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Goodness of Fit Metrics

Along with graphical assessment one may present metrics, actual numbers, that attempt to quantify the goodness of fit of the model. Two such metrics were presented in the previous section, SSE and MSE, and in this section other metrics will be presented. Formal hypothesis tests may be done on these metrics, such as comparing the metric from one model against another. However, many test statistics based on these metrics tend to be sensitive to the assumption of the underlying distribution, e.g., normally distributed, such that the results from these tests should be treated with skepticism (Cook and Weisberg, 1982). [Pg.16]

Common modifications to SSE and MSE lead to a class of metrics called discrimination functions. These functions, like the Akaike Information Criteria (AIC), are then used to choose between competing models. One problem with functions like the AIC and MSE is that the actual value of the function is impossible to interpret without some frame of reference. For instance, how can one interpret a MSE or an AIC of 45 Is that a good or bad Further, some discrimination functions are designed to be maximized whereas others are designed to be minimized. In this book, the model with the smallest discrimination function is superior to all other models having the same number of estimable parameters, unless otherwise noted. This class of functions will be discussed in greater detail in the section on Model Selection Criteria. [Pg.16]

Three goodness of fit metrics bear particular attention the coefficient of determination, the correlation coefficient, and the concordance coefficient. The coefficient of determination (R2) is simply [Pg.16]

the adjusted R2 may decrease when additional terms are added to the model and they do not contribute to the goodness of fit. [Pg.17]

Pearson s product-moment correlation coefficient, often simply referred to as the correlation coefficient, r, has two interesting properties. First, [Pg.17]


Table 6.10 Comparison of ML and REML goodness of fit metrics and p-values for significance of fixed effects for tumor growth example under the final model (unstructured G-matrix, spatial power R-matrix). Table 6.10 Comparison of ML and REML goodness of fit metrics and p-values for significance of fixed effects for tumor growth example under the final model (unstructured G-matrix, spatial power R-matrix).
This chapter has presented the detailed application of electronic tongues as analytical systems for multidetermination of species, in batch conditions, and also integrated in FIA and SIA systems. The preferred chemo-metrics tool to model its response, ANNs, has been presented in detail. The different precautions for its use together with options and configurations have been described. The ways employed to check the goodness of fit of a developed response model have also been explained. In our applications, we usually employ a multiple output ANN, but nobody impedes the use of a different ANN with a single output for each species considered, except for the training effort which is multiplied. [Pg.747]

An unbiased model should have residuals whose mean value is near zero. For a linear model the residuals always sum to zero, but for a nonlinear model this is not always the case. Conceptually one metric of goodness of fit is the squared difference between observed and predicted values, which has many different names, including the squared residuals, the sum of squares error (SSE), the residual sum of squares, or error sum of squares... [Pg.13]

In summary, the measures presented in this section represent metrics that assess the goodness of fit in a... [Pg.19]

BSV in CL was estimated at 32% with a residual error of 21%. The only covariates examined by Aarons et al. were weight, BSA, sex, CrCL, and age. Not examined were other weight-based metrics BSA, LBW, IBW, or BMI. The model by Aarons et al. and the model in Eq. (9.17) were similar but different in that in the model by Aarons et al. did not account for IOV. Further, the model by Aarons et al. included an intercept on VI. In this analysis, the goodness of fit when the intercept was added did not improve. The net effect of these differences was that residual variability in the... [Pg.335]

The error metric is a measure of a model s prediction accuracy. The software provides a number of error metrics such as squared error, worst-case error, logarithm error, median error, interquartile absolute error and signed difference for minimization. Additionally, options to maximize the correlation coefficient or the B goodness of fit or experimental hybrid that considers both absolute error and correlation are also available. Data sphtting is an important step which divides the data into a training set to generate solutions and a test set to check the accuracy of those solutions (Fig. 3.62). [Pg.187]

When using multivariate analyses, there are a variety of model metrics which evaluate the goodness of fit of a model to an individual spectrum (not to be confused with spectral band metrics previously discussed, which are simply some observed property of a band in the spectrum) [8]. These metrics should give a good indication of when the shift of a spectrum has passed outside of an acceptable range for an individual model. [Pg.302]

AU search algorithms have a goodness-of-fit or hit quality index metric to indicate which spectrum is the best match. In a true Euchdean distance metric, where the spectra are normalized to unity, the metric wiU report a value between zero and 1, where the value of zero represents a perfect match. Commercial software will often scale or adjust this number. For example, if the Euclidean distance is subtracted from 1 and the result multiplied by 1000, a perfect match gives rise to a hit quality index of 1000, and a complete mismatch gives a score of zero. Regardless, the algorithm to compare the spectra is virtually identical only the way the results are reported varies. [Pg.247]

The sum in Equation [13] is taken over N wavelength points (A ), z is a vector of the fitted parameters (in this case, d nterface df and A), and m is the dimensionality of z (i.e. 3). The quantities in the denominator (8Pexp( i)) re the errors in the experimental data. The is a good metric for the goodness of fit to ellipsometry data. If is near 1 the fit is a good fit, but if it is much greater than 1 the model does not fit the data. After the parameters are determined, it is also necessary to calculate the error limits as well as the correlation coefficients of all the fitted parameters. [Pg.409]

The number of Frenkel interstitials was obtained from a fit of the tensi-metric data to the observed pressure dependence behavior at 100 mm at 831°C. It has been assumed that the concentration of intrinsic interstitials is independent of pressure, whereas the concentration of extrinsic defects varies as the square root of the pressure. This is not strictly correct since they depend on the value of K. It should, however, be a good approximation at the lower temperatures. [Pg.270]


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