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1 even though there are many reasons for allowing relationships to be nonlinear, there are reasons for not testing the nonlinear components for significance, as this might tempt the analyst to simplify the model. 158 Testing for linearity is usually best done to justify to nonstatisticians the need for complexity to explain or predict outcomes. 2. , X 1 X 2 ) can be added to the model and its coefficient tested. 36) and testing H 0 : (33 = ... = (37 = 0. This formulation allows the shape of the X2 effect to be completely different for each level of X 1 .

Formal tests of no overall association, linearity, and additivity can readily be constructed. Confidence limits for the estimated regression function are derived by standard theory. 3. The fitted spline function directly estimates the transformation that a predictor should receive to yield linearity in C(YIX). , square root) of a predictor that can be used if one is not concerned about the proper number of degrees of freedom for testing association of the predictor with the response. 4. The spline function can be used to represent the predictor in the final model.

Disadvantages: Does not easily apply to censored Y, and does not easily handle multiple predictors. 5. Fit a flexible parametric model that allows for most of the departures from the linear additive model that you wish to entertain. Advantages: One framework is used for examining the model assumptions, fitting the model, and drawing formal inference. " Disadvantages: Complexity, and it is generally difficult to allow for interactions when assessing patterns of effects. The first four methods each have the disadvantage that if confidence limits or formal inferences are desired it is difficult to know how many degrees of freedom were effectively used so that, for example, confidence limits will have the stated coverage probability.

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A Bayesian procedure for the sequential estimation of the mean of a negative-binomial distribution by Marcus R.

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