Managing Multidimensionality

The US Department of Agriculture surveys thousands of people about their nutritional status. But what is one dimension to policy-makers is clearly two dimensions to consumers.

Policy-makers want to find out whether consumers are eating the right amount of the right things. Consumers think differently. We think (a) how much am I eating, and then (b) what am I eating?

There are 10 questions on the Healthy Eating Index (HEI). Six questions concern the five good foods we should eat and the variety of food we ingest. Four questions concern the four bad ingredients in food we should avoid. What happens? If you eat a lot, you get plenty of good stuff and plenty of bad. If you eat little, you cut down on the bad stuff, but also miss out on the good. This is perplexing for a simple-minded analysis.

When analyzed together, as the policy-makers would prefer, the 10 item test has a person separation of 1.6 (reliability of .7) -- we can barely distinguish the healthy eaters from the unhealthy. Even, worse, the items probing the 4 bad ingredients are negatively correlated with the 6 good items. The bad ingredients are not contributing to measuring healthy eating! There are two empirical dimensions fighting each other -- this is a practical problem in multidimensionality, not one of those figments of an overactive imagination.

Let's split the HEI into the 6 good items and the 4 bad, and analyze them separately. Now all correlations within tests are positive. Person separations are 2.15 (6 items) and 1.95 (4 items), giving reliabilities of .8 for each subtest. Each part measures better than the whole!

If policy-makers really want to learn about the nutritional status of the population, they will need to learn about it, and then attack it, on two fronts: quantity of food and quality of food. As long as they combine the two, their measures will give them little useful direction.

Benjamin D. Wright

Managing Multidimensionality. Wright B. D. … Rasch Measurement Transactions, 1997, 11:1 p. 540.

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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