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By Zhong X., Li H.

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Deletion of other terms can lead to intercept forms of the quadratic model, and these are now discussed. 1 Intercept Forms Referring again to the two-factor regression function Rq. 22, page 23, this function has [(2 + I )(2 + 2)]/2 = 6 terms, of which 2 + 1 = 3 must be deleted to obtain a full-rank mixture model. If we retain the intercept, then we may retain two more regressors from the remaining five. We cannot choose X\ and X2 together, as this will lead to an exact dependency and will not model the quadratic curvature, and so we have a choice of nine possible models, all of which will be full rank.

1. In both cases the constrained region is still simplex-shaped. Let us now add a second nonzero lower bound. Fig. 2 illustrates the result. Again, the shaded constrained regions are still shaped like a simplex. Finally, let us add a third nonzero lower bound. 1. 2. Two lower bounds in a 3- and a 4-simplex. 3. Three lower bounds in a 3-simplex. Fig. 3 illustrates the result tort/ = 3. ) Again the constrained region is simplex-shaped. From these examples, the following property is interred. 1 When there are only lower bounds on component proportions, the suhregion of interest is always shaped like a simplex.

4 (right)). 0. Clearly, we cannot state a simple property about the shape of the design region when there are upper bounds. The shape will depend on the nature of the particular bound(s). Before adding a third upper constraint and continuing with this example, it is useful to digress for a moment. Assume that there are the same two upper-bound constraints on X\ and X2, but now q — 4. In this case it may come as a bit of a surprise that the following constraints are consistent because neither Eqs.

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[Article] Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model by Zhong X., Li H.

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