| fitETE {biogeom} | R Documentation |
Data-Fitting Function for the Explicit Troscianko Equation
Description
fitETE is used to estimate the parameters of the explicit Troscianko equation.
Usage
fitETE(x, y, ini.val, control = list(), par.list = FALSE,
stand.fig = TRUE, angle = NULL, fig.opt = FALSE, np = 2000,
xlim = NULL, ylim = NULL, unit = NULL, main = NULL)
Arguments
x |
the |
y |
the |
ini.val |
the list of initial values for the model parameters. |
control |
the list of control parameters for using the |
par.list |
the option of showing the list of parameters on the screen. |
stand.fig |
the option of drawing the observed and predicted profiles of an egg at the standard state
(i.e., the egg's centre is located at (0, 0), and the mid-line is aligned to the |
angle |
the angle between the mid-line and the |
fig.opt |
an optional argument of drawing the observed and predicted profiles of an egg
at arbitrary angle between the major axis and the |
np |
the number of data points on the predicted explicit Troscianko curve. |
xlim |
the range of the |
ylim |
the range of the |
unit |
the unit of the |
main |
the main title of the figure. |
Details
Here, the major axis (i.e., the mid-line of an egg's profile) is the straight line trhough the two ends of
the egg's length. 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.
When angle = NULL, the observed egg's profile will be shown at its initial angle in the scanned image;
when angle is a numerical value (e.g., \pi/4) defined by the user, it indicates that the major axis
is rotated by the amount (\pi/4) counterclockwise from the x-axis.
Value
par |
the estimates of the model parameters. |
scan.length |
the observed length of the egg's profile. |
scan.width |
the observed width of the egg's profile. |
scan.area |
the observed area of the egg's profile. |
scan.perimeter |
the observed perimeter of the egg's profile. |
r.sq |
the coefficient of determination between the observed and predicted |
RSS |
the residual sum of squares between the observed and predicted |
sample.size |
the number of data points used in the data fitting. |
x.stand.obs |
the observed |
y.stand.obs |
the observed |
y.stand.pred |
the predicted |
x.obs |
the observed |
y.obs |
the observed |
y.pred |
the predicted |
Note
In the outputs, there are no x.stand.pred and x.pred, because y.stand.obs and
y.stand.pred share the same x values (i.e., x.stand.obs), and y.obs and
y.pred share the same x values (i.e., x.obs).
Author(s)
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
References
Biggins, J.D., Montgomeries, R.M., Thompson, J.E., Birkhead, T.R. (2022) Preston’s universal formula for avian egg shape. Ornithology 139, ukac028. doi:10.1093/ornithology/ukac028
Biggins, J.D., Thompson, J.E., Birkhead, T.R. (2018) Accurately quantifying
the shape of birds' eggs. Ecology and Evolution 8, 9728-9738. doi:10.1002/ece3.4412
Nelder, J.A., Mead, R. (1965) A simplex method for function minimization.
Computer Journal 7, 308-313. doi:10.1093/comjnl/7.4.308
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. doi:10.1111/nyas.14862
Shi, P., Wang, L., Quinn, B.K., Gielis, J. (2023) A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds. Symmetry 15, 231. doi:10.3390/sym15010231
Troscianko, J. (2014). A simple tool for calculating egg shape, volume and surface area from digital images.
Ibis, 156, 874-878. doi:10.1111/ibi.12177
See Also
Examples
data(eggs)
uni.C <- sort( unique(eggs$Code) )
ind <- 8
Data <- eggs[eggs$Code==uni.C[ind], ]
x0 <- Data$x
y0 <- Data$y
Res1 <- adjdata(x0, y0, ub.np=2000, times=1.2, len.pro=1/20)
x1 <- Res1$x
y1 <- Res1$y
dev.new()
plot( x1, y1, asp=1, cex.lab=1.5, cex.axis=1.5, type="l", col=4,
xlab=expression(italic("x")), ylab=expression(italic("y")) )
res1 <- lmTE( x1, y1, unit="cm", fig.opt=FALSE )
if(FALSE){
P0 <- c(res1$scan.length/2, res1$par)
xx <- seq(-res1$scan.length/2, res1$scan.length/2, len=2000)
yy1 <- ETE(P0, xx)
yy2 <- -ETE(P0, xx)
dev.new()
plot( xx, yy1, cex.lab=1.5, cex.axis=1.5, asp=1, col=2,
ylim=c(-res1$scan.length/2, res1$scan.length/2),
type="l", xlab=expression(x), ylab=expression(y) )
lines( xx, yy2, col=4 )
}
x0.ini <- mean( x1 )
y0.ini <- mean( y1 )
theta.ini <- res1$theta
a.ini <- res1$scan.length / 2
alpha0.ini <- res1$par[1]
alpha1.ini <- res1$par[2]
alpha2.ini <- res1$par[3]
ini.val <- list(x0.ini, y0.ini, theta.ini, a.ini, alpha0.ini, alpha1.ini, alpha2.ini)
res0 <- fitETE( x=x1, y=y1, ini.val=ini.val,
unit="cm", par.list=FALSE,
stand.fig=FALSE, angle=NULL, fig.opt=FALSE,
control=list(reltol=1e-30, maxit=50000),
np=2000 )
n.loop <- 12
Show <- FALSE
for(i in 1:n.loop){
ini.val <- res0$par
if(i==n.loop) Show <- TRUE
print(paste(i, "/", n.loop, sep=""))
res0 <- fitETE( x=x1, y=y1, ini.val=ini.val,
unit="cm", par.list=FALSE,
stand.fig=Show, angle=pi/4, fig.opt=Show,
control=list(reltol=1e-30, maxit=50000),
np=2000 )
}
# The numerical values of the location and model parameters
res0$par
# The root-mean-square error (RMSE) between
# the observed and predicted y values
sqrt(res0$RSS/res0$sample.size)
sqrt(sum((res0$y.stand.obs-res0$y.stand.pred)^2)/length(res0$y.stand.obs))
# To calculate the volume of the egg
VolumeETE(P=res0$par[4:7])
# To calculate the surface area of the egg
SurfaceAreaETE(P=res0$par[4:7])
graphics.off()