{"data":{"id":"10.6084/m9.figshare.c.2034698.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2034698.v1","prefix":"10.6084","suffix":"m9.figshare.c.2034698.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Kang, Lulu","nameType":"Personal","givenName":"Lulu","familyName":"Kang","affiliation":[],"nameIdentifiers":[]},{"name":"Salgado, Javier Cruz","nameType":"Personal","givenName":"Javier Cruz","familyName":"Salgado","affiliation":[],"nameIdentifiers":[]},{"name":"Brenneman, William A.","nameType":"Personal","givenName":"William A.","familyName":"Brenneman","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Comparing the Slack-Variable Mixture Model with Other Alternatives"}],"publisher":"Figshare","container":{},"publicationYear":2015,"subjects":[{"subject":"Science Policy"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Information And Computing Sciences"},{"subject":"Biological Sciences"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Earth and Environmental Sciences"}],"contributors":[],"dates":[{"date":"2015-12-05","dateType":"Created"},{"date":"2015-12-05","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/00401706.2014.985389","relatedIdentifierType":"DOI"},{"relationType":"IsPreviousVersionOf","relatedIdentifier":"10.6084/m9.figshare.c.2034698","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"http://creativecommons.org/licenses/by/3.0/us"}],"descriptions":[{"description":"There have been many linear regression models proposed to analyze mixture experiments including the Scheffé model, the slack-variable model, and the Kronecker model. The use of the slack-variable model is somewhat controversial within the mixture experiment research community. However, in situations that the slack-variable ingredient is used to fill in the formulation and the remaining ingredients have constraints such that they can be chosen independently of one another, the slack-variable model is extremely popular by practitioners mainly due to the ease of interpretation. In this paper, we advocate that for some mixture experiments the slack-variable model has appealing properties including numerical stability and better prediction accuracy when model-term selection is performed. We also explain how the effects of the slack-variable model components should be interpreted and how easy it is for practitioners to understand the components effects. We also investigate how to choose the slack-variable component, what transformation should be used to reduce collinearity, and under what circumstances the slack-variable model should be preferred. Both simulation and practical examples are provided to support the conclusions.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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