plot.nlreg.diag: Diagnostic Plots for Nonlinear Heteroscedastic Models
In hoa: Higher Order Likelihood Inference

Description Usage Arguments Details Value Side Effects Acknowledgments Note References See Also Examples

The nlreg.diag.plots routine generates diagnostic plots for a nonlinear heteroscedastic model using different types of residuals, influence measures and leverages. This is equivalent to using the plot.nlreg.diag method for function plot for objects inheriting from class nlreg.diag.

nlreg.diag.plots(fitted, which = "all", subset = NULL, iden = FALSE, 
                 labels = NULL, hoa = TRUE, infl = TRUE, 
                 trace = FALSE, ret = FALSE, ...)
## S3 method for class 'nlreg.diag'
plot(x, which = "all", subset = NULL, iden = FALSE, labels = NULL, 
     ...)

`fitted`	either a `nlreg` object, that is, the result of a call to `nlreg`, or a `nlreg.diag` object obtained from a call to `nlreg.diag`.
`x`	a `nlreg.diag` object obtained from a call to `nlreg.diag`.
`which`	which plot to draw. Admissible values are `2` to `9` which correspond to the choices below. The default is `"all"`, which pops up a menu that lists all available plots.
`subset`	the subset of the data used in the original `nlreg` fit. Must be the same than the `subset` option used in the call to `nlreg` that generated the `nlreg` object for which the diagnostic plots are to be drawn. Needed only if the `subset` option is used in the call to `nlreg`.
`iden`	logical argument. If `TRUE`, the user will be prompted after the plots are drawn. A positive integer will select a plot and invoke `identify()` on that plot. After exiting `identify`, the user is again prompted, this loop continuing until the user responds to the prompt with `0`. If `iden` is `FALSE` (default) the user cannot interact with the plots.
`labels`	a vector of labels for use with `identify` if `iden` is `TRUE`. If it is not supplied, the labels are derived from the `nlreg.diag` object argument `fitted` or `x`.
`hoa`	logical value indicating whether higher order asymptotics should be used for calculating the regression diagnostics. Needed only if `fitted` is a `nlreg` object. Default is `TRUE`.
`infl`	logical value indicating whether influence measures should be calculated on the basis of a leave-one-out analysis. Needed only if `fitted` is a `nlreg` object. Default is `TRUE`.
`trace`	logical value. If `TRUE` details of the iterations are printed. Needed only if `fitted` is a `nlreg` object. Default is `FALSE`.
`ret`	logical argument indicating whether the `nlreg.diag` object should be returned; the default is `FALSE`.
`...`	additional graphics parameters.

The diagnostics required for the plots are calculated by nlreg.diag, either by passing a nlreg.diag object or by applying nlreg.diag internally to the nlreg object specified through fitted. These are then used to produce the plots on the current graphics device. A menu lists all possible choices. They may be one or all of the following.

 Make a plot selection (or 0 to exit)

1:plot: Summary
2:plot: Studentized residuals against fitted values
3:plot: r* residuals against fitted values
4:plot: Normal QQ-plot of studentized residuals
5:plot: Normal QQ-plot of r* residuals
6:plot: Cook statistic against h/(1-h)
7:plot: Global influence against h/(1-h)
8:plot: Cook statistic against observation number
9:plot: Influence measures against observation number

Selection:

In the normal scores plots, the dotted line represents the expected line if the residuals are normally distributed, that is, it is the line with intercept 0 and slope 1.

In general, when plotting Cook's distance or the global influence measure against the standardized leverages, there will be two dotted lines on the plot. The horizontal line is at 8/(n-2p), where n is the number of observations and p is the number of regression coefficients estimated. Points above this line may be points with high influence on the model. The vertical line is at 2p/(n-2p) and points to the right of this line have high leverage compared to the variance of the raw residual at that point. If all points are below the horizontal line or to the left of the vertical line then the line is not shown.

Use of iden = TRUE is encouraged for proper exploration of these plots as a guide to how well the model fits the data and whether certain observations have an unduly large effect on parameter estimates.

If ret = TRUE, the nlreg.diag object is returned. Otherwise, there is no returned value.

The current device is cleared. If iden = TRUE, interactive identification of points is enabled. All screens are closed, but not cleared, on termination of the function.

This function is based on A. J. Canty's function glm.diag.plots contained in library boot.

Choices 3 and 5 are not available if hoa = FALSE in the call to nlreg.diag that generated the x argument. Choices 7 and 9 are not available if infl = FALSE in the same call. Plot number 9 is furthermore not available if the variance function is constant.

Brazzale, A. R. (2000) Practical Small-Sample Parametric Inference. Ph.D. Thesis N. 2230, Department of Mathematics, Swiss Federal Institute of Technology Lausanne. Section 6.3.1 and Appendix A.2.2.

Davison, A. C. and Snell, E. J. (1991) Residuals and diagnostics. In Statistical Theory and Modelling: In Honour of Sir David Cox (eds. D. V. Hinkley, N. Reid, and E. J. Snell), 83–106. London: Chapman & Hall.

Davison, A. C. and Tsai, C.-L. (1992) Regression model diagnostics. Int. Stat. Rev., 60, 337–353.

nlreg.diag, nlreg.object, identify

library(boot)
data(calcium)
calcium.nl <- nlreg( cal ~ b0*(1-exp(-b1*time)), weights = ~ ( 1+time^g )^2, 
                     start = c(b0 = 4, b1 = 0.1, g = 1), data = calcium, 
                     hoa = TRUE )
##
calcium.diag <- nlreg.diag( calcium.nl, trace = TRUE )
##
## menu-driven
## Not run: 
plot( calcium.diag )
##
##  Make a plot selection (or 0 to exit)
##
## 1:plot: Summary
## 2:plot: Studentized residuals against fitted values
## 3:plot: r* residuals against fitted values
## 4:plot: Normal QQ-plot of studentized residuals
## 5:plot: Normal QQ-plot of r* residuals
## 6:plot: Cook statistic against h/(1-h)
## 7:plot: Global influence against h/(1-h)
## 8:plot: Cook statistic against observation number
## 9:plot: Influence measures against observation number
##
## Selection:
## End(Not run)
##
## plot 5: Normal QQ-plot of r* residuals
plot( calcium.diag, which = 5, las = 1 )
##
nlreg.diag.plots( calcium.nl, which = 5, las = 1 )