Influence Diagnostics in Spatial Models with Censored Response

Thais S. Barbosa
Víctor H. Lachos
Dipak K. Dey

Environmental data is often spatially correlated and sometimes include below detection limit observations (i.e.,censored values reported as less than a level of detection). Existing work mainly concentrates on parameter estimation using Gibbs sampling, and work conducted from a frequentist perspective in spatial censored models areelusive. In this paper, we propose an exact estimation procedure to obtain the maximum likelihood estimates of thefixed effects and variance components, using a stochastic approximation of the EM (SAEM) algorithm (Delyonet al., 1999). This approach permits estimation of the parameters of spatial linear models when censoring is presentin 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 influence measures on the basis of the conditional expectation ofthe complete-data log-likelihood function which eliminates the complexity associated with the approach of Cook(1977, 1986) for spatial censored models. Some useful perturbation schemes are discussed. The newly developedmethodology is illustrated using data from a dioxin contaminated site in Missouri. In addition, a simulation studyis presented, which explores the accuracy of the proposed measures in detecting influential observations underdifferent perturbation schemes.

Censored data
Geostatistical data
SAEM Algorithm
Influential observations
Limit of detection (LOD)