Model selection regression

Rieckmann and Volker fitted their kinetic and mass transport data with simultaneous evaluation of experiments under different reaction conditions according to the multivariate regression technique [116], The multivariate regression enforces the identity of kinetics and diffusivities for all experiments included in the evaluation. With this constraint, model selection is facilitated and the evaluation results in one set of parameters which are valid for all of the conditions investigated. Therefore, kinetic and mass transfer data determined by multivariate regression should provide a more reliable data basis for design and scale-up. 

Primary model selection should be based on the experimental data observations but other Information may also be useful, such as knowledge of the drug s mechanism of action, results from earlier studies, or concentration-effect relationships of related compounds. The performance of different models can be systematically tested by using a nonlinear regression program, which has readymade routines for common models and also allows the user to formulate his own models. Model selection and validation Is an Important Issue, which Is however beyond the scope of this chapter. 

Shi, P. and Tsai, C.-L. (2002). Regression model selection—A residual likelihood approach. 

David Cummins is Principal Research Scientist at Eli Lilly and Company. His interests are in nonparametric regression, exploratory data analysis, simulation, predictive inference, machine learning, model selection, cheminformatics, genomics, proteomics, and metabonomics. 

Mallows Cp. Model selection criterion used to compare biased regression models with the full least squares regression model ... 

Description A QSAR toolkit with descriptor generation (topological, geometrical, electronic, and physicochemical descriptors), variable selection, regression and artificial neural network modelling. 

Arihood, S. A., Trowbridge, C. G. Model Selection and Parameter Evaluation by Nonlinear Regression, with an Application to Chymotrypsin Rate Data. Arch. Biochem. Biophys. 141. 131 (1970). 

Model Selection and Sequential Variable Selection Procedures In Multiple Linear Regression... 

Even though many different covariates may be collected in an experiment, it may not be desirable to enter all these in a multiple regression model. First, not all covariates may be statistically significant—they have no predictive power. Second, a model with too many covariates produces models that have variances, e.g., standard errors, residual errors, etc., that are larger than simpler models. On the other hand, too few covariates lead to models with biased parameter estimates, mean square error, and predictive capabilities. As previously stated, model selection should follow Occam s razor, which basically states the simpler model is always chosen over more complex models. ... 

Regression model selection <4 PL> with weighting factor... 

The next example presents an even more difficult problem when handling simultaneously immiscibility and azeotropy. Both the model selection and the regression procedure play a significant role. 

A note of caution should be made in connection with setting k= 1. In this case the selected regression model has full rank (i.e. the number of PLS factor is identical to the number of selected variables). The investigator should be careful not to use a model that might be unstable. 

The experimenter, we assume, has completed the model selection procedures, as previously discussed, and has found the linear regressirai models to be adequate. Figure 2.42 shows y (regression line) and the actual data at a 95% confidence interval for product A. Figure 2.43, likewise, shows the data for product B. 

TABLE 13 Statgraphics Output for Regression Model Selection for Steam... 

For all three methods the final model selected like any regression model should be evaluated to the regression diagnostics described earlier. 

Hurvich, C. and Tsai, C. Regression and time series model selection in small samples. 

Table 6 Analysis of Variance for a Model Selected by Stepwise Regression...

Ouyang Z, Clyde MA, Wolpert RL (2008) Bayesian kernel regression and elassification, bayesian model selection and objective methods. Gainesville, NC... 

Table 9.6. Selected regressions illustrating the key role of lake total phosphorus in predictive models. Many biological variables that would normally require determinations from extensive and expensive field and laboratory work may be estimated/predicted from one key, abiotic state variable, total-P. Some variables may be predicted with great precision, others with low. (Peters 1986 H kanson and Peters 1995)...

---