| fitEPE {biogeom} | R Documentation |
Data-Fitting Function for the Explicit Preston Equation
Description
fitEPE is used to estimate the parameters of the explicit Preston equation
or one of its simplified versions.
Usage
fitEPE(x, y, ini.val, simpver = NULL,
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. |
simpver |
an optional argument to use the simplified version of the explicit Preston equation. |
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 Preston curve. |
xlim |
the range of the |
ylim |
the range of the |
unit |
the unit of the |
main |
the main title of the figure. |
Details
The simpver argument should correspond to EPE. 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
Nelder, J.A., Mead, R. (1965) A simplex method for function minimization.
Computer Journal 7, 308-313. doi:10.1093/comjnl/7.4.308
Preston, F.W. (1953) The shapes of birds' eggs. The Auk 70, 160-182.
Shi, P., Chen, L., Quinn, B.K., Yu, K., Miao, Q., Guo, X., Lian, M., Gielis, J., Niklas, K.J. (2023)
A simple way to calculate the volume and surface area of avian eggs.
Annals of the New York Academy of Sciences 1524, 118-131. doi:10.1111/nyas.15000
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
Todd, P.H., Smart, I.H.M. (1984) The shape of birds' eggs. Journal of Theoretical Biology
106, 239-243. doi:10.1016/0022-5193(84)90021-3
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")) )
simpver <- NULL
res1 <- lmPE( x1, y1, simpver=simpver, dev.angle=seq(-0.05, 0.05, by=0.0001),
unit="cm", fig.opt=FALSE )
x0.ini <- mean( x1 )
y0.ini <- mean( y1 )
theta.ini <- res1$theta
a.ini <- res1$scan.length / 2
b.ini <- res1$scan.width / 2
c1.ini <- res1$par[2] / res1$par[1]
c2.ini <- res1$par[3] / res1$par[1]
c3.ini <- res1$par[4] / res1$par[1]
ini.val <- list(x0.ini, y0.ini, theta.ini, a.ini, b.ini, c1.ini, c2.ini, c3.ini)
res0 <- fitEPE( x=x1, y=y1, ini.val=ini.val,
simpver=simpver, unit="cm", par.list=FALSE,
stand.fig=FALSE, angle=NULL, fig.opt=FALSE,
control=list(reltol=1e-30, maxit=50000),
np=2000 )
n.loop <- 12
Show <- FALSE
for(i in 1:n.loop){
ini.val <- res0$par
if(i==n.loop) Show <- TRUE
print(paste(i, "/", n.loop, sep=""))
res0 <- fitEPE( x=x1, y=y1, ini.val=ini.val,
simpver=simpver, 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
VolumeEPE(P=res0$par[4:8])
# To calculate the surface area of the egg
SurfaceAreaEPE(P=res0$par[4:8])
graphics.off()