|
Non-linear
regression
Estimates the selected parameters in a regression for a
non-linear model. |
|
|
| .SelPar |
|
(Varying) selected parameters
in the model. |
| Decimal point is |
|
P
and s |
Parameters, p, and ¦ scale factors, s.
[Try s ∋ ~ p⁄s ∈ (0.1, 1).]
('¦' = 'new line'.)
• |
| n, nvar |
no.s of 'points' (n) and
independent 'variables' (nvar), counted from data. |
| Show D |
|
Shows (D) the data. |
| Graph abscissa |
(−1, no sort; 0, by y;
j, by xj, 1 ≤ j ≤ nvar) |
Graph abscissa to sort by. |
X
(n×nvar) |
X given as XT
[x(1..n, j), j = 1..nvar,
i.e.: x(1..n,1) ¦ x(1..n,2) ...
¦ x(1..n,nvar), for n points.]
• |
| Y |
• |
| krit |
1
2 (min. sq.)
3
4
∞ (minimax) |
Criterion (power of |ycalc−y|). |
| tol, maxit, mon |
(tol = 0 ⇒ εmach) |
Tolerance, max. no. of iterations, monitoring. |
| Graph |
|
Plots the initial or final graph. |
| Show GC |
|
Shows (GC) the graph coordinates. |
|
Estimates
the selected (or all the) parameters in the underlying model:
y(t) = α [1 − exp(β
t)]γ, with
P = (α β γ).
(To make β negative, −|β| is used instead.)
(The Nelder-Mead algorithm is used to optimize fit.)
Only the user-given parameters selected, '.SelPar', are optimized from
the initial guess, P, the others being kept constant. |
| References: |
Plate: Model090221 |
• Sharma,
Mahadev, and John Parton, 2007, "Height-diameter
equations for boreal tree species in Ontario using a mixed-effects modeling
approach", Forest Ecology and Management, 249, 187–198.
• 1796-02-22: Quetelet, Lambert A. J., birthday. |
