The actual working title of my dissertation is: Modeling Social Participation as Predictive of Life Satisfaction and Social Connectedness: Scale or Index?
When I tell people my topic, I usually start with the domain area: social participation as related to life satisfaction in older U.S. adults (my data set is people age 65 and over from the Health and Retirement Study), but really, the topic is a statistical and measurement one. Participation happens to be something I’m personally interested in and fits the statistical problem area, but I could do this same project in a variety of domains with a range of constructs. Maybe I ought to change my elevator speech to start with the statistical/measurement part.
Most psychometrics concerns itself with the measurement of latent psychological constructs like attitudes, intelligence, academic achievement and so forth. Psychometricians have developed sophisticated means of constructing instruments (surveys or assessments, for example) that can measure these latent constructs. The approach taken is often based on either classical test theory or item response theory. Either way, the assumption is that observed data (such as a student’s answers to test questions or a subject’s survey responses) are caused by whatever unobserved trait is intended to be measured.
However, there are some things we want to measure that don’t fit this model. Social participation is one of them. Participation instruments generally ask the respondent to report his or her level of participation in various activities. In a latent factor setting, you would then assume some underlying level of participation that gave rise to the observed frequencies of participation. That’s not quite right though. If someone increases their participation in some area — say by joining an investment club — their overall level of participation goes up. The increase in participation in the investment club seems causally prior to the increase in overall participation. This is the opposite direction of causality than that proposed by traditional psychometric models.
Some people call a measurement instrument developed by some sort of summation of disparate items an index rather than a scale, where a scale follows the latent factor model. The development of such indexes follows a so-called formative measurement model, where what you’re trying to measure is formed of what you observe, in contrast to the development of scales that follows a reflective measurement model, where what you observe reflects the underlying latent factor of interest. In the diagram, the first figure represents formative measurement (observed indicators x1-x3 cause the latent construct eta 1) and the second figure represents reflective (observed indicators y1 to y3 reflect the level of the latent construct).
There has been plenty of criticism of formative measurement, but I think it can be made useful, and that’s the aim of my dissertation project. I’m now at the analysis stage and just beginning to really understand the usefulness and potential of formative indexes.
As an aside, I don’t like to call formative measurement “measurement.” I prefer to think of it as “modeling.” I think what you’re doing with index development is constructing a one- or few-number summary of a lot of individual data items in a way that predicts outcomes of interest. Think of the Apgar score as a good example. It gives you a one number summary of the health of the baby and its likelihood to survive and thrive, but you’re not measuring one thing in particular about the baby. Well, maybe you are measuring overall health. Hmmmm.
To be continued…