Fitting a Slack-Variable Model to Mixture Data: Some Questions Raised

Designating one of the mixture components as the slack variable and leaving it out of the fitted model is known as the slack-variable (SV) approach. Some who use this approach rationalize they understand what information is provided by the resulting slack-variable model better than what the fitted Scheffé-type model in all the components gives them. The question addressed in this paper is, “Does it matter which one of the q mixture components is designated the slack variable when arriving at the final form of the slack-variable model?” Both the simplex region and a constrained subregion of the simplex cases are discussed with examples of each leading to some conclusions and recommendations.