Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T09:42:34.424Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Akaiki, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle”, in Petrov, B. N. and Csaki, F. (eds.), Second International Symposium on Information Theory. Budapest: Akademiai Kiado, 26–281.Google Scholar
Akaiki, H. (1987), “Factor Analysis and AIC”, Psychometrika 52: 317–332.CrossRefGoogle Scholar
Bandyopadhyay, Prasanta S. and Boik, Robert J. (1999), “The Curve Fitting Problem: A Bayesian Rejoinder”, Philosophy of Science 66 (Proceedings): S390–S402.CrossRefGoogle Scholar
Bandyopadhyay, Prasanta S. Boik, Robert J., and Basu, Prasun, (1996), “The Curve Fitting Problem: A Bayesian Approach”, Philosophy of Science 63 (Proceedings): S264–S272.CrossRefGoogle Scholar
Bollen, Kenneth A. (1989), Structural Equations with Latent Variables. New York: Wiley.CrossRefGoogle Scholar
Butterworth, G. (1983), “Structure of the Mind in Human Infancy”, Advances in Infancy Research 2: 1–29.Google Scholar
Browne, M. and Cudeck, R. (1992), “Alternative Ways of Assessing Model Fit”, Sociological Methods and Research 21: 230–258.CrossRefGoogle Scholar
Fisher, Ronald A. (1925), Statistical Methods for Research Workers. London: Oliver and Boyd.Google Scholar
Forster, Malcolm (2000), “Key Concepts in Model Selection: Performance and Generalizability”, Journal of Mathematical Psychology 44: 205–231.CrossRefGoogle ScholarPubMed
Forster, Malcolm and Sober, Elliott (1994), “How to Tell When Simple, More Unified or Less Ad Hoc Theories Will Provide More Accurate Predictions”, British Journal for the Philosophy of Science 45: 1–35.CrossRefGoogle Scholar
Gibson, James J. (1966), The Senses Considered As Perceptual Systems. London: George Allen and Unwin Ltd.Google Scholar
Gibson, James J. (1979), The Ecological Approach to Visual Perception. Boston: Houghton-Mifflin and Co.Google Scholar
Herschel, J. F. W. ([1830] 1966), A Preliminary Discourse on the Study of Natural Philosophy. New York: Johnson Reprint Corporation. Facsimile of 1830 edition published by Longman. Rees, Brown and Green and John Taylor, London.Google Scholar
Johnson, Mark (1987), The Body in the Mind. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Lakoff, George (1987), Women, Fire and Dangerous Things. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Lakoff, George (1993), “The Contemporary Theory of Metaphor”, in A. Ortony (ed.) Metaphor and Thought, 2nd edition. Cambridge: Cambridge University Press, 202–251.CrossRefGoogle Scholar
Lakoff, George and Johnson, Mark (1980), Metaphors We Live By. Chicago: University of Chicago Press.Google Scholar
Lakoff, George and Johnson, Mark (1999), Philosophy in the Flesh. New York: Basic Books.Google Scholar
Lakoff, George and Nuñez, Rafael (2001), Where Mathematics Comes From. New York: Basic Books.Google Scholar
McDonald, R. P. (1989), “An Index of Goodness of Fit Based on Noncentrality”, Journal of Classification 6: 97–103.CrossRefGoogle Scholar
McDonald, R. P. and Marsh, H. W. (1990), “Choosing a Multivariate Model: Noncentrality and Goodness of Fit”, Psychological Bulletin 107: 247–255.CrossRefGoogle Scholar
Mulaik, Stanley A. (1990), “An Analysis of the Conditions under Which the Estimation of Parameters Inflates Goodness of Fit Indices As Measures of Model Validity.” Paper presented at the annual meeting of the Psychometric Society, Princeton, NJ, June 28–30.Google Scholar
Mulaik, Stanley A. (1995), “The Metaphoric Origins of Objectivity, Subjectivity, and Consciousness in the Direct Perception of Reality”, Philosophy of Science 62: 283–303.CrossRefGoogle Scholar
Mulaik, Stanley A., Raju, N., and Harshman, R. (1997), “There Is a Time and a Place for Significance Tests”, in Harlow, L., Mulaik, S. A., and Steiger, J. (eds.), What If There Were No Significance Tests? Mahwah, NJ: Lawrence Erlbaum Associates, 65–115.Google Scholar
Mulaik, Stanley A., James, L. R., Alstine, J. Van, Bennett, N., Lind, S., and Stillwell, C. D. (1989), “An Evaluation of Goodness of Fit Indices for Structural Equation Models”, Psychological Bulletin 105: 430–445.CrossRefGoogle Scholar
Popper, Karl R. ([1934] 1961), The Logic of Scientific Discovery. Translated and revised by the author. New York: Science Editions. Originally published as Logik der Forschung.Google Scholar
Sakamoto, Y., Ishiguro, M., and Kitagawa, G. (1986). Akaike Information Criterion Statistics. Tokyo: KTK Scientific Publishers.Google Scholar
Thurstone, L. L. (1947), Multiple-factor Analysis. Chicago: University of Chicago Press.Google Scholar
Tiles, Mary (1984), Bachelard: Science and Objectivity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Whewell, William ([1847] 1966), The Philosophy Of The Inductive Sciences Founded Upon Their History, Volume 2. The Sources of Science, no. 41. New York and London: Johnson Reprint Corporation. Facsimile of the 2nd edition (London).Google Scholar
Williamson, Richard E., and Trotter, Hale F. (1979), Multivariable Mathematics. Englewood Cliffs, NJ: Prentice-Hall, Inc.Google Scholar