Biological and Neuropsychological Mechanisms: Life-Span Developmental Psychology

By Hayne W. Reese; Michael D. Franzen | Go to book overview

2 On the Mismatching of Levels
of Abstraction in
Mathematical-Statistical
Model Fitting

John R. Nesselroade
John J. McArdle
University of Virginia

In Are Theories of Learning Necessary?, Skinner ( 1950) used the term theory to refer to "any explanation of an observed fact which appeals to events taking place somewhere else, at some other level of observation, described in different terms, and measured, if at all, in different dimensions" (p. 193). Skinner thus identified several levels of abstraction between observable events and the explanations for those events, and he questioned the value of such multilevel explanatory systems. Hebb ( 1949), Reese and Overton ( 1970), and others elucidated the formal representations and empirical requirements for a "model." Cattell ( 1966b, 1966c) discussed the form of a model, especially one based on formal mathematical and statistical features (see also Learner, 1978; Salmon, 1971). Following these latter notions we presume that there is merit in fitting abstract models to empirical data, but we take a critical look at some issues that arise because of the involvement of model fitting with different levels of abstraction of concepts and relationships.


The Growth of Model Fitting

Mathematical-statistical model fitting of data was given considerable attention in the 1940s and 1950s. Although modeling seemed to be a major "growth industry" in physics, chemistry, economics, and biology it did not become so in psychology and sociology until the later 1960s. The delay is somewhat surprising because the need was certainly there -- the problems facing psychology and sociology were no simpler than those in the other disciplines. Doubtless, there were many reasons for this longer lag time, one

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