Selection of the dependent variable

In the previous sections it has been stipulated that there are several response variables which can be modeled. The success of the optimization procedure depends on the selection of the response variable(s). There are several criteria which can be used to select a response variable [12,17]. The response variable should have a homoscedastical error structure and have to change continuously and smoothly. Both experimental data and chromatographic theory can be used to check these properties. 

From chromatographic theory [2] it is clear that the R value should result in simple models. For this reason it is preferred over, the k or the Rj. These latter response values can be calculated from predicted R values. It is more difficult to determine the error structure of the R . It is believed however that logarithmic transformation of the k values should result in homoscedastical error structures [3]. 

If there is no theory available to determine a suitable transformation, statistical methods can be used to determine a transformation. The Box-Cox transformation [18] is a common approach to determine if a transformation of a response is needed. With the Box-Cox transformation the response, y, is taken to different powers A, (e.g. -2 A 2) and it is determined how well the resulting transformed response can be fitted by a predefined (simple) model. Both an optimal value and a confidence interval for A can be estimated. The transformation which results in the lowest value for the residual variance is the optimal value and should give a combination of a homoscedastical error structure and be suitable for the predefined model. When A=0 the trans- 

It is decided that is the response which is preferred. When however, there are convincing contradicting results from the Box-Cox transformation then an alternative response has to be used. 

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Warning When the third alternative is adopted, the elements of the vector must be properly sorted in line with the selection of the dependent variables used in the evaluation of the null space. 

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