Summarizing and Bootstrapping Fitted Ellipses or Loops

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Description

summary methods for classes ellipsefit and fittedloop created by the functions fel and floop. Can bootstrap results to produce parameter estimates with reduced bias and standard errors.

Usage

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## S3 method for class 'ellipsefit'
summary(object,boot=TRUE, N = 1000, 
studentize=TRUE, center=FALSE, cbb=NULL, joint=FALSE,seed=NULL,...)
## S3 method for class 'fittedloop'
summary(object,boot=TRUE,N=1000,
cbb=NULL,joint=FALSE,seed=NULL,...)
## S3 method for class 'loop2r'
summary(object,boot=TRUE,N=1000,
cbb=NULL,joint=FALSE,seed=NULL,...)

Arguments

object

an object of class ellipsefit or fittedloop, a result of a call to fel or floop.

boot

logical. Whether to perform bootstrapping to get standard errors, which is the default TRUE, or to get standard errors through the delta method if FALSE.

N

optional number of bootstrap replicates. Default of 1000.

studentize

studentize the residuals to improve performance. Default is true.

center

center x and y residuals around zero. Default is false. Irrelevant for "harmonic2" method.

cbb

allows for circular block bootstrapping. The default is NULL in which case circular block bootstrapping is not performed. If cbb is an integer greater than 1 which is a divisor of either the number of observations for methods "nls", "lm", "geometric" or the number of observations minus 3 for method="harmonic2" then it is used as the block size for circular block bootstrapping.

joint

logical that defaults to false. Resample input and output residuals paired by observation, instead of separately.

seed

either NULL or a positive integer. Set the random number seed.

...

further arguments passed to or from other methods.

Details

Bootstrap objects created by fitting hysteretic data with one of the functions fel or floop and produce statistical summaries. Bootstrapping reduces the bias on estimates and also gives standard errors. Bootstrap estimates are created by subtracting original estimates from bootstrap means to get a bias estimate, and then subtracting this bias from the original estimate.

Residuals are studentized as if they were produced using the harmonic2 method, regardless of which method was actually used to produce them. However, unpublished simulation studies show that these studentized residuals provide better 95 percent coverages for all methods despite this. This studentization is not true studentization as in rstudent.ellipsefit as it only accounts for the influence matrix and does not divide by the standard deviation.

If residuals are serially correlated than the argument cbb may be used to sample blocks of length cbb instead of individual residuals. Circular block bootstrapping is used, which means that all residuals are equally likely to be included and blocks can be made up of the last points on the ellipse together with the first.

When using the 'nls', 'geometric' or 'lm' methods individual bootstrap replications may occasionally fail to converge, when this occurs an extra replication will take the place of the one that failed to converge and a warning message will be produced.

Value

call

function call for original fit.

method

fitting method used. Only for summary.ellipsefit. See fel.

x

the input x.

y

the output y.

pred.x

the bootstrap fitted values for x.

pred.y

the bootstrap fitted values for y.

values

matrix containing parameter and standard error estimates, bootstrap quantiles, and bootstrapped parameter estimates for a wide variety of parameters. See loop.parameters.

Delta.Std.Errors

the delta method standard errors.

fit.statistics

rudimentary measures, based on the "harmonic2" method, include the Multivariate Final Prediction Error (MFPE) and the AIC for both the output alone and the two variables in combination. Although degree of freedom adjustments are made for other methods, measures of fit require further study

For bootstrapping

summarycall

the function call.

boot.data

parameter estimates from individual bootstrap replications.

Boot.Estimates

bootstrapped estimates.

Boot.Std.Errors

bootstrap standard errors.

Author(s)

Spencer Maynes, Fan Yang, and Anne Parkhurst.

References

Yang, F. and A. Parkhurst, Efficient Estimation of Elliptical Hysteresis (submitted)

Correa, Solange, Extended Bootstrap Bias Correction with Application to Multilevel Modelling of Survey Data under Informative Sampling.

See Also

fel for fitting points that form an ellipse and creating an ellipsefit object and plot.ellipsesummary for plotting an ellipsesummary object.

Examples

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#Loop example with circular block bootstrapping
loop1 <- mloop(n=1,m=2,sd.x=0.05,sd.y=0.05)
loop1.fit <- floop(loop1$x,loop1$y,m=2,n=1)
boot.loop1 <- summary(loop1.fit,cbb=3)
boot.loop1
plot(boot.loop1)

#Ellipse example.
ellipse1 <- mel(sd.x=0.2,sd.y=0.04)
ellipse1.fit <- fel(ellipse1$x,ellipse1$y)
boot.ellipse1.fit <- summary(ellipse1.fit)
boot.ellipse1.fit
plot(boot.ellipse1.fit,xlab="Input",ylab="Output",
main="Bootstrapped Ellipse",putNumber=TRUE)