Aircraft Accident Patterns Over Time

In gamclass: Functions and Data for a Course on Modern Regression and Classification

library(knitr)
options(replace.assign=FALSE,width=72)
opts_chunk$set(fig.align='center', fig.width=5.5,
               fig.height=4.25, par=TRUE,
               tidy=FALSE,  comment=NA)
knit_hooks$set(par=function(before, options, envir){
if (before && options$fig.show!='none') par(mar=c(4,4,2.6,.1),
              cex.lab=.95,cex.axis=.9,mgp=c(2,.7,0),tcl=-.3)
}, crop=hook_pdfcrop)
oldopt <- options(digits=4)

Prepare data -- Weekly and daily counts

The interest is in broad patterns over time. Weekly counts give numbers that are easier to work with.

We use the function gamclass::eventCounts() to create counts of accidents, i) by week, and ii) by day, in both cases from January 1, 2006:

airAccs <- gamclass::airAccs
fromDate <- as.Date("2006-01-01")
dfDay06 <- gamclass::eventCounts(airAccs, dateCol="Date",
                       from= fromDate, by="1 day",
                       prefix="num")
dfDay06$day <- julian(dfDay06$Date, origin=fromDate)
dfWeek06 <- gamclass::eventCounts(airAccs, dateCol="Date", from=fromDate,
                        by="1 week", prefix="num")
dfWeek06$day <- julian(dfWeek06$Date, origin=fromDate)

Fits, to the daily data, and to the weekly data

Figure 1 shows the fits to the weekly data:

cap1 <- "Figure 1: Fitted number of events (aircraft accidents) per week
  versus time."

library(grid)
library(mgcv)
year <- seq(from=fromDate, to=max(dfDay06$Date), by="1 year")
atyear=julian(year, origin=fromDate)
dfWeek06.gam <- gam(num~s(day, k=200), data=dfWeek06, family=quasipoisson)
av <- mean(predict(dfWeek06.gam))
plot(dfWeek06.gam, xaxt="n", shift=av, trans=exp, rug=FALSE,
     xlab="", ylab="Estimated rate per week", fg='gray')
axis(1, at=atyear, labels=format(year, "%Y"))
grid(lw=2,nx=NA,ny=NULL)
abline(v=atyear, lwd=2, lty=3, col='lightgray')
mtext(side=3, line=0.75, "Figure 1: Events per week, vs date", cex=1.25, adj=0)

The fitted curve and confidence band that results from modeling and plotting events per day is very similar. Code to plot events per day is:

cap2 <- "Figure 2: Fitted number of events (aircraft accidents) per day
  versus time."

```r dfDay06.gam <- , out.width='60%', fig.width=6, fig.height=4, fig.cap=cap2} gam(formula = num ~ s(day, k=200), family = quasipoisson, data = dfDay06) av <- mean(predict(dfDay06.gam)) plot(dfDay06.gam, xaxt="n", shift=av, trans=exp, rug=FALSE, xlab="", ylab="Estimated rate per day", fg='gray') axis(1, at=atyear, labels=format(year, "%Y")) grid(lw=2,nx=NA,ny=NULL) abline(v=atyear, lwd=2, lty=3, col='lightgray') mtext(side=3, line=0.75, "A: Events per day, vs date", cex=1.25, adj=0)}

gamclass documentation built on Aug. 21, 2023, 5:07 p.m.