All-Bias Designs for Spline Functions Joined at the Axes

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Abstract
Often, a sensible approach to a general design problem is to slightly expand the appropriate all-bias designs. This idea is applied to situations involving polynomial spline models in which it is necessary to (i) guard against second-degree models in some part, or all, of a cuboidal region of interest, while fitting first-degree models; (ii) guard against third-degree models, while fitting second-degree models. All joins are made on the axes. For (i), suitable designs include 2 IV k—p factorial designs in each 2 k -tant. For (ii), consideration of symmetrical designs leads to cuboidal designs of the type previously considered in Draper and Lawrence (1965).

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