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Measurement Model Approach to the Construction of Simple Linear Composite Measures

NCJ Number
92505
Author(s)
T Connolly
Date Published
1979
Length
40 pages
Annotation
This paper suggests the circumstances under which the devising of optimal composite measures, rather than the use of standard rules of thumb, might be justified by the resulting improvement in measurement quality.
Abstract
In cases where a researcher is interested in some variable or construct that is not directly measurable without error, a number of indicators or measures may be available, each tapping the variable of interest in an imperfect way. The researcher should combine these several indicators into a single 'composite measure' that will reflect the underlying variable better than does any one of the indicators alone. This paper considers several alternative approaches to the construct of such composites and assesses the adequacy of the resulting measures. A simple linear measurement model is proposed for a setting in which several measures are associated with a single underlying variable of interest. The adequacy of three strategies for forming composite measures is examined. The composite measures are assessed in terms of their validity and their mean squared error. A general algebraic treatment is illustrated using a number of examples ranging from the simplest case (equally valid measures with no shared method variance) to the most complex (unequally valid measures with shared method variance'. Substantively, the examples have been chosen to show both the general robustness and the possible weaknesses of some familiar rules of thumb and standard practices in developing composite measures. It is argued that the use of any standard practice without examination of the implicit measurement model is a dangerous procedure. Eighteen references are provided, and the appendixes detail the mathematical computations.

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