Model Adequacy Tests

There is a plethora of model adequacy tests that the user can employ to decide whether the assumed mathematical model is indeed adequate. Generally speaking these tests are based on the comparison of the experimental error variance estimated by the model to that obtained experimentally or through other means. 

Let us now consider models that have only more than one measured variable (w>l). The previously described model adequacy tests have multivariate extensions that can be found in several advanced statistics textbooks. For example, the book Introduction to Applied Multivariate Statistics by Srivastava and Carter (1983) presents several tests on covariance matrices. 

Although all the underlying assumptions (local linearity, statistical independence, etc.) are rarely satisfied, Bartlett s jf-test procedure has been found adequate in both simulated and experimental applications (Dumez et al., 1977 Froment, 1975). However, it should be emphasized that only the x2-test and the F-test are true model adequacy tests. Consequently, they may eliminate all rival models if none of them is truly adequate. On the other hand, Bartlett s x2-test does not guarantee that the retained model is truly adequate. It simply suggests that it is the best one among a set of inadequate models ... 

Step 6. Perform the appropriate model adequacy test (x2-test, F-test or Bartlett s -/2-test) for all rival models (just in case one of the models... 

Table 12.7 Chemostat Kinetics Results from Model Adequacy Tests Assuming af. is Known (yftest) Performed at a=0.0I Level of Significance...

With this book the reader can expect to learn how to formulate and solve parameter estimation problems, compute the statistical properties of the parameters, perform model adequacy tests, and design experiments for parameter estimation or model discrimination. 

Addresses practical issues such as cost, feasibility, model adequacy-testing, and forecasting... 

Tests 1 and 2 determine the true model adequacy test 3 can only yield the best model. Applying the above statistics to models that are nonlinear in the parameters requires the model to be locally linear. For the particular application considered here, this means that the residual mean square distribution is approximated to a reasonable extent by the distribution. Furthermore, care has to be taken for outliers, since appears to be rather sensitive to departures of the data from normality. In Example 2.7.1.1.A, given below, this was taken care of by starting the elimination from scratch again after each experiment. Finally, the theory requires the variance estimates that are tested on homogeneity to be statistically independent. It is hard to say to what extent this restriction is fulfilled. From the examples given, which have a widely different character, it would seem that the procedure is efficient and reliable. 

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