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2b_more_nonlinear

# 2b_more_nonlinear - Outline Advanced Topics in Forest...

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Advanced Topics in Forest Biometrics - FOR6934 More Non-linear regression Outline 1. Assumptions of nonlinear regression 2. Assessing goodness of fit in nonlinear regression 3. Plateau models 4. Using NLMIXED versus NLIN Assumptions of nonlinear regression ± The model is correctly specified, e.g., you are not trying to fit a power function when the “real” relationship is a hyperbola ± The dependent variable is normally distributed. ± The dependent variable is homoscedastic , i.e., the variability in y is approximately constant over all values of x. ± The values of the independent variable are known or measured without error. ± The observations are independent. Is my nonlinear regression any good? ± Did the fitting algorithm converge? ± Is the curve close to the data (i.e., low MSE)? ± Is the equation biologically plausible? ² Consider both the shape of the curve and the values of the estimated coefficients (i.e., intercepts) ± Is there any lack of fit? ² Look for systematic deviations from the curve ± Are the independent variables significant predictors of the dependent variable? ± Did you find the local or global minimum? ² Try altering the starting values – do you get the same fit? What is a plateau model? ± Plateau models describe a situation where a function (e.g., quadratic) describes the relationship between the dependent and independent variables up to a join point, but thereafter the dependent variable is constant, i.e., hits a plateau 0 5 10 15 20 25 30 35 40 45 50 0 1 02 03 04 05 06 07 0 dbh (cm) height (m) quadratic relationship dbh0 constant 0 5 10 15 20 25 30 35 40 45 50 0 dbh (cm) quadratic relationship dbh0 constant Challenges in plateau model ± In addition to estimating the coefficients in the

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2b_more_nonlinear - Outline Advanced Topics in Forest...

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