Further Consideration of Heteroscedasticity in Fitting Kinetic Models

Box and Hill [6] recently proposed a method for using power transformation weighting in least squares analysis to account for changing variance. Such an approach can be useful when the original data are heteroscedastic but adequate weight estimates are not available, and when the original data are homoscedastic but heteroscedasticity is induced by the data analyst in linearising a nonlinear model. Several aspects of their proposal are examined for practical implications in fitting chemical kinetic models and a more direct algorithm is recommended for fitting nonlinear models to heteroscedastic data. Methods for testing model adequacy and assessing parameter precision in such situations are also discussed.

[1]  H. Jeffreys.  The Theory of Probability , 1922 .

[2]  Bartlett Ms.  The use of transformations. , 1947 .

[3]  E. Beale,et al.  Confidence Regions in Non‐Linear Estimation , 1960 .

[4]  J. Downie,et al.  Kinetics of the vapor‐phase oxidation of napthalene over a vanadium catalyst , 1960 .

[5]  George E. P. Box,et al.  FITTING EMPIRICAL DATA * , 1960 .

[6]  N. L. Carr.  Kinetics of Catalytic Isomerization of n-Pentane , 1960 .

[7]  H. Levene.  Robust tests for equality of variances , 1961 .

[8]  Irwin Guttman,et al.  On Beale's Measures of Non-linearity , 1965 .

[9]  N. Draper,et al.  Unequal group variances in the fixed-effects one-way analysis of variance: a Bayesian sidelight. , 1966, Biometrika.

[10]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[11]  M. J. Box.  A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems , 1966, Comput. J..

[12]  Re-examination of Hougen-Watson Rate Models Including a Weighted Least Squares Approach , 1968 .

[13]  J. Downie,et al.  The vapor-phase oxidation of benzene over a vanadium oxide catalyst , 1969 .

[14]  J. Downie,et al.  The kinetics of the vapor-phase oxidation of o-xylene over a vanadium oxide catalyst , 1970 .

[15]  George E. P. Box,et al.  Correcting Inhomogeneity of Variance with Power Transformation Weighting , 1974 .

[16]  Parameters estimation in heterogeneous catalysis , 1974 .

[17]  David W. Bacon,et al.  Statistical assessment of chemical kinetic models , 1975 .

[18]  D. W. Bacon,et al.  Accounting for Heteroscedasticity in Experimental Design , 1977 .