Biomaterial Database

Evaluation of nonlinear regression with extended least squares: simulation study. 1985

A H Thomson, and A W Kelman, and B Whiting

A new approach to nonlinear least-squares regression analysis using extended least squares (ELS) was compared with three conventional methods: ordinary least squares (OLS); weighted least squares 1/C (WLS-1) and weighted least squares 1/C2 (WLS-2). With Monte Carlo simulation techniques, 3 X 200 data sets were constructed with constant proportional error (5, 10, and 15% error) and 3 X 200 with constant additive error (0.05, 0.10, and 0.15 g/mL) from an initial (perfect) data set based on known parameters. Two sampling strategies were employed: one with 17 time points and one with 10 time points. All data sets were fitted by each of the four methods, and parameter estimation bias was assessed by comparing the mean parameter estimate with the known value. The relative precision of each method was investigated by examination of the absolute deviations of each individual parameter estimate from the known value. ELS performed as well as the appropriate weighting scheme (WLS-2 for constant proportional error sets and OLS for constant additive error sets) and was superior with regard to both bias and precision to less appropriate methods.

UI	MeSH Term	Description	Entries
D007700	Kinetics	The rate dynamics in chemical or physical systems.
D008962	Models, Theoretical	Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.	Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D009010	Monte Carlo Method	In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)	Method, Monte Carlo
D012044	Regression Analysis	Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.	Regression Diagnostics,Statistical Regression,Analysis, Regression,Analyses, Regression,Diagnostics, Regression,Regression Analyses,Regression, Statistical,Regressions, Statistical,Statistical Regressions