Use of Diagnostic Parameters

Recently certain diagnostic parameters have been exploited to allow a discrimination among several rival models. These diagnostic parameters can be grouped into two broad classes—those that are inherently present in the model, and those that are introduced solely for the purpose of model discrimination. 

A nonintrinsic parameter is one that is introduced into a model for the purpose of allowing the specification of a preferred model from a larger group of rival models. To be useful, such a parameter must simplify the analysis procedures, allow a broadening of the data base of the analysis, or both. One type of nonintrinsic parameter useful in this regard enters as a multiplier of each of a series of predicted responses (C3, C4). For two models, such a method reduces (W4, W5) to defining a dependent variable 

This variable is then to be fitted using the equation 

The procedure to be followed, then, is to estimate the parameters K within each reaction-rate model by some appropriate technique (K8). The intrinsic parameter A can then be estimated by linear least squares. Owing to experimental error in the data, this estimate of A will typically be neither plus nor minus one-half. Hence the remaining portion of the analysis is to estimate the 

In the above analysis, y was considered to be a reaction rate. Clearly, any dependent variable can be used. Note, however, that if the dependent variable, y, is distributed with constant error variance, then the function z will also have constant error variance and the unweighted linear least-squares analysis is rigorous. If, in addition, y has error that is normal and independent, the least-squares analysis would provide a maximum likelihood estimate of A. On the other hand, if any transformation of the reaction rate is felt to fulfill more nearly these characteristics, the transformation may be made on y, ru r2 and the same analysis may be applied. One common transformation will be logarithmic. 

---