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Large-scale assessments typically cover domains with multiple sub-domains. For example, a reading test might include two scales: reading for literary experience and reading for information. These scales, measured indirectly through the test items and background variables, are assumed to be correlated (though not perfectly) with one another, and conceptually distinct. A summary measure of one’s reading performance is formed as a weighted average of these two scales. These summary scales are known as composite scales.
Procedures developed to accommodate the analysis of composite scales are based on either numerical integration or an approximation to the integrals (Thomas, 1993), and prove dauntingly slow. MML composite regression develops an extremely efficient alternative procedure for the analysis of composite scales that does not require more than two-dimensional numerical integration or a complex approximation, resulting in a computationally very fast algorithm that does not sacrifice statistical efficiency.
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