By Maurice G. Kendall, William R. Buckland

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For Model 2, qt = PO P l Y t - 1 P 2 Y t - 2 , etc. 2 provides diagnostics statistics pertaining to these models. These include the sum of squares of the working residuals (WR), (X - f i t ) / ( a p i / a q t ) ,evaluated at the mean sum of squares (MSE) of the response or raw residuals, Yt - fit, the sum of squares of Pearson residuals x2,the scaled deviance D with df = N - p degrees of freedom, and the AIC and BIC computed up to an additive constant from the deviance as 1) 2p and D + p l o g ( N ) ,respectively.

I... I . Series : log(C0) lOS(C0) 2: 0 ......... . ....... &.. 1 Weekly data of filtered total mortality and temperature, and log-filteredCO, and the corresponding estimated autocorrelation functions. N = 508. 1 Covariates and qt used in Poisson regression. S = SO2, N = NOz. To recover qt, insert the P’s. For Model 2, qt = PO P l Y t - 1 P 2 Y t - 2 , etc. 2 provides diagnostics statistics pertaining to these models. These include the sum of squares of the working residuals (WR), (X - f i t ) / ( a p i / a q t ) ,evaluated at the mean sum of squares (MSE) of the response or raw residuals, Yt - fit, the sum of squares of Pearson residuals x2,the scaled deviance D with df = N - p degrees of freedom, and the AIC and BIC computed up to an additive constant from the deviance as 1) 2p and D + p l o g ( N ) ,respectively.

Furthermore, even when the fit is good and the approximation holds, D can still be large with an expected value of iV - p approximately. The deviance itself is defined as q5D, and is free of 05. From this we obtain an approximately unbiased moment estimator for 4, - - xh-p & Deviance N-p The so called analysis of deviance of nested models is a reiteration of the log partial likelihood ratio test procedure. Let DOcorrespond to Ho : fi = Po, and D1 to HI : p = PI, where PI is a p-dimensional vector and Po is a subvector of with dimension q x 1, q < p.

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