# Lec19.Nonlin1 - Nonlinear Regression KNNL Chp 13.1-13.5...

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Unformatted text preview: Nonlinear Regression KNNL Chp 13.1-13.5 Lec19.Nonlin1.ssc Splus/R: library(MASS), function nlminb, vcov.nlminb Note that vcov.nlminb may be missing from some MASS libraries Linear vs. Nonlinear Linear Models Nonlinear Models i i i i i i i i i i i i i i i i i i i i i x x y x y x y x x x y x x y x y + + = + = + = + + + + = + + + = + = ) 1 /( ) exp( ) exp( ) log( 1 1 1 2 3 2 1 2 2 1 1 Linear If you can write it in this form: 1 1 1 where 1 2 1 1 12 11 = = m mn m m n X X X X X X X X The Matrix ) ) ' ( ' (1 ) ( ) ' ( ' ) ( ) ' ( ) ( ' ) ' ( 1 ) ( 2 ) ( 1 2 1 2 1 h h new h h new h h h h h h MSE s MSE s MSE s X X X X Y X Y X X X X Y X Y X X Y X X X X Y---- + = = = = = = + = When to go nonlinear Empirically indicated Theoretically justified Examples Growth Density-dependent biological effects Population dynamics Thermodynamics Economics www.allposters.com Growth Rougheye Rockfish Sebastes aleutianus Size: To 97 cm (38 inches). Range/Habitat: Japan into Bering Sea, throughout Aleutian Islands, and south to San Diego, California. Depth: Deepwater, 14 to 478 fm, on bottom. Credits : Bill Barss ODFW Rougheye rockfish rougheye[1:10,] age length 1 2 18 2 3 4 3 3 3 4 3 17 5 3 17 6 3 23 7 3 10 8 4 18 9 4 16 10 4 16 Age Length (cm) 20 40 60 80 20 40 60 80 Rougheye rockfish Age Length (cm) 20 40 60 80 20 40 60 80 Rougheye rockfish library(MASS) plot(rougheye[,1],rougheye[,2], xlab=&quot;Age&quot;,ylab=&quot;Length (cm)&quot;) lines( supsmu( rougheye[,1], rougheye[,2] ), lwd=4,col=2) Von Bertalanffy Growth Model L dt dL - = Von Bertalanffy Growth Model ) ( L L dt dL- = Von Bertalanffy Growth Model ) 1 ( ) ( t t t e L L-- - = Length vs. Time Time Length 2 4 6 8 10 2 4 6 8 10 12 L(t) = Linf*(1-exp(-K*(t-T0))) Sensitivity to changes in K Length vs. Time Time Length 2 4 6 8 10 2 4 6 8 10 12 L(t) = Linf*(1-exp(-K*(t-T0))) Sensitivity to changes in Linf Additive and Multiplicative Error t e e L L e L L t t t t t t t ) 1 ( ) 1 ( ) ( ) (-- -- - = +- = Rougheye rockfish Age log(Length) (cm) 20 40 60 80 1 2 3 4 Age Length (cm) 20 40 60 80 20 40 60 80 Rougheye rockfish...
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## Lec19.Nonlin1 - Nonlinear Regression KNNL Chp 13.1-13.5...

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