It is important that we choose the appropriate secondary outputs and inputs to use in developing the inferential measurement model. The number of these 'explanatory' variables employed will influence the size and complexity of the final model. This impacts on the size of the data set that has to be used in model development. In particular, using a large number of explanatory variables also means that a larger number of parameters are needed to define the model. For an adaptive system, this would imply longer adaptation periods when attempting to track changes in process characteristics.

The objective here, and indeed for all process modelling activity, is for parsimony, i.e. to make use of the least number of variables to develop a model of sufficient accuracy. A variety of tools and techniques can help in this selection, as indicated by the following chart.

After collecting and conditioning the historical data, time plots and scatter diagrams can be used to establish quickly, whether relations exists between secondary and primary variables. The scatter diagrams should also show whether the relationships are linear or not. When linear models are being developed, non-linear relationships should be linearised in some manner, usually through the definition of new derived variables. For example, instead of the original data, the log. of the variable (the derived variable) is used.

In many situations, there will be a number of variables that will show relationships with the primary output. The task then is to choose those with the strongest relationships and to weed out those that are redundant (those which provide the same amount of information). Here, knowledge of the process is a distinct advantage. Never discard process knowledge in favour of black box modelling tools. However, statistical measures are useful in quantifying comparisons and to help in the selection procedure. We  use partial correlation coefficients to help us choose secondary variables. Loosely speaking, partial correlation coefficients are the multivariate versions of the more familiar correlation coefficient. The correlation between two variables are calculated, taking into account the possible effects that the other variables in the multivariate data set may have on them.

Once a set of potential secondary variables is selected, the inferential model can be developed and tested.

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