# graphres.fun: Plot NHPP residuals versus time or monotonous variables In NHPoisson: Modelling and Validation of Non Homogeneous Poisson Processes

## Description

This function plots residuals of a NHPP (raw or scaled, overlapping or disjoint) versus time or other variables which are monotonous functions.

## Usage

 1 2 3 4 graphres.fun(objres = NULL, typeRes = "Raw", t = NULL, res = NULL, lint = NULL, posE = NULL, fittedlambda = NULL, typeI = "Disjoint", Xvariables = NULL, namXv = NULL, histWgraph=TRUE, plotDisp=c(2,2), addlow = FALSE, lwd = 2, tit = "", flow = 0.5, xlegend = "topleft", legcex = 0.5) 

## Arguments

 objres Optional. A list with (at least) elements t, typeI and Rawres and/or ScaRes, depending on the value of typeRes. For example, the output list from the functions CalcRes.fun or CalcResD.fun; see those functions for details. typeRes Label indicating the type of residuals ("Raw" or any type of scaled residuals such as "Pearson"). t Optional. Time vector of the PP observation period. res Optional. Vector of residuals. lint Optional. Length of the intervals used to calculate the residuals. posE Optional. Numeric vector of the PP occurrence times. Only used when typeI = "Overlapping". fittedlambda Optional. Vector of the cumulative fitted PP intensity over the intervals. Used to calculate the envelopes when typeRes="Raw". typeI Label indicating the type ("Overlapping" or "Disjoint") of intervals. Xvariables Optional. Matrix of the variables for the residual plots (each column is a variable). namXv Optional. Vector of the names of the variables in Xvariables. histWgraph Logical flag. If it is TRUE, a new graphical device is opened with the option record=TRUE, so that the history of all plots is recorded in the new device. This option may not work on some platforms; for example, RStudio does not allow the user to open new graphical devices. plotDisp A vector of the form c(nr, nc). The residual plots will be drawn in a nr\timesnc array. It is used as argument mfrow in par. By default, a 2 \times 2 window is used. tit Character string. A title for the plots. addlow Logical flag. If it is TRUE, a lowess is added to the residual plots. lwd Argument lwd for plotting the lowess lines, see par for details. flow Argument f for the lowess, see lowess for details. xlegend Label giving the position of the graph where the legend will be located. legcex Argument cex for the legend, see par for details.

## Details

Either argument objres or pair of arguments (t,res) must be specified. If objres is provided, arguments t,res, typeRes, typeI, posE and fittedlambda are ignored.

A residual plot versus time is always performed. These plots are intended for time or variables which are monotonous functions, since residuals are calculated over a given time interval and plotted versus the value of the variables in the mean point of the interval.

A smoother (lowess) of the residuals can be optionally added to the plots. In the case of overlapping intervals, the residuals of the occurrence points are marked differently from the rest. In the case typeRes="Raw" (if argument fittedlambda is available) or typeRes="Pearson", envelopes for the residuals are also plotted. The envelopes are based on an approach analogous to the one shown in Baddeley et al. (2005) for spatial Poisson processes. The envelopes for raw residuals are,

\pm {2 \over l_2-l_1} √{∑_{ i \in (l_1,l_2)} \hat λ(i)}

where index i runs over the integers in the interval (l_1,l_2). The envelopes for the Pearson residuals are,

\pm 2/√{l_2-l_1}.

These plots allow us to analyze the effect on the intensity, of the covariates included in the model or other potentially influent variables. They show if the mean or the dispersion of the residuals vary sistematically, see for example residual analysis in Atkinson (1985) or Collett (1994).

## References

Atkinson, A. (1985). Plots, transformations and regression. Oxford University Press.

Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005). Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B, 67, 617-666.

Cebrian, A.C., Abaurrea, J. and Asin, J. (2015). NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes. Journal of Statistical Software, 64(6), 1-24.

Collett, D. (1994). Modelling survival data in medical research. Chapman & Hall.

graphrate.fun
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 #Example using objres as input X1<-c(1:1000)**0.5 modE<-fitPP.fun(tind=TRUE,covariates=cbind(X1), posE=round(runif(40,1,1000)), inddat=rep(1,1000), tim=c(1:1000), tit="Simulated example", start=list(b0=1,b1=0), modSim = TRUE, dplot = FALSE) ResDE<-CalcResD.fun(mlePP=modE,lint=50) graphres.fun(objres=ResDE, typeRes="Raw", Xvariables=cbind(X1), namXv=c("X1"), plotDisp=c(2,1), addlow=TRUE,tit="Example") #Example using the set of arguments res, t and fittedlambda as input #In this case, with typeI="Disjoint", only values of t, fittedlambda and Xvariables #in the midpoint of the intervals must be provided. #Since a 1X1 layout is specified in plotDisp and only one #graphical device is opened by default, the two resulting plots can be scrolled #up and down with the "Page Up" and "Page Down" keys. X1<-c(1:500)**0.5 graphres.fun(res=rnorm(50),posE=round(runif(50,1,500)), fittedlambda=runif(500,0,1)[seq(5,495,10)], t=seq(5,495,10), typeRes="Raw", typeI="Disjoint",Xvariables=X1[seq(5,495,10)], namXv=c("X1"), plotDisp=c(1,1), tit="Example 2",lint=10)