fitcurve: Estimatinng the parameters of the nonlinear curve fitted to...

In ForestFit: Statistical Modelling for Plant Size Distributions

Estimatinng the parameters of the nonlinear curve fitted to the height-diameter(H-D) observations

Description

Estimates the parameters of the nine well-known nine three-parameter nonlinear curves fitted to the height-diameter observations. These nine models are given by the following.

• Richards (Richards(1959))

  H=1.3+β_1+\frac{β_2}{D+β_3},

• Gompertz (Winsor(1992))

  H=1.3+β_1 e^{-β_2e^{-β_3 D}},

• Hossfeld IV (Zeide(1993))

  H=1.3+\frac{β_1}{1+\frac{1}{β_2 D^{β_3}}},

• Korf (Flewelling and De Jong(1994))

  H=1.3+β_1 e^{-β_2D^{-β_3}},

• logistic (Pearl and Reed (1920))

  H=1.3+\frac{β_1}{1+β_2e^{-β_3D}},

• Prodan (Prodan(1968))

  H=1.3+\frac{D^2}{β_1 D^2+β_2 D+β_3},

• Ratkowsky (Ratkowsky(1990))

  H=1.3+β_1 e^{-\frac{β_2}{D+β_3}},

• Sibbesen (Huang et al. (1992))

  H=1.3+β_1 D^{β_2 D^{-β_3}},

• Weibull (Yang et al. (1978))

  H=1.3+β_1\Bigl(1-e^{-β_2 D^{β_3}}\Bigr),

Usage

fitcurve(h,d,model,start)

Arguments

h	Vector of height observations.
d	Vector of diameter observations.
model	The name of the fitted model including "chapman-richards", "gompertz", "hossfeldiv", "korf", "logistic", "prodan" , "ratkowsky", "Sibbesen", and "weibull".
start	A vector of starting values for the parameters β_1, β_2, and β_3.

Value

A list of objects in four parts as

1. Estimated parameters and corresponding summaries including standard errors, computed t-statistics, and p-values.

2. Residuals.

3. Covariance matrix of the estimated model parameters (coefficients) \hat{β}_1, \hat{β}_2, and \hat{β}_3.

4. Residual standard error, i.e., \hat{σ}.

5. number of trials for attaining convergence.

6. The hieght-diameter scatterplot superimposed by the fitted model.

Author(s)

Mahdi Teimouri

References

J. W. Flewelling and R. De Jong. (1994). Considerations in simultaneous curve fitting for repeated height-diameter measurements, Canadian Journal of Forest Research, 24(7), 1408-1414.

S. Huang, S. J. Titus, and D. P. Wiens. 1992. Comparison of nonlinear height±diameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22, 1297-1304.

R. Pearl and L. J. Reed. (1920). On the rate of growth of the population of the United States since 1790 and its mathematical representation, Proceedings of the National Academy of Sciences of the United States of America, 6(6), 275.

M. Prodan. 1968. The spatial distribution of trees in an area. Allg. Forst Jagdztg, 139, 214-217.

D. A. Ratkowsky. 1990. Handbook of nonlinear regression, New York, Marcel Dekker, Inc.

F. J. Richards. 1959. A flexible growth function for empirical use. Journal of Experimental Botany, 10, 290-300.

S. B. Winsor. 1992. The Gompertz curve as a growth curve. Proceedings of National Academic Science, USA, 18, 1-8.

R. C. Yang, A. Kozak, J. H. G. Smith. 1978. The potential of Weibull-type functions as a flexible growth curves. Canadian Journal of Forest Research, 8, 424-431.

B. Zeide. 1993. Analysis of growth equation. Forest Science, 39, 594-616.

Examples

# use the heigth and diameter at breast height (dbh) of the plot 55 in DBH data set.
# The first column of DBH dataset contains the plot number. Also, H and D denote the
# height and dbh variables that located at columns 10 and 11 of data set DBH, respectively.
 data(DBH)
 D<-DBH[DBH[,1]==55,10]
 H<-DBH[DBH[,1]==55,11]
 start<-c(9,5,2)
 fitcurve(H,D,"weibull", start=start)
 

ForestFit documentation built on March 7, 2023, 8:27 p.m.