fitsigmoid() R function from [biogeom]

Data-Fitting Function for the Sigmoid Growth Equation

fitsigmoid is used to estimate the parameters of a sigmoid growth equation based on the integral of a performance equation or one of its simplified versions. UTF-8


fitsigmoid(expr, x, y, ini.val, simpver = 1, 
           control = list(), par.list = FALSE, fig.opt = FALSE,
           xlim = NULL, ylim = NULL, xlab = NULL, ylab = NULL,         
           main = NULL, subdivisions = 100L,
           rel.tol = .Machine$double.eps^0.25, 
           abs.tol = rel.tol, stop.on.error = TRUE, 
           keep.xy = FALSE, aux = NULL)

Arguments

expr: a performance equation or one of its simplified versions that is used to build a sigmoid growth equation.
x: the observed investigation times.
y: the observed $y$ values (i.e., biomass, height, body length, etc.).
ini.val: the initial values of the model parameters.
simpver: an optional argument to use the simplified version of the performance equation.
control: the list of control parameters for using the optim function in package stats.
par.list: the option of showing the list of parameters on the screen.
fig.opt: an optional argument to draw the observations and the predicted sigmoid curve.
xlim: the range of the $x$ -axis over which to plot a sigmoid growth curve.
ylim: the range of the $y$ -axis over which to plot a sigmoid growth curve.
xlab: the label of the $x$ -axis when showing a sigmoid growth curve.
ylab: the label of the $y$ -axis when showing a sigmoid growth curve.
main: the main title of the figure.
subdivisions: please see the arguments for the integrate function in package stats.
rel.tol: please see the arguments for the integrate function in package stats.
abs.tol: please see the arguments for the integrate function in package stats.
stop.on.error: please see the arguments for the integrate function in package stats.
keep.xy: please see the arguments for the integrate function in package stats.
aux: please see the arguments for the integrate function in package stats.

Details

Here, ini.val only includes the initial values of the model parameters as a list. The Nelder-Mead algorithm (Nelder and Mead, 1965) is used to carry out the optimization of minimizing the residual sum of squares (RSS) between the observed and predicted $y$ values. The optim

function in package stats was used to carry out the Nelder-Mead algorithm. The performance equations denote MbetaE, MBriereE, MLRFE, MPerformanceE and their simplified versions. The arguments of P and simpver should correspond to expr (i.e., MbetaE or MBriereE

or MLRFE or MPerformanceE). The sigmoid equation is the integral of a performance equation or one of its simplified versions.

Returns

par: the estimates of the model parameters.
r.sq: the coefficient of determination between the observed and predicted $y$ values.
RSS: the residual sum of squares between the observed and predicted $y$ values.
sample.size: the number of data points used in the data fitting.
x: the observed $x$ values.
y: the observed $y$ values.
y.pred: the predicted $y$ values.

Note

Here, the user can define other performance equations, but new equations or their simplified versions should include the lower and upper thresholds on the $x$ -axis corresponding to $y = 0$ , whose indices should be the same as those in MbetaE or MBriereE

or MLRFE or MPerformanceE.

Author(s)

Peijian Shi pjshi@njfu.edu.cn , Johan Gielis johan.gielis@uantwerpen.be , Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca .

References

Jin, J., Quinn, B.K., Shi, P. (2022) The modified Brière equation and its applications. Plants 11, 1769. tools:::Rd_expr_doi("10.3390/plants11131769")

Lian, M., Shi, P., Zhang, L., Yao, W., Gielis, J., Niklas, K.J. (2023) A generalized performance equation and its application in measuring the Gini index of leaf size inequality. Trees $-$ Structure and Function 37, 1555 $-$ 1565. tools:::Rd_expr_doi("10.1007/s00468-023-02448-8")

Nelder, J.A., Mead, R. (1965) A simplex method for function minimization. Computer Journal 7, 308 $-$ 313. tools:::Rd_expr_doi("10.1093/comjnl/7.4.308")

Shi, P., Fan, M., Ratkowsky, D.A., Huang, J., Wu, H., Chen, L., Fang, S., Zhang, C. (2017) Comparison of two ontogenetic growth equations for animals and plants. Ecological Modelling 349, 1 $-$ 10. tools:::Rd_expr_doi("10.1016/j.ecolmodel.2017.01.012")

Shi, P., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences 1516, 123 $-$ 134. tools:::Rd_expr_doi("10.1111/nyas.14862")

Examples


# The shrimp growth data(See the supplementary table in West et al., 2001)
# West, G.B., Brown, J.H., Enquist, B.J. (2001) A general model for ontogenetic growth. 
#     Nature 413, 628-631.
t0 <- c(3, 60, 90, 120, 150, 180, 384)
m0 <- c(0.001, 0.005, 0.018, 0.037, 0.06, 0.067, 0.07)

dev.new()
plot( t0, m0, cex.lab=1.5, cex.axis=1.5, col=4,
      xlab=expression(italic(x)), ylab=expression(italic(y)) )

xopt0   <- seq(100, 150, by=5)
ini.val <- list(0.035, xopt0, 200, 1)
resu1   <- fitsigmoid(MLRFE, x=t0, y=m0, ini.val=ini.val, simpver=1, fig.opt=TRUE, par.list=TRUE)

  xopt0   <- seq(100, 150, by=5)
  ini.val <- list(0.035, xopt0, 200, 1)
  resu1   <- fitsigmoid(MbetaE, x=t0, y=m0, ini.val=ini.val, simpver=1, fig.opt=TRUE)

  m.ini   <- c(0.5, 1, 2, 3, 4, 5, 10, 20)
  ini.val <- list(1e-8, m.ini, 200, 1)
  resu2   <- fitsigmoid(MBriereE, x=t0, y=m0, ini.val=ini.val, simpver=1, 
             fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000, trace=FALSE), 
             subdivisions=100L, rel.tol=.Machine$double.eps^0.25, 
             abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
             keep.xy=FALSE, aux=NULL)

  delta0  <- c(0.5, 1, 2, 5, 10, 20)
  ini.val <- list(0.035, 150, -100, 200, delta0)
  resu3   <- fitsigmoid(MLRFE, x=t0, y=m0, ini.val=ini.val, simpver=NULL, 
               fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000), 
               subdivisions = 100L, rel.tol=.Machine$double.eps^0.25, 
               abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
               keep.xy=FALSE, aux=NULL)

  a.ini   <- c(0.1, 1, 10, 100, 200)
  b.ini   <- 200
  ini.val <- list(0.001, 0.02, 0.15, 0, 200, a.ini, b.ini)
  resu4   <- fitsigmoid(MPerformanceE, x=t0, y=m0, ini.val=ini.val, simpver=NULL, 
             fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000, trace=FALSE), 
             subdivisions=100L, rel.tol=.Machine$double.eps^0.25, 
             abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
             keep.xy=FALSE, aux=NULL)
  resu5   <- fitsigmoid(MPerformanceE, x=t0, y=m0, ini.val=resu4$par, simpver=NULL, 
               fig.opt=TRUE, control=list(reltol=1e-30, maxit=200000, trace=FALSE))

  ini.val <- list(0.001, 0.01, c(0.1, 1, 10), 0, 200)
  resu6   <- fitsigmoid(MPerformanceE, x=t0, y=m0, ini.val=ini.val, simpver=2, 
             fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000, trace=FALSE), 
             subdivisions=100L, rel.tol=.Machine$double.eps^0.25, 
             abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
             keep.xy=FALSE, aux=NULL)

graphics.off()

biogeom package Read PDF manual

Maintainer: Peijian Shi
License: GPL (>= 2)
Last published: 2024-03-29

Useful links

fitsigmoid function