Some Improved Regression Estimators of Heritability

Three new improved regression estimators of heritability viz. modified range restricted estimator, minimum quadratic loss estimator and minimax linear restricted estimator are proposed. In addition, these estimators are illustrated and compared numerically with the existing restricted estimator based on linear stochastic constraint.     

Estimation of regression models under linear restrictions

The variance-covariance matrices of restricted regression and mixed regression estimators are compared and the consequences of introducing variability in the restrictions are examined.     

Parametric modal regression with varying precision

In this paper, we propose a simple parametric modal linear regression model where the response variable is gamma distributed using a new parameterization of this distribution that is indexed by mode and precision parameters, that is, in this new regression model, the modal and precision responses are related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. The main advantage of our new parameterization is the straightforward interpretation of the regression coefficients in terms of the mode of the positive response variable, as is usual in the context of generalized linear models, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we discuss residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, we illustrate the usefulness of the new model by two applications, to biology and demography.     

Comparability of segmented line regression models

Segmented line regression models, which are composed of continuous linear phases, have been applied to describe changes in rate trend patterns. In this article, we propose a procedure to compare two segmented line regression functions, specifically to test (i) whether the two segmented line regression functions are identical or (ii) whether the two mean functions are parallel allowing different intercepts. A general form of the test statistic is described and then the permutation procedure is proposed to estimate the p-value of the test. The permutation test is compared to an approximate F-test in terms of the p-value estimation and the performance of the permutation test is studied via simulations. The tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states.     

Long-Term Ecological Research on Chlorophyll Cycling in the Yuanyang Lake Nature Preserve I. The Grey Prediction Models on Chlorophyll Degradation of Chamaecyparis var. Formosana Leaf

We applied the grey system theory to evaluation of chlorophyll (Chl) degradation in Chamaecyparis Sieb. & Zucc. var. formosana (Hayata) Rehder needle-leaf in the Yuanyang Lake Nature Preserve of northern Taiwan. Pigment analysis was finished within 12 h after collecting the samples. Four grey prediction models for the degradation of Chl a, Chl b, and for the change of Chl a/b ratio and water content were established and compared with the results of linear and exponential regression analysis. The residual error and accuracy range show that the grey prediction process is much better than regression analysis. The degradation of Chl a and b contains two phases, one being fast and the other slow.     

Discretizing a Normal Prior for Change Point Estimation in Switching Regressions

Bayes decision procedures are considered for change point estimation in the simple bilinear segmented model. A discretized normal prior density is employed as the prior distribution for the change point index. Posterior probability functions are developed for this index under a vague prior formulation on the regression parameters. The procedure is applied to an example involving mercury toxicity data.     

Bias correction of bounded location error in binary data

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.     

On a generalization of a result of W. G. Cochran

A relationship due to W.G. Cochran showing the effect on leastsquares regression coefficients of marginalizing over or conditioningon an explanatory variable is generalized to quantile regressioncoefficients. The condition under which conditioning does notinduce interaction or effect reversal is shown. Examples aregiven. The discussion is simplest when all variables are continuous;the extension to discrete variables is outlined.     

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.     

When is Piece-Wise Regression Really Necessary?

Results are obtained showing that when a response surface can be modelled as a single function, then a single regressor is more efficient and less biased than a segmented regression. However, if the surface is segmented, a segmented regressor is less biased than a single regressor. Areas of application are indicated.     

A Comparison of Regression Models for Small Counts

ABSTRACT Count data with means <2 are often assumed to follow a Poisson distribution. However, in many cases these kinds of data, such as number of young fledged, are more appropriately considered to be multinomial observations due to naturally occurring upper truncation of the distribution. We evaluated the performance of several versions of multinomial regression, plus Poisson and normal regression, for analysis of count data with means <2 through Monte Carlo simulations. Simulated data mimicked observed counts of number of young fledged (0, 1, 2, or 3) by California spotted owls (Strix occidentalis occidentalis). We considered size and power of tests to detect differences among 10 levels of a categorical predictor, as well as tests for trends across 10-year periods. We found regular regression and analysis of variance procedures based on a normal distribution to perform satisfactorily in all cases we considered, whereas failure rate of multinomial procedures was often excessively high, and the Poisson model demonstrated inappropriate test size for data where the variance/mean ratio was <1 or >1.2. Thus, managers can use simple statistical methods with which they are likely already familiar to analyze the kinds of count data we described here.     

A geographically variable model of hemlock woolly adelgid spread

The hemlock woolly adelgid (HWA) (Adelges tsugae) has spread through the range of eastern hemlock (Tsuga canadensis) leaving dead hemlock trees in its wake. We combined county and previously unavailable township level infestation records with geographic variables including plant hardiness zone, elevation, forest cover type, urbanization, precipitation, temperature, and hemlock range in a geographic information system to build models linking HWA spread to the structure and characteristics of the environment. We explored the connections between site variables and spread rate using quantile regression, Tobit regression, a parametric model for heterogeneous error variance, and classification and regression tree modeling. The results show that since 1990 HWA has spread at a rate closer to 12.5 km/yr rather than the 20–30 km/yr previously estimated, however spread rates vary significantly with environmental variables. County-based data show a faster rate of range expansion in the south, 15.6 km/yr, and very slow spread in the northern part of the current range of HWA. The rate of spread based on township records for Pennsylvania and north is 8.13 km/yr. Our study suggests that HWA spreads more slowly in colder areas, with a mean minimum temperature of  − 26.1°C (plant hardiness zone 5B) delineating areas of slower range expansion. HWA also spreads more slowly during cold years, those with lower than average mean January temperatures. Our analysis demonstrates the value of quantile regression, Tobit regression, and classification and regression tree models for understanding the spread of invasive, exotic insects.     

A Method of Estimation of Change Points in Multiphasic Growth Models

The least-squares estimation (LSE) of change points and the phase parameters is considered for two growth models with piecewise continuously connected exponential and stationary phases. The calculation of a LSE is reduced to the solution of a finite number of simpler least-squares problems for which methods of calculation are well known.