Assessing the Accuracy of Mixture Model Regression Calculations

The Scheffé and Becker models for mixture systems present special computing problems because neither of these models contains a constant term. Scientists may find that the associated least-squares calculations are inaccurate because of computer roundoff errors or, worse yet, that the available regression program does not have the capability of fitting a zero-intercept model. It is shown that these two problems can be circumvented by dropping one of the linear terms from the model and replacing it with a constant term. The resulting intercept model produces all the coefficients, predictions and significance tests appropriate to the Scheffé or Becker models. Methods for detecting roundoff error are discussed and recommendations concerning preferred computing procedures are included. Examples illustrating the effectiveness of the proposed methodology are presented.