plot.marg {marg}

Generate Plots for an Approximate Marginal Inference Object

Description

Creates a set of plots for an object of class marg.

Usage

## S3 method for class 'marg'
plot(x = stop("nothing to plot"), from = x.axis[1], to = x.axis[n], 
     which = NULL, alpha = 0.05, add.leg = TRUE, loc.leg = FALSE, 
     add.labs = TRUE, cex = 0.7, cex.lab = 1, cex.axis = 1, 
     cex.main = 1, lwd1 = 1, lwd2 = 2, lty1 = "solid", 
     lty2 = "dashed", col1 = "black", col2 = "blue", tck = 0.02, 
     las = 1, adj = 0.5, lab = c(15, 15, 5), ...)           

Arguments

x

a marg object. This is assumed to be the result returned by the cond.rsm function.

from

the starting value for the x-axis range. The default value has been set by cond.rsm.

to

the ending value for the x-axis range. The default value has been set by cond.rsm.

which

which plot to print. Admissible values are 2 to 7 corresponding to the choices in the menu below.

alpha

the level used to read off confidence intervals; the default is 5%.

add.leg

if TRUE, a legend is added to each plot; default is TRUE.

loc.leg

if TRUE, the position of the legend can be located by hand; default is FALSE.

add.labs

if TRUE, labels are added; default is TRUE.

cex, cex.lab, cex.axis, cex.main

the character expansions relative to the standard size of the device to be used for printing text, labels, axes and main title. See par for details.

lwd1, lwd2

the line widths used to compare different curves in the same plot; default is lwd2 = 2 for higher order solutions and lwd1 = 1 for first order solutions.

lty1, lty2

line type used to compare different curves in the same plot; default is lty2 = "dashed" for the Wald statistic and lty1 = "solid" for the remaining first and higher order statistics.

col1, col2

colors used to compare different curves in the same plot; default is col2 = "blue" for higher order solutions, and col1 = "black" for the remaining first order statistics.

tck, las, adj, lab

further graphical parameters. See par for details.

...

optional graphical parameters; see par for details.

Details

Several plots are produced for an object of class marg. A menu lists all the plots that can be produced. They may be one or all of the following ones:

 Make a plot selection (or 0 to exit)

1: All
2: Profile and modified profile log likelihoods
3: Profile and modified profile likelihood ratios
4: Profile and modified likelihood root
5: Lugannani-Rice approximation
6: Confidence intervals
7: Diagnostics based on INF/NP decomposition

Selection:
  

If no nuisance parameters are presented, a subset of the above pictures is produced. A message is printed if this is the case. More details and examples are given in Brazzale (2000, Sections 6.5 and 5.3.2).

This function is a method for the generic function plot() for class marg. It can be invoked by calling plot or directly plot.marg for an object of the appropriate class.

Value

A plot is created on the current graphics device.

Side Effects

The current device is cleared. When add.leg is TRUE, a legend is added to each plot. Furthermore, if loc.leg is TRUE, the location of the legend can be set by the user. All screens are closed, but not cleared, on termination of the function.

Note

If the parameter of interest is the scale parameter, all calculations are performed on the log scale, though most results are reported on the original scale.

Four diagnostic plots are provided. The two panels on the right trace the information and nuisance correction terms, INF and NP, against the likelihood root statistic. These are generally smooth functions and used to approximate the information and nuisance parameter aspects as a function of the parameter of interest, as shown in the two panels on the left. This procedure has the advantage of largely eliminating the numerical instabilities that affect the statistics around the MLE. All four pictures are intended to give an idea of the order of magnitude of the two correction terms while trying to deal with the numerical problems that likely occur for these kinds of data.

More details can be found in Brazzale (2000, Appendix B.2).

References

Brazzale, A. R. (2000) Practical Small-Sample Parametric Inference. Ph.D. Thesis N. 2230, Department of Mathematics, Swiss Federal Institute of Technology Lausanne.

See Also

cond.rsm, marg.object, summary.marg

Examples

# Sea Level Data
data(venice)
attach(venice)
Year <- 1:51/51
c11 <- cos(2*pi*1:51/11) ; s11 <- sin(2*pi*1:51/11)
c19 <- cos(2*pi*1:51/18.62) ; s19 <- sin(2*pi*1:51/18.62)
#
# quadratic model fitted to the sea level, includes 18.62-year 
# astronomical tidal cycle and 11-year sunspot cycle
venice.rsm <- rsm(sea ~ Year + I(Year^2) + c11 + s11 + c19 + s19, 
                  family = extreme)
venice.marg <- cond(venice.rsm, I(Year^2))
plot(venice.marg, which = 4)
##
detach()