MODEL GOODNESS-OF-FIT ANALYSIS USING REGRESSION AND RELATED TECHNIQUES

Four related approaches for assessing model goodness-of-fit (GOF) are discussed in this paper: linear regression of observed versus predicte d values, the sum of squared prediction errors, a reliability index su mmarizing predictions as being within a factor K-s of observed values, and correlation-like measures of fit that normalize the sum of square d prediction error to be between zero and one. Relationships among the four measures are derived and alternative decompositions of the measu res into components relating to bias, variance, and consistency are pr esented. The measures are extended to include lack-of-fit terms when m ultiple observations are available for each prediction, and except for the reliability index, extended to include the multivariate case of m ultiple prediction variables. Application of the GOF measures to model predictions and observed radon-222 concentrations (a univariate examp le) showed significant lack-of-fit for high concentrations. Applicatio n of the GOF measures to predicted and observed mean lengths and densi ties of winter flounder larvae (a multivariate example) showed predict ed densities were good with most of the lack-of-fit attributed to simi lar to 0.44 mm bias in predicted mean lengths. The role of GOF analysi s in evaluating model performance is discussed.