Health does seem multidimensional — you have respiratory health, brain health, digestive health. Reflective models handle multidimensionality quite well but if you were to use Apgar’s indicators to model health reflectively you’d likely find multiple latent factors and you wouldn’t come up with a one-number summary. You could use a second-order factor model, but the real purpose is to quantify in terms of predicted outcomes… how well will this baby survive and thrive? Introducing predicted outcomes into a formative model actually expresses the situation of interest. Besides that, there is not necessarily a higher order factor of health even though it’s useful for us to conceive of one. A baby might have had an insult to one system but everything else is fine.

Formative modeling is not illogical just like multiple regression is not illogical — it is merely a way of expressing that sometimes multiple things combine together to predict other things. I don’t necessarily take a composite variable as something real though. Formative modeling is pragmatic, whereas reflective models often assume a realist epistemology in which latent factors have objective, independent existence.

Thanks for your comment, and for your blog post summarizing Edwards’ critiques of formative measurement. I know I have a lot more to think about here and feedback is helpful. Meanwhile, I find Bollen’s writings on formative measurement have some good answers to Edwards’ critiques.

“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. ”

That’s not quite right either – the latent factor would be some psychological trait – e.g. belongingness, desire to participate – which in turn caused both of those participation rates to increase. You can’t conceptualize that form of participation as causing the other – rather, they are alternate indicators of the same underlying phenomenon (or are possibly at different levels of measurement).

Your observation about Agpar, as far as I can tell not being familiar with it specifically, is right on – you are collecting disparate specific bits of information and ultimately measuring overall health (the latent trait). The latent trait cannot be measured directly, but the operationalizations that reflect it can. The complexity really comes in when the latent trait is multidimensional, and it is that complexity level that lead many to flee to the relative (although illogical) simplicity of formative measurement.

Where I think that it’s interesting is in the idea that a robust private school sector offers a kind of competition that charter schools can’t. Charter schools are still public schools subject to many rules and regulations that don’t apply to private schools. And charter schools are not really subject to market discipline as they get the same amount of money per pupil no matter what they do.

I find all of this laughable. I pay taxes. My house is on a gravel road, on a private 1/2 of road, on well and septic. Until this past year all three of my children were home schooled.

So as I taxpayer, because I was paying into the system but not using the services, now I’m an added burden? Interesting concept.