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ERIC Number: EJ779376
Record Type: Journal
Publication Date: 2007-Dec
Pages: 8
Abstractor: Author
Reference Count: 17
ISSN: ISSN-0020-739X
Unitary Response Regression Models
Lipovetsky, S.
International Journal of Mathematical Education in Science and Technology, v38 n8 p1113-1120 Dec 2007
The dependent variable in a regular linear regression is a numerical variable, and in a logistic regression it is a binary or categorical variable. In these models the dependent variable has varying values. However, there are problems yielding an identity output of a constant value which can also be modelled in a linear or logistic regression with this constant in place of a numerical or binary response. In a linear model with a positive response, dividing by its values yields a regression of constant output by the relative shares of individual predictors into the total response. Chemical reaction models use the agents' concentration, summing to a constant 100%. Another example can be found in priority modelling by Thurstone scaling for ranked or paired comparison data. The Thurstone scale can be estimated by probit or logit models with identical output across all the responses. Models with a unitary output can be constructed by software for regular regressions, but they give a different interpretation of results. For instance, the coefficient of multiple determination is not an estimate of the explained variance in the total response variance (which is zero), but a measure of the fitting quality of the constant approximated by an aggregate of predictors. (Contains 2 tables.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A