Influence diagnostics observations

Influential observations are ones that significantly affect the values of the parameter estimates, their standard errors, and the predicted values. One statistic used to detect influential observations has already been presented, the HAT matrix. An obvious way to detect these observations is to remove an observation one at a time and examine how the recalculated parameter estimates compare to their original values. This is the row deletion approach to influence diagnostics and on first glance it would appear that this process requires n-iter-ations—a numerically intensive procedure. Statisticians, however, have derived equations that directly reflect the influence of the ith observation without iteration. One useful diagnostic is DFFITS... 

Research and development of influence diagnostics for nonlinear models have not received as much attention as for the linear model. One obvious approach to determine the influence an observation has on the data would be to delete the ith observation, refit the model,... 

Available space is insufficient to permit demonstrating the partial plots for the example. However, Table 9 lists the leverages and the four influence diagnostics associated with individual observations... 

In real situations, the question arises frequently as to whether or not a marked influence of heat and mass transfer on the observable reaction rate may be expected under certain reaction conditions. Quite often then, one has to deal with reactions obeying complex kinetics where either none or only a very cumbersome analytical solution is possible based upon the methods described in Section 6.2.3. For such cases a number of useful diagnostic criteria have been developed in the past, either derived from asymptotic solutions of the governing differential equations or from perturbation methods [86], Most of these criteria have been explained in a detailed review by Mears [76]. More recent surveys of diagnostic transport criteria have been given by Butt [12] and by Madon and Boudart [74],... 

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