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A note on fitting one‐compartment models: Non‐linear least squares versus linear least squares using transformed data
Author(s) -
Bailer A. John,
Portier Christopher J.
Publication year - 1990
Publication title -
journal of applied toxicology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.784
H-Index - 87
eISSN - 1099-1263
pISSN - 0260-437X
DOI - 10.1002/jat.2550100413
Subject(s) - least squares function approximation , non linear least squares , generalized least squares , linear least squares , total least squares , mathematics , linear model , iteratively reweighted least squares , lack of fit sum of squares , statistics , explained sum of squares , regression analysis , estimator
Drug concentrations in one‐compartment systems are frequently modeled using a single exponential function. Two methods of estimation are commonly used for determining the parameters of such a model. In the first method, non‐linear least‐squares regression is used to calculate the parameters. In the second method, the data are first transformed by a logarithmic function, and then the log‐concentration data are fit using linear least‐squares regression. The assumptions for fitting these models are discussed with special emphasis on which data points are most influential in determining parameter values. The similarities between fitting a linear regression model to the log‐concentration data and fitting a weighted regression model to the original data are noted. An example is presented that illustrates the differences in fitting a model to the log‐transformed data versus fitting unweighted and weighted models to the original‐scale data.