Feature significance in generalized additive models

This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several data sets.     

Prediction Performance of Correlated Error Procedures for Spatial Counts

Abstract

Few guidelines exist for the application of geostatistical methods to spatial counts and the prediction to unsampled areas is an important aspect of experimental field research. The prediction performances of kriging and a correlated errors Poisson model are compared through simulation. Counts with a known spatial covariance structure are generated in an investigation involving several factors: area size, overall mean, range of correlation, spatial covariance function, and the presence of trend. The correlated errors Poisson model generally gives superior prediction performance when an exponential covariance structure is used.     

Point and block prediction in log-Gaussian random fields: The non-constant mean case

This work considers the problems of point and block prediction in log-Gaussian random fields for the case when the mean of the log-process is not constant and depends linearly on unknown parameters. First, we propose a new point predictor that is optimal within a certain family of predictors, which extend a result in De Oliveira [2006. On optimal point and block prediction in log-Gaussian random fields. Scand. J. Statist. 33, 523–540.] that holds in the case when the mean of the log-process is constant. Second, we show that the results in De Oliveira [2006. On optimal point and block prediction in log-Gaussian random fields. Scand. J. Statist. 33, 523–540.] regarding optimal block prediction cannot be extended to the case when the mean of the log-process is not constant. Specifically, we show that the two families of block predictors considered by De Oliveira lack an optimal predictor. Finally, we numerically compare the predictive efficiency of the proposed point and block predictors.     

Childhood malaria in the Gambia: a case-study in model-based geostatistics

Summary. The paper develops a spatial generalized linear mixed model to describe the variation in the prevalence of malaria among a sample of village resident children in the Gambia. The response from each child is a binary indicator of the presence of malarial parasites in a blood sample. The model includes terms for the effects of child level covariates (age and bed net use), village level covariates (inclusion or exclusion from the primary health care system and greenness of surrounding vegetation as derived from satellite information) and separate components for residual spatial and non-spatial extrabinomial variation. The results confirm and quantify the progressive increase in prevalence with age, and the protective effects of bed nets. They also show that the extrabinomial variation is spatially structured, suggesting an environmental effect rather than variation in familial susceptibility. Neither inclusion in the primary health care system nor the greenness of the surrounding vegetation appeared to affect the prevalence of malaria. The method of inference was Bayesian using vague priors and a Markov chain Monte Carlo implementation.     

Weighting Elementary Prices in Consumer Price Index Construction Using Spatial Autocorrelation

The Consumer Price Indexes (CPI) are used in current economic systems to measure inflation. When constructing CPIs, however, official institutions have systematically overlooked the spatial dimension of elementary prices. Ignoring the fact that prices are collected at geographical locations implicitly implies considering prices as spatially independent, when in fact they are not. To solve this problem, this article proposes to weight basic price data by taking into account the spatial correlation they display. The weighted geometric and arithmetic means suggested generalize and improve the simple geometric and arithmetic means currently in use.     

Recent advances to model anisotropic space–time data

Building new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research in the last years. The goal of this paper is to present an up-to-date overview of recent spatio-temporal covariance models taking into account the problem of spatial anisotropy. The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability. In particular, we focus on the problem of modelling anisotropy through isotropy within components. We present the Bernstein class, and a generalisation of Gneiting’s approach (2002a) to obtain new classes of space–time covariance functions which are spatially anisotropic. We also discuss some methods for building covariance functions that attain negative values. We finally present several differentiation and integration operators acting on particular space–time covariance classes.      

On the choice of the mesh for the analysis of geostatistical data using R-INLA

Abstract

Many methods used in spatial statistics are computationally demanding, and so, the development of more computationally efficient methods has received attention. A important development is the integrated nested Laplace approximation method which is carry out Bayesian analysis more efficiently This method, for geostatistical data, is done considering the SPDE approach that requires the creation of a mesh overlying the study area and all the obtained results depend on it. The impact of the mesh on inference and prediction is investigated through simulations. As there is no formal procedure to specify it, we investigate a guideline to create an optimal mesh.     

Bayesian Spatial Modeling of Housing Prices Subject to a Localized Externality

This work proposes a non stationary random field model to describe the spatial variability of housing prices that are affected by a localized externality. The model allows for the effect of the localized externality on house prices to be represented in the mean function and/or the covariance function of the random field. The correlation function of the proposed model is a mixture of an isotropic correlation function and a correlation function that depends on the distances between home sales and the localized externality. The model is fit using a Bayesian approach via a Markov chain Monte Carlo algorithm. A dataset of 437 single family home sales during 2001 in the city of Cedar Falls, Iowa, is used to illustrate the model.     

Variable selection in spatial regression via penalized least squares

We consider variable selection in linear regression of geostatistical data that arise often in environmental and ecological studies. A penalized least squares procedure is studied for simultaneous variable selection and parameter estimation. Various penalty functions are considered including smoothly clipped absolute deviation. Asymptotic properties of penalized least squares estimates, particularly the oracle properties, are established, under suitable regularity conditions imposed on a random field model for the error process. Moreover, computationally feasible algorithms are proposed for estimating regression coefficients and their standard errors. Finite‐sample properties of the proposed methods are investigated in a simulation study and comparison is made among different penalty functions. The methods are illustrated by an ecological dataset of landcover in Wisconsin. The Canadian Journal of Statistics 37: 607–624; 2009 © 2009 Statistical Society of Canada