Model building with multiple dependent variables and constraints

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    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.
    Original languageEnglish
    Pages (from-to)371-378
    JournalJournal of the Royal Statistical Society: Series D (The Statistician)
    Issue number3
    Publication statusPublished - 1999


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