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.     

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.     

Body size and area‐incidence relationships: is there a general pattern?

Aim This paper tests firstly for the existence of a general relationship between body size of terrestrial animals and their incidence across habitat patches of increasing size, and secondly for differences in this relationship between insects and vertebrates. Location The analysis was based on the occupancy pattern of 50 species from 15 different landscapes in a variety of ecosystems ranging from Central European grassland to Asian tropical forest. Methods The area‐occupancy relationship was described by incidence functions that were calculated using logistic regression. A correlation analysis between body size of the species and the patch area referring to the two given points of the incidence function was performed. In order to test for an effect of taxon (insects vs. vertebrates), an analysis of covariance was conducted. Results In all species, the incidence was found to increase with increasing patch area. The macroecological analysis showed a significant relationship between the incidence in habitat patches and the body size of terrestrial animals. The area requirement was found to increase linearly with increasing body size on a log‐log scale. This relationship did not differ significantly between insects and vertebrates. Conclusions The approach highlighted in this paper is to associate incidence functions with body size. The results suggest that body size is a general but rather rough predictor for the area requirements of animals. The relationship seems valid for a wide range of body sizes of terrestrial animals. However, further studies including isolation of habitats as well as additional species traits into the macroecological analysis of incidence functions are needed.     

Comparing Stochastically Restricted Linear Estimators in a Regression Model

Conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix are derived when the vector parameter of a regression model is subject to competing stochastic restrictions. The restrictions may also consist both of a deterministic part and a stochastic part.     

Effect of pea bacterial blight (Pseudomonas syringae pv. pisi) on the yield of spring sown combining peas (Pisum sativum)

Field trials to examine the effect of pea bacterial blight (Pseudomonas syringae pv. pisi) (Psp) on the yield of combining peas were carried out at five sites (HRI Wellesbourne, ADAS Rosemaund, ADAS Terrington, PGRO, SASA East Craigs) in the UK in 1990, 1991 and 1992. Healthy seed, cv. Solara, and seed naturally infected with Psp Race 2 was sown in large plots (c. 200 m²) in the open or under nets to prevent bird damage by pigeons. Despite relatively low disease severity levels (< 15% leaf area) and separation by at least 12 m of cv. Consort (resistant to Race 2) between plots there was considerable spread of disease into plots sown with healthy seed. Regression analysis demonstrated a significant relationship between yield and disease. Of the disease measurements examined, disease severity on the leaves (stipules) at growth stage 208 was found to be the best predictor of yield. A model containing environmental and bird damage terms, in addition to disease, suggested that a yield loss of 0.98 t/ha would be expected for a disease severity score of 1, equivalent to 5% leaf area affected, at growth stage 208.     

Seemingly Unrelated Generalized Linear Models

By using deviance standardized residuals, the seemingly unrelated regression estimation procedure is extended to generalized linear models, and fitted by an iterative procedure. The matrix of cross products of standardized residuals is asymptotically multivariate normal, and can be used for further multivariate analyses and for hypothesis testing.     

Assessment of Optimal Selected Prognostic Factors

The identification and assessment of prognostic factors is one of the major tasks in clinical research. The assessment of one single prognostic factor can be done by recently established methods for using optimal cutpoints. Here, we suggest a method to consider an optimal selected prognostic factor from a set of prognostic factors of interest. This can be viewed as a variable selection method and is the underlying decision problem at each node of various tree building algorithms. We propose to use maximally selected statistics where the selection is defined over the set of prognostic factors and over all cutpoints in each prognostic factor. We demonstrate that it is feasible to compute the approximate null distribution. We illustrate the new variable selection test with data of the German Breast Cancer Study Group and of a small study on patients with diffuse large B‐cell lymphoma. Using the null distribution for a p‐value adjusted regression trees algorithm, we adjust for the number of variables analysed at each node as well. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear and non-linear regression analysis of genotype X environment interactions in pearl millet

Summary Regression analysis was computed on the grain yield of 15 single cross F₁ hybrids of pearl millet (Pennisetum typhoides (Burm.) S. & H.) evaluated in 20 environments at 19 sites in India to assess the nature of genotype X environment interactions. Linear, quadratic, cubic, twoand three-intersecting straight line models were examined for fit. The interactions of six hybrids viz. MH 110, MH 113, MH 114, MH 115, MH 120 and MBH 110 were explained by the linear regression model. The response of the remaining nine hybrids was largely non-linear. The two and three-intersecting straight line models fit better than the quadratic and cubic models and explained non-linearity of response. The two-intersecting straight line models fit for 6 hybrids MH 106, MH 107, MH 112, MH 116, MH 117 and BJ 104. The response of MH 109 was best explained by a three-intersecting straight line model, but there still existed a significant remainder variation. The truncation of environmental range by assuming moving division points was more efficient than the fixed division points for the segmental regression models. The stability of hybrid varieties on the best fitting model has been discussed.