Model Building with Multiple Dependent Variables and Constraints

TL;DR

This paper introduces a generalized modeling method for multiple dependent variables with constraints, based on maximizing correlation, suitable for spreadsheet implementation and overcoming limitations of traditional regression.

Contribution

It presents a new approach extending multiple regression to multiple dependent variables with constraints, inspired by canonical correlation analysis, and highlights its advantages over least squares methods.

Findings

The method allows models with multiple dependent variables and constraints.

It can be easily implemented in spreadsheet programs.

Least squares approach is shown to be inadequate for this problem.

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 maximising 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.