Model Building with Multiple Dependent Variables and Constraints

The Statistician, Vol. 48, No. 3, pp. 371-378, 1999

9 Pages Posted: 5 Mar 2009 Last revised: 2 Mar 2016

Chris Tofallis

University of Hertfordshire Business School

Date Written: 1999

Abstract

The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with multiple variables on both sides of an equation and which can be computed easily using a spreadsheet program. The underlying principle (originating from canonical correlation analysis) is that of maximizing the correlation between the two sides of the model equation.

This paper presents a fitting procedure which makes it possible to force the estimated model to satisfy constraint conditions which it is required to possess, these may arise from theory, prior knowledge or be intuitively obvious. We also show that the least squares approach to the problem is inadequate as it produces models which are not scale invariant. By contrast the proposed approach leads to equivalent results whatever measurement units are chosen.

Keywords: canonical correlation analysis, regression, model building

JEL Classification: C2

Suggested Citation

Tofallis, Chris, Model Building with Multiple Dependent Variables and Constraints (1999). The Statistician, Vol. 48, No. 3, pp. 371-378, 1999. Available at SSRN: https://ssrn.com/abstract=1353202

Chris Tofallis (Contact Author)

University of Hertfordshire Business School ( email )

College Lane
Hatfield, Hertfordshire AL10 9AB
United Kingdom

HOME PAGE: http://tinyurl.com/tofallis

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