How to define and test explanations in populations

Peter J. Veazie


Solving applied social, economic, psychological, health care and public health problems can require an understanding of facts or phenomena related to populations of interest.  Therefore, it can be useful to test whether an explanation of a phenomenon holds in a population.  However, different definitions for the phrase “explain in a population” lead to different interpretations and methods of testing.  In this paper, I present two definitions:  The first is based on the number of members in the population that conform to the explanation’s implications; the second is based on the total magnitude of explanation-consistent effects in the population.  I show that claims based on either definition can be tested using random coefficient models, but claims based on the second definition can also be tested using the more common, and simpler, population-level regression models.   Consequently, this paper provides an understanding of the type of explanatory claims these common methods can test.


62A01; 62F03

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E.T. Higgins, Promotion and prevention: Regulatory focus as a motivational principle, in: M.P. Zanna (Ed.) Adv Exp Soc Psychol, Academic Press, New York, 1998, pp. 1-46.

P.J. Veazie, S. McIntosh, B. Chapman, J.G. Dolan, Regulatory focus affects physician risk tolerance, Health Psychology Research, 2 (2014) 85-88.

E. Demidenko, Mixed models : theory and applications, Wiley-Interscience, Hoboken, N.J., 2004.

R.B. Darlington, A.F. Hayes, Regression analysis and linear models : concepts, applications, and implementation, Guilford Press, New York, 2017.

M. Bunge, Philosophy of science: From Explanation to Justification, Rev. ed., Transaction Publishers, New Brunswick, N.J., 1998.

T. Sider, Writing the book of the world, Clarenson Press ; Oxford University Press, Oxford, New York, 2011.

N.C.A. da Costa, S. French, Science and partial truth : a unitary approach to models and scientific reasoning, Oxford University Press, Oxford ; New York, 2003.

M. Strevens, Depth : an account of scientific explanation, Harvard University Press, Cambridge, Mass., 2008.

P.J. Veazie, Understanding Scientific Inquiry, Science and Philosophy, 6 (2018) 3-14.

N. Bohr, On the Constitution of Atoms and Molecules, Philos Mag, 26 (1913) 857-875.

N. Bohr, On the Constitution of Atoms and Molecules, Philos Mag, 26 (1913) 476-502.

N. Bohr, On the Constitution of Atoms and Molecules, Philos Mag, 26 (1913) 1-25.

S. DellaVigna, Psychology and Economics: Evidence from the Field, J. Econ. Lit., 47 (2009) 315-372.

M. Rabin, A perspective on psychology and economics, Eur Econ Rev, 46 (2002) 657-685.

E.F. Loftus, J.W. Schooler, Information-Processing Conceptualizations of Human Cognition: Past, present, and future, in: G.D. Ruben (Ed.) Informatoin and Behavior, Transaction Books, New Brunswick, NJ, 1985, pp. 225-250.

P. Ylikoski, J. Kuorikoski, Dissecting explanatory power, Philos Stud, 148 (2010) 201-219.

M.P. Cohen, On Three Measures of Explanatory Power with Axiomatic Representations, Brit J Philos Sci, 67 (2016) 1077-1089.

J.N. Schupbach, J. Sprenger, The Logic of Explanatory Power, Philosophy of Science, 78 (2011) 105-127.

J.N. Schupbach, Comparing Probabilistic Measures of Explanatory Power, Philosophy of Science, 78 (2011) 813-829.

V. Crupi, K. Tentori, A Second Look at the Logic of Explanatory Power (with Two Novel Representation Theorems), Philosophy of Science, 79 (2012) 365-385.

J.B. Freeman, Acceptable premises : an epistemic approach to an informal logic problem, Cambridge University Press, Cambridge, UK ; New York, 2005.

E.T. Higgins, Beyond pleasure and pain, Am. Psychol., 52 (1997) 1280-1300.

P. Veazie, What makes variables random : probability for the applied researcher, CRC Press, Taylor & Francis Group, Boca Raton, 2017.

A. Spanos, Revisiting Haavelmo's structural econometrics: bridging the gap between theory and data, Journal of Economic Methodology, 22 (2015) 171-196.

J.T. Fox, K.I. Kim, C.Y. Yang, A simple nonparametric approach to estimating the distribution of random coefficients in structural models, Journal of Econometrics, 195 (2016) 236-254.

J.T. Fox, K.I. Kim, S.P. Ryan, P. Bajari, A simple estimator for the distribution of random coefficients, Quant Econ, 2 (2011) 381-418.

G. Efron, R.J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, New York, 1993.

P.J. Veazie, Understanding Statistical Testing, Sage Open, 5 (2015).

J.J. Heckman, E. Vytlacil, Econometric Evaluation of Social Programs, Part 1: Causal models, structural models and econometric policy evaluation, in: J. Heckman, E. Leamer (Eds.) Handbook of Econometrics, Elsevier, Amsterdam, 2007, pp. 4779-4874.



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