Pseudocomponents
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Constrained designs (those in which you specify lower or upper bounds) produce coefficients which are highly correlated.

·    Lower bounds are necessary when any of the components must be present in the mixture. For example, lemonade must contain lemon juice.

·    Upper bounds are necessary when the mixture cannot contain more than a given proportion of an ingredient. For example, a cake mix cannot contain more than 5% baking powder.

Generally, you can reduce the correlations among the coefficients by transforming the components to pseudocomponents. For complete discussion, see [1] and [3].

Pseudocomponents, in effect, rescale the constrained data area so the minimum allowable amount (the lower bound) of each component is zero. This makes a constrained design in pseudocomponents the same as an unconstrained design in proportions.

The table below shows two components expressed in amounts, proportions, and pseudocomponents. Suppose the total mixture is 50 ml. Let X1 and X2 be the amount scale. Thus X1 + X2 = 50. Suppose X1 has a lower bound of 20 (this means that the upper bound of X2 is 50 minus 20, or 30). Here are some points on the three scales: