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Unformatted text preview: Nonlinear Least Squares Regression ESM 206C May 27 2008 Nonlinear least squares regression • Some models cannot be made linear in parameters – E.g., thetalogistic stockrecruitment model • Solution: nonlinear least squares (NLS) • All other assumptions from OLS (normal residuals, etc.) still apply • Conceptually the same: find the values of parameters that minimize the sum of squared residuals ( 29 1 , 2 , 3 , 4 , i i i i i i y f x x x x ε = + L 1 log log (1 )log t t S c t t t t t t R S e R c S S θ β ε θ α α β ε + + = = + + + Nonlinear least squares regression • Numerically intensive: can’t be done by hand – As number of parameters gets “large” – say above 10 or so – can take substantial time even on modern computers • Not guaranteed to get the “right” answer – Computer algorithms find “local” minima; sometimes there are more than one – Need to provide “pretty good” initial guesses for the parameter values – Base guesses on • scientific information • If only a few nonlinear parameters, try fixing them at a few values and using OLS to estimate the rest; choose the best overall combination Alewife StockRecruitment Set up the problem in Excel...
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 Spring '08
 KENDALL,BERKLEY
 Environmental Science, Least Squares, Regression Analysis, AIC, Nonlinear Fit Plot

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