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Spatial assessment of model errors from four regression techniques

FOREST SCIENCE 2005年第4期51卷 334-346页

作者： Zhang, LJ Gove, JH SUNY Coll Environm Sci & Forestry Fac Forest & Nat Resources Management Syracuse NY 13210 USA USDA Forest Serv NE Res Stn Durham NH 03824 USA

Forest modelers have attempted to account for the spatial autocorrelations among trees in growth and yield models by applying alternative regression techniques such as linear mixed models (LMM), generalized additive models (GAM), and geographically weighted regression (GWR). However, the model errors are commonly assessed using average errors across the entire study area and across tree size classes. Little attention has been paid to the spatial heterogeneity of model performance. In this study, we used local Moran coefficients to investigate the spatial distributions of the model errors from the four regression models. The results indicated that GAM improved model-fitting to the data and provided better predictions for the response variable. However, it is nonspatial in nature and, consequently, generated spatial distributions for the model errors similar to the ones from ordinary least-squares (OLS). Furthermore, OLS and GAM yielded more clusters of similar (either positive or negative) model errors, indicating that trees in some subareas were either all underestimated or all overestimated for the response variable. In contrast, LMM was able to model the spatial covariance structures in the data and obtain more accurate predictions by accounting for the effects of spatial autocorrelations through the empirical best linear unbiased predictors. GWR is a varying-coefficient modeling technique. It estimated the model coefficients locally at each tree in the example plot and resulted in more accurate predictions for the response variable. Moreover, the spatial distributions of the model errors from LMM and GWR were more desirable, with fewer clusters of dissimilar model errors than the ones derived from OLS and GAM.

关键词： spatial autocorrelation and heterogeneity local indicator of spatial autocorrelation ordinary least-squares linear mixed model generalized additive model geographically weighted regression

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Analyzing the spread of beech canker

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FOREST SCIENCE 2005年第5期51卷 438-448页

作者： Augustin, NH Kublin, E Metzler, B Meierjohann, E von Wühlisch, G Univ Freiburg Freiburg Ctr Data Anal & Modeling D-79104 Freiburg Germany Forest Res Ctr Baden Wurttemberg D-79100 Freiburg Germany Fed Res Ctr Forestry & Forest Prod D-22927 Grosshansdorf Germany

We investigate the spread of Nectria canker of beech, which is a fungal chronic disease caused by Nectria ditissima Tul. et C. Tul. Data are available from a beech provenance trial. A possible influential factor on the proportion of infected trees per plot is the wind dispersal zone(s) (wdz), a categorical variable describing the distance and wind direction from diseased shelterwood, the source of infection. We investigate the effect of wdz and whether the disease incidence in the regeneration can be explained alone by the wdz using different approaches accounting for spatial correlation in the data. One method uses generalized estimating equations (GEE) where, through specification of a general variance-covariance matrix allowing for nonindependence, spatial correlation can be accounted for in the model. The second method uses generalized additive models (GAM) and the spatial autocorrelation is dealt with by modeling it as a spatial trend. The third method uses generalized linear mixed models (GLMM) with a random effect accounting for spatial correlation and heterogeneity. We show that, in the beech data, some spatial correlation is present that is over and above that accounted for by the wdz. Therefore, methods not accounting for this correlation are inappropriate. The GLMM is the most appropriate model because it manages to model the biological process best: It explains the variation in disease incidence by the wdz and by secondary infection. Hence it yields the most precise estimates.

关键词： Nectria ditissima beech canker generalized linear mixed model generalized additive model generalized linear model binomial data spatial correlation

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GIS-based application of resource selection functions to the prediction of snow petrel distribution and abundance in East Antarctica: Comparing models at multiple scales

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ECOLOGICAL modelLING 2005年第1-2期189卷 105-129页

作者： Olivier, F Wotherspoon, SJ Univ Tasmania Inst Antarctic & So Ocean Studies Hobart Tas 7001 Australia Univ Tasmania Sch Math & Phys Hobart Tas 7001 Australia

Snow petrel numbers must be of the order of several millions. However, accurate population estimates are sparse although such information is necessary to monitor potential changes in the Antarctic ecosystem. A census of snow petrel nests was conducted at Casey (East Antarctica) during summer 2002-2003. Twenty percent of the ice-free areas (available nesting habitat for snow petrels) was surveyed using a "random block design". During this survey, approximately 5000 nests were located. generalized additive and linear modelling techniques and classification trees (GAM, GLM and CT) were used to fit resource selection functions, which modelled snow petrel abundance or presence-absence in relation to a set of environmental predictors (elevation, slope, aspect, curvature and substrate types estimated in percentage cover). The effect of spatial scale on the processes that influence habitat selection was investigated using GIS as a tool to create and test models at a hierarchical range of scales-from 200 m grid-sites level to 20 m quadrats. The strong predictive value of aspect, slope and percent cover in boulder and SCREE were identified at all scales. However, the significance of environmental predictors varied with scale, indicating that spatial scale matters in detecting habitat selection processes. In general, models were improved with the addition of spatial dependence terms representing the effect of conspecific attraction (coloniality), but these models were less applicable for predictive purposes. By predicting abundance from environmental characteristics (acquired for example, using aerial photography), resource selection functions may be a useful tool to refine population estimates of several petrel species in Antarctica without requiring intensive ground surveys. (c) 2005 Elsevier B.V. All rights reserved.

关键词： habitat selection generalized additive model generalized linear model classification tree model comparison scale conspecific attraction population estimate

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Bayesian semiparametric isotonic regression for count data

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2005年第470期100卷 618-627页

作者： Dunson, DB NIEHS Biostat Branch Res Triangle Pk NC 27709 USA

This article proposes a semiparametric Bayesian approach for inference on an unknown isotonic regression function, f(x), characterizing the relationship between a continuous predictor, X, and a count response variable, Y, adjusting for covariates, Z. A Dirichlet process mixture of Poisson distributions is used to avoid parametric assumptions on the conditional distribution of Y given X and Z. Then, to also avoid parametric assumptions on f(x), a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association. Through the use of carefully tailored hyperprior distributions, we allow for borrowing of information across different regions of X in estimating f(x) and in assessing hypotheses about local increases in the function. Due to conjugacy properties, posterior computation is straightforward using a Markov chain Monte Carlo algorithm. The methods are illustrated using data from an epidemiologic study of sleep problems and obesity.

关键词： Dirichlet process mixture generalized additive model log linear mixture prior multiple testing nonparametric regression smoothing variable selection

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Functional adaptive model estimation

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2005年第470期100卷 565-576页

作者： James, GM Silverman, BW Univ So Calif Marshall Sch Business Los Angeles CA 90089 USA Univ Oxford St Peters Coll Oxford OX1 2DL England

In this article we are interested in modeling the relationship between a scalar, Y, and a functional predictor, X(t). We introduce a highly flexible approach called functional adaptive model estimation (FAME), which extends generalized linear models (GLMs), generalized additive models (GAMs), and projection pursuit regression (PPR) to handle functional predictors. The FAME approach can model any of the standard exponential family of response distributions that are assumed for GLM or GAM while maintaining the flexibility of PPR. For example, standard linear or logistic regression with functional predictors, as well as far more complicated models, can easily be applied using this approach. We use a functional principal components decomposition of the predictor functions to aid visualization of the relationship between X(t) and Y. We also show how the FAME procedure can be extended to deal with multiple functional and standard finite-dimensional predictors, possibly with missing data. We illustrate the FAME approach on simulated data, as well as on the prediction of arthritis based on bone shape. We end with a discussion of the relationships between standard regression approaches. their extensions to functional data, and FAME.

关键词： functional predictor functional principal components generalized additive model generalized linear model projection pursuit regression

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Distribution patterns of boreal marshland birds: modelling the relationships to land cover and climate

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JOURNAL OF BIOGEOGRAPHY 2005年第11期32卷 1957-1970页

作者： Virkkala, R Luoto, M Heikkinen, RK Leikola, N Finnish Environm Inst Res Dept Res Programme Biodivers FIN-00251 Helsinki Finland

Aim The aims of this work were (1) to study how well land-cover and climatic data are capable of explaining distribution patterns of ten bird species breeding and/or feeding primarily on marshes and other wetlands and (2) to compare the differences between red-listed and common marshland species in explanatory variables, and to study the predictability of their distribution patterns. Location Finland, northern Europe. Methods The data of the bird atlas survey carried out in 1986-89 using a 10 x 10 km uniform grid system in Finland were used in the analyses. Land-cover data based on CORINE (Coordination of Information on the Environment) classification and climatic variables were compiled using the same 10 x 10 km grid. generalized additive models (GAM) with a stepwise selection procedure were used to select relevant explanatory variables and to examine the complexity of the response shapes of the different species to each variable. The original data set was randomly divided into model training (70%) and model evaluation (30%) sets. The final models of common and red-listed bird species richness were validated by fitting them to the model evaluation set, and the correlation between observed and predicted species richness was calculated. We assessed the discrimination ability of the binary models (single species) with the area under the curve (AUC) of a receiver operating characteristic (ROC) plot and the Kappa coefficient. Results Cover of marshland, shoreline length and mean temperature in April-June were significantly (P < 0.01) related to the common marshland species richness. Cover and clumping of marshland and mean temperature and precipitation in April-June were selected in the model of red-listed marshland species richness. The level of discrimination in our single species models varied in ROC from fair to excellent (AUC values 0.70-0.95). Cover of marshland was included in all GAM models built for the target species, but clumping of marshland, shoreline lengt

关键词： Birds climatic variables clumping distribution Finland generalized additive model land cover marshland prediction receiver operating characteristic

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Regression analysis with longitudinal measurements

Regression analysis with longitudinal measurements

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作者： Ryu, Duchwan Texas A&M University

Bayesian approaches to the regression analysis for longitudinal measurements are considered. The history of measurements from a subject may convey characteristics of the subject. Hence, in a regression analysis with longitudinal measurements, the characteristics of each subject can be served as covariates, in addition to possible other covariates. Also, the longitudinal measurements may lead to complicated covariance structures within each subject and they should be modeled properly. When covariates are some unobservable characteristics of each subject, Bayesian parametric and nonparametric regressions have been considered. Although covariates are not observable directly, by virtue of longitudinal measurements, the covariates can be estimated. In this case, the measurement error problem is inevitable. Hence, a classical measurement error model is established. In the Bayesian framework, the regression function as well as all the unobservable covariates and nuisance parameters are estimated. As multiple covariates are involved, a generalized additive model is adopted, and the Bayesian backfitting algorithm is utilized for each component of the additive model. For the binary response, the logistic regression has been proposed, where the link function is estimated by the Bayesian parametric and nonparametric regressions. For the link function, introduction of latent variables make the computing fast. In the next part, each subject is assumed to be observed not at the prespecifiedtime-points. Furthermore, the time of next measurement from a subject is supposed to be dependent on the previous measurement history of the subject. For this outcome- dependent follow-up times, various modeling options and the associated analyses have been examined to investigate how outcome-dependent follow-up times affect the estimation, within the frameworks of Bayesian parametric and nonparametric regressions. Correlation structures of outcomes are based on different correlation coefficient

关键词： Bayesian Smoothing Spline generalized additive model Measurement Error Outcome-Dependent Follow-Up Conditional Predictive Ordinate Book Thesis

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generalized additive model and regression tree analyses of blue shark (Prionace glauca) catch rates by the Hawaii-based commercial longline fishery

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FISHERIES RESEARCH 2001年第2期53卷 115-131页

作者： Walsh, WA Kleiber, P Univ Hawaii Joint Inst Marine & Atmospher Res Honolulu HI 96822 USA

generalized additive model (GAM) and regression tree analyses were conducted with blue shark, Prionace glauca, catch rates (catch per set) as reported by National Marine Fisheries Service observers serving aboard Hawaii-based commercial longline vessels from March 1994 through December 1997 (N=2010 longline sets). The objective was to use GAM and regression tree methodology to relate catch rates to a tractable suite of readily measured or computed variables. Because the predictor variables are also either provided in or easily computed from the logbooks that commercial vessels submit upon landing fish for sale, it is likely that a model or models fitted to accurate observer data could then be applied on a fleet-wide basis to serve as a standard of comparison for the logbooks. The GAM included nine spatio-temporal, environmental, and operational variables and explained 72.1% of the deviance of blue shark catch rates. Latitude exerted the strongest effects of any individual variable;longitude was the most influential variable when adjusted for the effects of all other factors. Relatively cold sea surface temperatures were associated with high catch rates. The initial regression tree included 68 terminal nodes and I I predictors. It was refined to a final tree with 42 terminal nodes, which reduced the root mean deviance by 65.3%. The tree was partitioned first on latitude 26.6 degreesN, and then branched out to reach terminal nodes after 2-8 additional partitionings. Sets south of this latitude were characterized by lower catch rates and partitionings on a greater number and variety of predictors. Northerly sets were characterized by higher and more variable blue shark catch rates. Predictions from the two analyses were highly correlated (r=0.903. P much less than0.001). Moreover, use of these methods in combination aided greatly in the interpretation of results. We conclude that GAM and regression tree analyses can be usefully employed in the assessment of blue shark

关键词： blue shark catch rates generalized additive model regression tree

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Semiparametric models for capture-recapture studies with covariates

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2004年第4期47卷 729-743页

作者： Zwane, EN van der Heijden, PGM Univ Utrecht Dept Methodol & Stat NL-3508 TC Utrecht Netherlands

A flexible method for modelling capture-recapture data with continuous covariates that describe heterogeneous catchability is developed. The well established generalized additive modelling framework is used. An estimator of population size is developed using this method. The performance of the method is demonstrated using neural tube defect capture-recapture data from the Netherlands, with the birth weight of a child as a covariate. The parametric bootstrap is used for variance estimation. (C) 2003 Elsevier B.V. All rights reserved.

关键词： capture-recapture generalized additive model multinomial logit model nonparametric population size estimation

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A spatio-temporal framework for efficient inventories of natural resources: A case study with submersed macrophytes

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JOURNAL OF VEGETATION SCIENCE 2004年第6期15卷 807-816页

作者： Schmieder, K Lehmann, A Univ Hohenheim Inst Landscape & Plant Ecol D-70593 Stuttgart Germany Swiss Ctr Faunal Cartog CH-2000 Neuchatel Switzerland

Questions: Does a reduced nutrient load in open water increase species richness and the importance of regional and local site characteristics for species abundance and spatial distribution? Can we build lake-specific models of macrophyte abundance and distribution based on site characteristics in order to prepare a cost-efficient framework for future surveys? Location: Lake Constance, 47degrees39' N, 9degrees18' E. Methods: generalized additive models (GAMs) were used to predict the potential distributions of eight species and overall species richness. Submersed macrophyte distribution in 1993 was compared with corresponding data from 1978, when eutrophication was at its maximum. Results: Spatial predictions for eight species and overall species richness were relatively accurate and independent of water chemistry. Depth was confirmed as a main predictor of species distribution, while effective fetch distance was retained in many models. Mineralogical variables of sediment composition represent allogenic and autogenic sediment sources and their east-west gradient in Lake Constance corresponded to east-west gradients of species distribution and richness. GAMs appeared more efficient than generalized linear models (GLMs) for modelling species responses to environmental gradients. Conclusions: Reduced trophic status increases species richness and the importance of regional and local site characteristics for species abundance and distribution. Our models represent a spatio-temporal framework for future lake monitoring purposes and allow the development of effective monitoring;this could be generalized for many ecosystem types and would be particularly efficient for large takes such as Lake Constance.

关键词： generalized additive model geographic information system GRASP lake constance species distribution modelling spatial prediction

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