What do recipes for gingerbread cookies and health status components have in common? A lot, and hopefully a



discovery while following a very popular holiday recipe will help to explain why recipes for summary health components require the subtraction of some ingredients.

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While in the kitchen during the holidays, I discovered that recipes for health measures and cookies have a lot in common, but I noticed a very important difference while watching Kate, my daughter, carefully mixing sugar, flour, ginger and other ingredients in a bowl. To make gingerbread,she simply had to measure the exact amount of each ingredient called for by the recipe and pour it into the mixing bowl. I took a look at her Joy of Cooking cookbook and noticed that, although the recipes for different holiday treats used some of the same ingredients, the measured amounts determine whether you end up with gingerbread or sugar cookies. The same holds true for recipes used in the construction of health measures although the algorithms are more complicated.

Why are recipes for cookies so much simpler? I looked carefully at the measures of the various ingredients my daughter was mixing. They were all very pure. When she added three teaspoons of ginger to the cup of sugar already in her mixing bowl, she could be confident that that was all she was adding. She never had to subtract anything back out of her mixing bowl.

Wouldn’t it be nice if the same were true for the ingredients used to construct measures of the major components of health? A “cup” of “physical disability” wouldn’t contain any “psychological well-being.” Much like the food ingredients that make completely independent contributions to the mixing bowl, pure health measures would also each make a unique contribution to the summary score. Accordingly, for example, we could simply add up the right amounts of the physical health measures called for by the recipe for the summary physical component of health.

Wondering if my daughter realized how much simpler it is to follow a recipe from a cookbook, I asked her, “Kate, what would you do if someone had already mixed one of the three teaspoons of ginger called for by your recipe when they filled your cup with sugar?” She quickly replied, “That’s easy, I would add another teaspoon of sugar to the cup of sugar and ginger and I would subtract one teaspoon of ginger from the three called for by the recipe.” Now, her recipe for gingerbread was beginning to sound more like the more complicated scoring algorithms we use for summary measures of health. Her answer made a lot of sense and helped me to understand why psychometricians do what they do when they estimate principal components. Once they have added the amount of each domain of health called for by the recipe, they subtract back out any additional amounts of that domain contained in subsequent measures.

An insight gained during a very pleasant holiday cooking session helped me understand how recipes work and why it is sometimes necessary to use a little subtraction to remove measures that would otherwise have been added to the mixing bowl twice.

We’re still enjoying looking at Kate’s gingerbread house (see figure), but I am hoping for a “taste test” soon.

Happy Holidays!