practical and nonmathematical manner to answer the following questions: Why is nonlinear regression superior to linear regression of transformed data? How does nonlinear regression differ from polynomial regression and cubic spline? How do nonlinear regression programs work? What choices must an investigator make before performing nonlinear regression? What do the final results mean? How can two sets of data or two fits to one set of data be compared? What problems can cause the results to be wrong? This review is designed to demystify nonlinear regression so that both its power and its limitations will be appreciated.     

Maximum likelihood analysis of logistic regression models with incomplete covariate data and auxiliary information

This article presents a new method for maximum likelihood estimation of logistic regression models with incomplete covariate data where auxiliary information is available. This auxiliary information is extraneous to the regression model of interest but predictive of the covariate with missing data. Ibrahim (1990, Journal of the American Statistical Association 85, 765-769) provides a general method for estimating generalized linear regression models with missing covariates using the EM algorithm that is easily implemented when there is no auxiliary data. Vach (1997, Statistics in Medicine 16, 57-72) describes how the method can be extended when the outcome and auxiliary data are conditionally independent given the covariates in the model. The method allows the incorporation of auxiliary data without making the conditional independence assumption. We suggest tests of conditional independence and compare the performance of several estimators in an example concerning mental health service utilization in children. Using an artificial dataset, we compare the performance of several estimators when auxiliary data are available.     

Median regression with censored cost data

Because of the skewness of the distribution of medical costs, we consider modeling the median as well as other quantiles when establishing regression relationships to covariates. In many applications, the medical cost data are also right censored. In this article, we propose semiparametric procedures for estimating the parameters in median regression models based on weighted estimating equations when censoring is present. Numerical studies are conducted to show that our estimators perform well with small samples and the resulting inference is reliable in circumstances of practical importance. The methods are applied to a dataset for medical costs of patients with colorectal cancer.     

Immunization with nonstructural proteins E1 and E2 of cottontail rabbit papillomavirus stimulates regression of virus-induced papillomas.

Cottontail rabbit papillomavirus is the major animal model for cancer-associated papillomaviruses. Here we show that vaccination with the nonstructural proteins E1 and E2 induces the regression of virus-induced papillomas and that vaccination is equally effective when proteins are given with and without adjuvant. There was no correlation between antibody levels and regression, suggesting that tumor regression may be due to a cell-mediated response.     

Generalized estimating equations for ordinal categorical data: arbitrary patterns of missing responses and missingness in a key covariate

We propose methods for regression analysis of repeatedly measured ordinal categorical data when there is nonmonotone missingness in these responses and when a key covariate is missing depending on observables. The methods use ordinal regression models in conjunction with generalized estimating equations (GEEs). We extend the GEE methodology to accommodate arbitrary patterns of missingness in the responses when this missingness is independent of the unobserved responses. We further extend the methodology to provide correction for possible bias when missingness in knowledge of a key covariate may depend on observables. The approach is illustrated with the analysis of data from a study in diagnostic oncology in which multiple correlated receiver operating characteristic curves are estimated and corrected for possible verification bias when the true disease status is missing depending on observables.     

Spontaneous regression of the primary lesion of a metastatic maligvant melanoma.

An atypical elderly patient with spontaneous regression of a primary lesion of malignant melanoma is presented. The 12 previously reported cases are also reviewed. The histological diagnosis of spontaneous regression of a melanoma can still be made after the regression appears to be grossly complete. All localized areas of depigmentation, or of scarring, should be biopsied when searching for an "occult" primary.     

A comment on phylogenetic correction

Statistical methods are now commonly used to take into account the expected lack of independence of observations across different species (due to their phylogenetic relatedness) when computing correlations or regressions among traits. The methods are often interpreted as removing that part of the regression or correlation that is an artifact due to phylogeny and there is an expectation that the corrected regression or correlation coefficients will usually be closer to zero. It is shown here that this is not an accurate way to interpret these methods. The effect of taking phylogeny into account is to reduce the variance of the estimated regression or correlation coefficients. Their means are not because since estimates of regression coefficients are unbiased whether or not the correct phylogeny is taken into account. Estimates of correlations are only slightly biased (and in the opposite direction that many expect).     

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.     

BIOASSAY SYSTEMS FOR THE PYRETHRINS: V. EXPERIMENTS WITH A RESISTANT STRAIN OF CALANDRA GRANARIA L.

Some principles of testing for resistance in wild and laboratory stocks of insects are discussed, and experiments with Calandra granaria L. are described in which these insects are selected for pyrethrum resistance.
A new method is described of expressing relative tolerances when the relevant regression lines are not parallel, based on the 'generalized distance' of Mahalanobis. The method may equally be used for the comparison of two insecticides giving rise to lines of different slope. A limited increase in resistance occurred on selection. Non-random oscillatory sequences of slopes were observed when the resistant strain was assayed, and regression parameters computed. The nature of these oscillations is considered.     

Semiparametric Regression in Size-Biased Sampling

Summary .  Size-biased sampling arises when a positive-valued outcome variable is sampled with selection probability proportional to its size. In this article, we propose a semiparametric linear regression model to analyze size-biased outcomes. In our proposed model, the regression parameters of covariates are of major interest, while the distribution of random errors is unspecified. Under the proposed model, we discover that regression parameters are invariant regardless of size-biased sampling. Following this invariance property, we develop a simple estimation procedure for inferences. Our proposed methods are evaluated in simulation studies and applied to two real data analyses.