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.     

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.     

Empirical regression as a conditional expected value of a special distribution-mixture for a modelfree quantitative recording of stochastical relations

An “empirical” distribution function F?(x, y) is estimated from measured points (xi, yi), i =1(1)n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y). The density function F?(x, y) of F?(x, y) is a mixture of n two-dimensional normal densities. The first order moments of F?(x, y) are the sample means x and y, whilst the second order moments are only proportional to the sample variances and the sample covariance. This “empirical” distribution F?(x, y) is used for evaluation of an empirical regression curve where a free parameter has to be fixed by an optimality criterion. The procedure is demonstrated by an example from morphometrical research.     

Offspring-parent regression for a binary trait

Summary Offspring-parent regression is often used to estimate the heritability of a quantitative trait. It is shown that for a purely binary trait, the regression of offspring on one parent is always linear, while that on both parents or mid-parent is generally nonlinear. However, the regressions are linear on a logistic scale.     

Eight (and a half) deadly sins of spatial analysis

Biogeography is spatial by nature. Over the past 20 years, the literature related to the analysis of spatially structured data has exploded, much of it focused on a perceived problem of spatial autocorrelation and ways to deal with it. However, there are a number of other issues that permeate the biogeographical and macroecological literature that have become entangled in the spatial autocorrelation web. In this piece I discuss some of the assumptions that are often made in the analysis of spatially structured data that can lead to misunderstandings about the nature of spatial data, the methods used to analyse them, and how results can be interpreted.     

Skeletal estimates of Gigantopithecus based on a Gorilla analogy

Mandibular metrics of Gorilla gorilla are used to generate multiple regression equations using long bones metrics as criterion variables. These equations are then used to predict skeletal estimates of Gigantopithecus based upon mandibular metrics. On the average, the long bones of Gigantopithecus were 20–25% longer and more robust than those of living gorillas.     

Empirical modelling of lake water-temperature relationships: a comparison of approaches

1.  As a result of the role that temperature plays in many aquatic processes, good predictive models of annual maximum near-surface lake water temperature across large spatial scales are needed, particularly given concerns regarding climate change. Comparisons of suitable modelling approaches are required to determine their relative merit and suitability for providing good predictions of current conditions. We developed models predicting annual maximum near-surface lake water temperatures for lakes across Canada using four statistical approaches: multiple regression, regression tree, artificial neural networks and Bayesian multiple regression.
2.  Annual maximum near-surface (from 0 to 2 m) lake water-temperature data were obtained for more than 13 000 lakes and were matched to geographic, climatic, lake morphology, physical habitat and water chemistry data. We modelled 2348 lakes and three subsets thereof encompassing different spatial scales and predictor variables to identify the relative importance of these variables at predicting lake temperature.
3.  Although artificial neural networks were marginally better for three of the four data sets, multiple regression was considered to provide the best solution based on the combination of model performance and computational complexity. Climatic variables and date of sampling were the most important variables for predicting water temperature in our models.
4.  Lake morphology did not play a substantial role in predicting lake temperature across any of the spatial scales. Maximum near-surface temperatures for Canadian lakes appeared to be dominated by large-scale climatic and geographic patterns, rather than lake-specific variables, such as lake morphology and water chemistry.     

Bayesian survival analysis using a MARS model

A Bayesian multivariate adaptive regression spline fitting approach is used to model univariate and multivariate survival data with censoring. The possible models contain the proportional hazards model as a subclass and automatically detect departures from this. A reversible jump Markov chain Monte Carlo algorithm is described to obtain the estimate of the hazard function as well as the survival curve.     

Survival analysis with time-varying regression effects using a tree-based approach

Nonproportional hazards often arise in survival analysis, as is evident in the data from the International Non-Hodgkin's Lymphoma Prognostic Factors Project. A tree-based method to handle such survival data is developed for the assessment and estimation of time-dependent regression effects under a Cox-type model. The tree method approximates the time-varying regression effects as piecewise constants and is designed to estimate change points in the regression parameters. A fast algorithm that relies on maximized score statistics is used in recursive segmentation of the time axis. Following the segmentation, a pruning algorithm with optimal properties similar to those of classification and regression trees (CART) is used to determine a sparse segmentation. Bootstrap resampling is used in correcting for overoptimism due to split point optimization. The piecewise constant model is often more suitable for clinical interpretation of the regression parameters than the more flexible spline models. The utility of the algorithm is shown on the lymphoma data, where we further develop the published International Risk Index into a time-varying risk index for non-Hodgkin's lymphoma.     

Comparison of viable cell concentration estimation methods for a mammalian cell cultivation process

Various mechanistic and black-box models were applied for on-line estimations of viable cell concentrations in fed-batch cultivation processes for CHO cells. Data from six fed-batch cultivation experiments were used to identify the underlying models and further six independent data sets were used to determine the performance of the estimators. The performances were quantified by means of the root mean square error (RMSE) between the estimates and the corresponding off-line measured validation data sets. It is shown that even simple techniques based on empirical and linear model approaches provide a fairly good on-line estimation performance. Best results with respect to the validation data sets were obtained with hybrid models, multivariate linear regression technique and support vector regression. Hybrid models provide additional important information about the specific cellular growth rates during the cultivation.     

On a supplemented case-control design

The supplemented case-control design consists of a case-control sample and of an additional sample of disease-free subjects who arise from a given stratum of one of the measured exposures in the case-control study. The supplemental data might, for example, arise from a population survey conducted independently of the case-control study. This design improves precision of estimates of main effects and especially of joint exposures, particularly when joint exposures are uncommon and the prevalence of one of the exposures is low. We first present a pseudo-likelihood estimator (PLE) that is easy to compute. We further adapt two-phase design methods to find maximum likelihood estimates (MLEs) for the log odds ratios for this design and derive asymptotic variance estimators that appropriately account for the differences in sampling schemes of this design from that of the traditional two-phase design. As an illustration of our design we present a study that was conducted to assess the influence to joint exposure of hepatitis-B virus (HBV) and hepatitis-C virus (HCV) infection on the risk of hepatocellular carcinoma in data from Qidong County, Jiangsu Province, China.     

旅游业对目的地生态系统服务价值的影响——以神农架为例

旅游业在给目的地带来经济增长的同时,也会对其生态环境造成一定影响。既有研究多关注旅游业对生态环境的压力,而较少关注旅游业对目的地生态系统服务价值(Ecosystem service value, ESV)的影响。为此,研究以“旅游社会-生态系统”为基础,构建了旅游业对目的地ESV的影响框架。以神农架为例,基于土地利用格局变化以及修正ESV价值当量,计算其2005—2018年ESV以及时空变化特点。通过地理加权回归(Geographically weighted regression, GWR)与增强回归树(Boosting regression tree, BRT)模型对距居民点距离、距景区距离、距酒店距离以及距道路距离等旅游因素对ESV的影响以及空间差异进行了研究,并得到以下主要结论：(1)神农架土地利用格局变化显著,耕地、林地、草地和未利用地面积总体减少,水域及建设用地面积总体增加。(2)神农架ESV呈逐年递增趋势,由2005年的33.58亿元增加至2018年的89.10亿元。11项生态系统服务功能所占价值比例稳定,以气候调节、水文调节、土壤保持及生物多样性为主。ESV在空间上呈现...     

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.     

Distribution-free Estimation of a Monotonic pth Quantile Function

When analyzing biological data sets, a frequent problem is to estimate the pth quantile of a distribution, when that quantile is assumed to depend on a covariate; in the present paper the dependence of the quantile on the covariate is assumed to be monotonic. Some properties of an isotonic pth quantile regression, considered as an estimator of an increasing pth quantile function, are presented.