It might instead seem that separate parameter values would be superior; estimating parameters from the data and then using these parameters to “predict” those same data seems dubious. In fact, however, separate parameters suffers two shortcomings—invalidity and unreliability—both likely to be serious.
Invalidity can be avoided by estimating parameter values from the data at hand. This gives the model its best opportunity to fit the data. This is done in Anova, which avoids the ambiguity that troubles the regression analysis and provides a valid test of goodness of fit. A statsig discrepancy can thus be unambiguously attributed to the model itself.
Unreliability in the separate parameter values will generally introduce bias. This bias problem was illustrated with Ancova for nonrandom groups (Section 13.2). Without working familiarity with statistical theory of “errors in variables, ” reliance on separate predictor values is dangerous. Other difficulties with regression analysis of substantive models are noted in Section 20.2 and in Anderson (1982, Sections 4.3 and 6.1.1).
Regression analysis can be extended to estimate stimulus values in the same way as Anova, as noted in Chapters 9 and 16. Bogartz put this approach to good use in the study of infant perception/cognition of Note 8.1.2d. The present criticism concerns use of prior stimulus metrics without allowance for unreliability or invalidity.