Advanced Topics in Forest
Biometrics  FOR6934
More Nonlinear 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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 Spring '08
 Staff
 Regression Analysis, AIC, NLIN, NLMIXED Output

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