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The Curve-Fitting Problem: An Objectivist View

Published online by Cambridge University Press:  01 April 2022

Stanley A. Mulaik
Stanley A. Mulaik*
Affiliation:
Georgia Institute of Technology
*
†Send requests for reprints to the author, School of Psychology, Georgia Institute of Technology, Atlanta, GA 30332; email: pscccsm@prism.gatech.edu.
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Abstract

Model simplicity in curve fitting is the fewness of parameters estimated. I use a vector model of least squares estimation to show that degrees of freedom, the difference between the number of observed parameters fit by the model and the number of explanatory parameters estimated, are the number of potential dimensions in which data are free to differ from a model and indicate the disconfirmability of the model. Though often thought to control for parameter estimation, the AIC and similar indices do not do so for all model applications, while goodness of fit indices like chi-square, which explicitly take into account degrees of freedom, do. Hypothesis testing with prespecified values for parameters is based on a metaphoric regulative subject/object schema taken from object perception and has as its goal the accumulation of objective knowledge.

Type
Research Article
Information
Philosophy of Science , Volume 68 , Issue 2 , June 2001 , pp. 218 - 241
Copyright
Copyright © 2001 by the Philosophy of Science Association

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Footnotes

‡

The author is indebted to Roderick P. McDonald and Han Oud for discussions of the AIC index that led to a better understanding of its characteristics in large samples.

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