Influence diagnostics in spatial models with censored response

Abstract

Environmental data are often spatially correlated and sometimes include observations below or above detection limits (i.e., censored values reported as less or more than a level of detection). Existing research studies mainly concentrate on parameter estimation using Gibbs sampling, and most research studies conducted from a frequentist perspective in spatial censored models are elusive. In this paper, we propose an exact estimation procedure to obtain the maximum‐likelihood estimates of fixed effects and variance components, using a stochastic approximation of the expectation–maximization algorithm (Delyon, Lavielle, & Moulines). This approach permits estimation of the parameters of spatial linear models when censoring is present in an easy and fast way. As a by‐product, predictions of unobservable values of the response variable are possible. Motivated by this algorithm, we develop local and global influence measures on the basis of the conditional expectation of the complete‐data log‐likelihood function, which eliminates the complexity associated with the approach of Cook for spatial censored models. Some useful perturbation schemes are discussed. The newly developed method is illustrated using data from a dioxin‐contaminated site in Missouri that contain left‐censored data and a data set related to the depths of a geological horizon that contains both left‐ and right‐censored observations. In addition, a simulation study is presented that explores the accuracy of the proposed measures in detecting influential observations under different perturbation schemes. The methodology addressed in this paper is implemented in the R packageCensSpatial.