# 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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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" <cli113@aucklanduni.ac.nz>

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```### 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.
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