On the practical value of rigorous modeling

What is the practical value of modeling real things in the world in terms requiring separable parameters?

If the parameters are separable, the stage is set for the validation of a model that is relevant to and applies to any individual person or challenge belonging to the infinite populations of those classes of all possible people and challenges.

Parameter separation does not automatically translate into representations of that conjoint relationship, though. Meaningful and consistent variation in responses requires items written to provoke answers that cohere across respondents and across the questions asked.

In addition, enough questions have to be asked to drive down uncertainty relative to the variation. Response patterns can be reproduced meaningfully only when there is more variation than uncertainty. Precision and reliability are functions of that ratio.

But when reliable and meaningful parameter separation is obtained, the laboratory model represents something real in the world. Moreover, the model stands for the object of interest in a way that persists no matter which particular people or challenges are involved.

This is where the practical value kicks in. This is what makes it possible to export the laboratory model into the real world. The specific microcosm of relationships isolated and found reproducible in research is useful and meaningful to the extent that those relationships take at least roughly the same form in the world. Instead of managing the specific indicators that are counted up in the concrete observations, it becomes possible to manage the generic object of interest, abstractly conceived. Adaptively selecting the relevant indicators according to their practical relevance on the ground in real world applications has the practical consequence of unifying measurement, management, and accountability in a single sphere of action.

Plainly there’s a lot more that needs to be said about this. For instance, the identifiability of models with separable parameters translates into the identifiability of the thing measured as something in the world that can be meaningfully represented in words. There’s a real need for more of this kind of practical translation between mathematical technicalities and practical reasons for taking the trouble to do things in particular ways.

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LivingCapitalMetrics Blog by William P. Fisher, Jr., Ph.D. is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Based on a work at livingcapitalmetrics.wordpress.com.
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