Parametric bootstrap and penalized quasi-likelihood inference in conditional autoregressive models

This paper discusses a variety of conditional autoregressive (CAR) models f or mapping disease rates, beyond the usual first-order intrinsic CAR model. We illustrate the utility and scope of such models for handling different types of data structures. To encourage their routine use for map production at statistical and health agencies, a simple algorithm for fitting such mo dels is presented. This is derived from penalized quasi-likelihood (PQL) in ference which uses an analogue of best-linear unbiased estimation for the r egional risk ratios and restricted maximum likelihood for the variance comp onents. We offer the practitioner here the use of the parametric bootstrap for inference. It is more reliable than standard maximum likelihood asympto tics for inference purposes since relevant hypotheses for the mapping of ra tes lie on the boundary of the parameter space. We illustrate the parametri c bootstrap test of the practically relevant and important simplifying hypo thesis that there is no spatial autocorrelation. Although the parametric bo otstrap requires computational effort, it is straightforward to implement a nd offers a wealth of information relating to the estimators and their prop erties. The proposed methodology is illustrated by analysing infant mortali ty in the province of British Columbia in Canada. Copyright (C) 2000 John W iley & Sons, Ltd.