plot.glarma: Plot Diagnostics for a 'glarma' Object

In glarma: Generalized Linear Autoregressive Moving Average Models

Description

Ten plots (selectable by which) are currently available: a time series plot with observed values of the dependent variable, fixed effects fit, and GLARMA fit; an ACF plot of residuals; a plot of residuals against time; a normal Q-Q plot; the PIT histogram; a uniform Q-Q plot for the PIT; a histogram of the normal randomized residuals; a Q-Q plot of the normal randomized residuals; a plot of the autocorrelation of the normal randomized residuals; and a plot of the partial autocorrelation of the normal randomized residuals. By default, six plots are provided, numbers 1, 3, 5, 7, 8 and 9 from this list of plots.

Usage

## S3 method for class 'glarma'
plot(x, which = c(1L,3L,5L,7L,8L,9L), fits = 1L:3L,
     ask = prod(par("mfcol")) < length(which) && dev.interactive(),
     lwdObs = 1, lwdFixed = 1, lwdGLARMA = 1,
     colObs = "black", colFixed = "blue", colGLARMA = "red",
     ltyObs = 2, ltyFixed = 1, ltyGLARMA = 1,
     pchObs = 1, legend = TRUE, residPlotType = "h", bins = 10,
     line = TRUE, colLine = "red", colHist = "royal blue",
     lwdLine = 2, colPIT1 = "red", colPIT2 = "black",
     ltyPIT1 = 1, ltyPIT2 = 2, typePIT = "l", 
     ltyQQ = 2, colQQ = "black", titles, ...)

Arguments

x	An object of class "glarma", obtained from a call to glarma.
which	Numeric; if a subset of the plots is required, specify a subset of the numbers 1:10. 1 is the time series plot with observed values of the dependent variable, fixed effects fit, and GLARMA fit. 2 is the ACF plot of residuals. 3 is a plot of residuals against time. 4 is the normal Q-Q plot. 5 is the PIT histogram. 6 is the uniform Q-Q plot for the PIT. 7 is the histogram of the normal randomized residuals. 8 is the Q-Q plot of the normal randomized residuals. 9 is the autocorrelation of the normal randomized residuals. 10 is the partial autocorrelation of the normal randomized residuals. By default, plots 1, 3, 5, 7, 8 and 9 are provided.
fits	Numeric; if a subset of fits on the time series plot is required, specify a subset of the numbers 1:3. 1 is the observed values of the dependent variable, 2 is the fixed effects fit, and 3 is GLARMA fit. By default, all fits are provided.
ask	Logical; if TRUE, the user is asked before each plot, see par(ask = .).
lwdObs	Numeric; the line widths for lines of the observed values of the dependent variable appearing in the time series plot.
lwdFixed	Numeric; the line widths for lines of the fixed effects fit appearing in the time series plot.
lwdGLARMA	Numeric; the line widths for lines of GLARMA fit appearing in the time series plot.
ltyObs	An integer or character string; the line types for the line of the observed data of the dependent variable appearing in the time series plot, see par(lty = .).
ltyFixed	An integer or character string; the line types for the line of the fixed effects fit appearing in the time series plot, see par(lty = .).
ltyGLARMA	An integer or character string; the line types for the line of GLARMA fit appearing in the time series plot, see par(lty = .).
pchObs	Numeric; the point type for the point of the observed data of the dependent variable appearing in the time series plot.
colObs	Numeric or character; the colour of lines or points of the observed data of the dependent variable appearing in the time series plot.
colFixed	Numeric or character; the colour of lines of the fixed effects fit appearing in the time series plot.
colGLARMA	Numeric or character; the colour of lines of GLARMA fit appearing in the time series plot.
legend	Logical; if TRUE, the legend for the fits in the time series plot would be shown. By default, it would be shown.
residPlotType	A 1-character string giving the type of plot desired. The following values are possible, for details, see plot: "p" for points, "l" for lines, "b" for both points and lines, "c" for empty points joined by lines, "o" for overplotted points and lines, "s" and "S" for stair steps and "h" for histogram-like vertical lines. Finally, "n" does not produce any points or lines.
bins	Numeric; the number of bins shown in the PIT histogram and of the number of breaks in the histogram of the normal randomized residuals. By default, it is 10.
line	Logical; if TRUE, the line for displaying the standard uniform distribution will be shown for the purpose of comparison. The default is TRUE.
colLine	Numeric or character; the colour of the line for comparison in the PIT histogram.
lwdLine	Numeric; the line widths for the comparison line in the PIT histogram.
colHist	Numeric or character; the colour of the histogram for the PIT, and of the histogram of the normal randomized residuals.
colPIT1	Numeric or character; the colour of the sample uniform Q-Q plot in the PIT.
colPIT2	Numeric or character; the colour of the theoretical uniform Q-Q plot in the PIT.
ltyPIT1	An integer or character string; the line types for the sample uniform Q-Q plot in the PIT, see par(lty = .).
ltyPIT2	An integer or character string; the line types for the theoretical uniform Q-Q plot in the PIT, see par(lty = .).
typePIT	A 1-character string; the type of plot for the sample uniform Q-Q plot in the PIT.
ltyQQ	An integer or character string; the line type for the normal Q-Q plot of the normal randomized residuals, see par(lty = .).
colQQ	Numeric or character; the colour of the line in the normal Q-Q plot of the normal randomized residuals.
titles	A list of the same length as which. For any elements which are NULL, useful titles will be created for the corresponding plot.
...	Further arguments passed to plot.default and plot.ts.

Details

plot.glarma is an S3 generic function for objects of class glarma.

The plots in this method display the fixed effects fit, GLARMA fit and various types of residuals for the GLARMA fit under the Poisson distribution, the binomial distribution or the negative binomial distribution, plus a number of plots of the randomized residuals (see normRandPIT for details of the randomized residuals). In all, ten plots can be produced. The observed values of the dependent variable shown in the time series plot are mainly used to compare with the two fits.

The fixed effects fit is calculated from eta, the multiplication of the data matrix X and beta coefficients in GLARMA model. In contrast, the GLARMA fit is calculated from W, the product of the data matrix X and delta in the GLARMA model, which is the combination of both the beta and ARMA coefficients, and is also called the state variable of the series.

There are some major differences for computing the fixed effects fit from eta and the GLARMA fit from W under different distributions.

Under the Poisson distribution and negative binomial distribution,

fixed effects fit = exp(eta)

and

glarma fit = exp(W).

Under the binomial distribution,

fixed effects fit = 1 / (1 + exp(-eta))

and

glarma fit = 1 / (1 + exp(-W)).

The residuals are calculated from the observed data and GLARMA fit. The exact computation for the residuals depends on the type of residuals used. The details are given in glarma. The ACF plot, the residuals against time and the normal Q-Q plot are all based on these residuals. Further details about those three plots are passed to acf and qqnorm.

There are four plots based on the randomized residuals calculated using normRandPIT. These are a histogram, a Q-Q plot, an autocorrelation plot and a partial autocorrelation plot.

The number of plots to be shown in the window depends on the value of the graphical parameter mfrow (or mfcol). If the displayed window is set to be large enough to show all ten plots, they will be shown at one time. Otherwise, the required number of plots will appear each time in the displayed window, and the user will need to enter return to see subsequent plots. By default, six plots are produced.

For the time series plot in the function, the fit displayed is specified by the argument fits. The legend will be shown if legend is TRUE. It will appear under the title of the time series plot. Also the legend and the title will alter automatically according to the fits shown in the plot.

Author(s)

"Cenanning Li" <[e-mail]>

See Also

plot.ts, qqnorm, acf, plot.default, normRandPIT.

Examples

### A example from Davis, Dunsmuir Wang (1999)
## MA(1,2,5), Pearson Residuals, Fisher Scoring
data(Polio)
y <- Polio[, 2]
X <- as.matrix(Polio[, 3:8])
glarmamod <- glarma(y, X, thetaLags = c(1, 2, 5), type = "Poi",method = "FS",
                    residuals = "Pearson", maxit = 100 , grad = 1e-6)

## The default plots are shown
plot(glarmamod)

## The plots used only to compared GLARMA fit and the observed data
plot(glarmamod, which = 1L, fits = c(1, 3))

Example output

glarma documentation built on May 2, 2019, 6:33 a.m.