| Title: | Sequential Event Interval Analysis |
|---|---|
| Description: | Functions for analysis of rate changes in sequential events. |
| Authors: | Jim Lemon <[email protected]>, |
| Maintainer: | Jim Lemon <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.3 |
| Built: | 2024-10-29 04:15:59 UTC |
| Source: | https://github.com/cran/eventInterval |
Functions for analysis of rate changes in sequential events. Appropriate data are the times of observation of well defined events, such as equipment failures or deaths.
| Package: | eventInterval |
| Version: | 1.0 |
| Date: | 2013-05-28 |
| Depends: | MASS |
| License: | GPL (>=2) |
| Packaged: | 2013-05-28 11:12:16 UTC; root |
| Built: | R 3.0.0; ; 2013-05-28 11:12:19 UTC; unix |
Index:
EIglm Perform a GLM with intervals as response variable EIdensity Plot the empirical and theoretical densities of intervals EIplot Plot the intervals against the occurrence of the events rescale scale numeric values into a new range
The basic model is of events that are independent and uniformly distributed in time. This assumption underlies the use of the exponential distribution in the generalized linear models produced by ‘EIglm’. In general, it is expected that deviations from uniformly distributed intervals follow a function that is expressed in one or more of the predictors. A predictor that is included by default is the times of the occurrence of the events. This will reveal linear changes in the rate. Other predictors may test for non-linear or cyclic changes in rate.
Event interval analysis can be a useful alternative to Poisson based analysis when few events occur in the counting intervals. Its advantage in power to detect changes in rate diminishes as the number of events increases.
This type of analysis was known as event history analysis, but the phrase is now usually applied to the analysis of the antecedents of events, whether sequential or not.
Jim Lemon <[email protected]>, Maintainer: Jim Lemon <[email protected]>
Maguire, B.A., Pearson, E.S. & Wynn, A.H.A. (1952) The time intervals between industrial accidents. Biometrika, 39(1/2): 168-180.
Whitworth, W.A. (1901) Choice and chance. (3rd ed.) Cambridge: Deighton Bell.
Lemon, J. (2014) The analysis of event rates using intervals. The Quantitative Methods for Psychology, 10 (1), 68-76.
Plot the empirical distribution of a set of values.
EIdist(event_times,nbreaks=10,main="",xlab="",ylab="", xaxticks=NA,xaxlabs=NA)EIdist(event_times,nbreaks=10,main="",xlab="",ylab="", xaxticks=NA,xaxlabs=NA)
event_times |
A numeric vector of times of occurrence of events. |
nbreaks |
The number of breaks desired (but not always delivered). |
main |
Title for the plot. |
xlab |
X axis label for the plot. |
ylab |
Y axis label for the plot. |
xaxticks |
Optional X tick mark positions. |
xaxlabs |
Optional X tick labels. |
‘EIdist’ calculates the intervals between the times passed in ‘event_times’ and plots a histogram of their distribution. It adds a smoothed line based on the ‘mids’ and ‘counts’. It then calls ‘fitdistr’ from MASS to get an estimated rate for a model exponential distribution. A second line is added to the plot for comparison with the smoothed empirical distribution.
nil
Jim Lemon
## Not run: # won't pass check due to the call to fitdistr data(florida_hurr20) oldloc<-Sys.setlocale("LC_TIME", "C") fh_dates<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") fh_days<-as.numeric(fh_dates) fh_ints<-diff(fh_days) fh_counts<-tabulate(florida_hurr20$year[-1]-1899,nbins=100) require(MASS) EIdist(fh_days,main="Empirical distribution of hurricanes", xlab="Intervals in days",ylab="Frequencies") Sys.setlocale("LC_TIME", oldloc) ## End(Not run)## Not run: # won't pass check due to the call to fitdistr data(florida_hurr20) oldloc<-Sys.setlocale("LC_TIME", "C") fh_dates<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") fh_days<-as.numeric(fh_dates) fh_ints<-diff(fh_days) fh_counts<-tabulate(florida_hurr20$year[-1]-1899,nbins=100) require(MASS) EIdist(fh_days,main="Empirical distribution of hurricanes", xlab="Intervals in days",ylab="Frequencies") Sys.setlocale("LC_TIME", oldloc) ## End(Not run)
Perform a GLM with the intervals between events as the response and the times of the events as a predictor.
EIglm(event_times,event_vars=list(),formula=NULL)EIglm(event_times,event_vars=list(),formula=NULL)
event_times |
A numeric vector of times of occurrence of events. |
event_vars |
Optional predictors to include in the GLM. |
formula |
A optional string that can be coerced to a valid formula. |
‘EIglm’ calculates the intervals between the times passed in ‘event_times’ and calls ‘glm’ with ‘family="Gamma"’. If the times are not in increasing order, they will be sorted. If there are any zero length intervals, the events that occur in the same time increment are spread out over that time increment.
If more predictors are passed in ‘event_vars’ these will be added to the formula passed to ‘glm’. When passing predictors based on the events, remember to discard the first value as the intervals are calculated between events. This means that the interval is unknown for the first event.
‘EIglm’ only tests the effects of the variables specified and does not test interactions. If a more complex model is to be tested, the user must directly call ‘glm’ and compose a formula for the model (see the last example). Note that because there is no ‘data’ argument in EIglm, each term in the model must be specified explicitly.
An object of class ‘glm’.
Jim Lemon
Blake, E.S., Rappaport, E.N. & Landsea, C.W. (2007) The deadliest, costliest, and most intense United States tropical cyclones from 1851 to 2006 (and other frequently requested hurricane facts). NOAA Technical Memorandum NWS TPC-5, Miami: National Weather Service.
Florida Climate Center (2013) Florida statewide averaged temperature data (in degrees Fahrenheit). URL: http://climatecenter.fsu.edu/products-services/data/statewide-averages/temperature accessed 28/5/2013
## Not run: # Florida hurricane analysis (20th century) data(florida_hurr20) oldloc<-Sys.setlocale("LC_TIME", "C") fh_dates<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") fh_days<-as.numeric(fh_dates) fh_ints<-diff(fh_days) fh_counts<-tabulate(florida_hurr20$year[-1]-1899,nbins=100) # run a Poisson analysis on the counts print(summary(glm(fh_counts~I(1900:1999),family="poisson"))) EIglm(fh_days) data(florida_temp20) plot(florida_temp20$year,florida_temp20$Annual,type="b", main="Average temperature in Florida",xlab="Year",ylab="degrees F") lines(supsmu(florida_temp20$year,florida_temp20$Annual),lwd=2) # define a function to match values findval<- function(x,set) return(which(set %in% x)) ftemp_years<-florida_temp20$Annual[unlist(sapply(florida_hurr20$year, FUN=findval,florida_temp20$year))] EIglm(fh_days,list(ft=ftemp_years[-1])) Sys.setlocale("LC_TIME", oldloc) ## End(Not run) # manually performing an event interval GLM # get the Florida hurricane data data(florida_hurr20) # create date values for the events florida_hurr20$date<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") # convert the dates to numeric values (offsets from 1/1/1970) florida_hurr20$days<-as.numeric(florida_hurr20$date) # calculate the intervals, adding NA for the first unknown value florida_hurr20$ints<-c(NA,diff(florida_hurr20$days)) # first test the default model in EIglm, dropping the first event summary(glm(ints~days,florida_hurr20[-1,],family="Gamma")) # test a model predicting intervals with times of occurrence, # the intensities of the hurricanes and their interaction, # again dropping the first event summary(glm(ints~days*category,florida_hurr20[-1,],family="Gamma"))## Not run: # Florida hurricane analysis (20th century) data(florida_hurr20) oldloc<-Sys.setlocale("LC_TIME", "C") fh_dates<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") fh_days<-as.numeric(fh_dates) fh_ints<-diff(fh_days) fh_counts<-tabulate(florida_hurr20$year[-1]-1899,nbins=100) # run a Poisson analysis on the counts print(summary(glm(fh_counts~I(1900:1999),family="poisson"))) EIglm(fh_days) data(florida_temp20) plot(florida_temp20$year,florida_temp20$Annual,type="b", main="Average temperature in Florida",xlab="Year",ylab="degrees F") lines(supsmu(florida_temp20$year,florida_temp20$Annual),lwd=2) # define a function to match values findval<- function(x,set) return(which(set %in% x)) ftemp_years<-florida_temp20$Annual[unlist(sapply(florida_hurr20$year, FUN=findval,florida_temp20$year))] EIglm(fh_days,list(ft=ftemp_years[-1])) Sys.setlocale("LC_TIME", oldloc) ## End(Not run) # manually performing an event interval GLM # get the Florida hurricane data data(florida_hurr20) # create date values for the events florida_hurr20$date<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") # convert the dates to numeric values (offsets from 1/1/1970) florida_hurr20$days<-as.numeric(florida_hurr20$date) # calculate the intervals, adding NA for the first unknown value florida_hurr20$ints<-c(NA,diff(florida_hurr20$days)) # first test the default model in EIglm, dropping the first event summary(glm(ints~days,florida_hurr20[-1,],family="Gamma")) # test a model predicting intervals with times of occurrence, # the intensities of the hurricanes and their interaction, # again dropping the first event summary(glm(ints~days*category,florida_hurr20[-1,],family="Gamma"))
Plot the intervals between times against the times.
EIplot(event_times,main="",xlab="",ylab="",xaxticks=NA,xaxlabs=NA)EIplot(event_times,main="",xlab="",ylab="",xaxticks=NA,xaxlabs=NA)
event_times |
A numeric vector of times of occurrence of events. |
main |
Title for the plot. |
xlab |
X axis label for the plot. |
ylab |
Y axis label for the plot. |
xaxticks |
Optional X tick mark positions. |
xaxlabs |
Optional X tick labels. |
‘EIplot’ calculates the intervals between the times passed in ‘event_times’ and plots a scattergram of intervals against times. It adds a smoothed line and a "rug" of the event times to allow visual inspection for trend.
nil
Jim Lemon
# Florida hurricane analysis (20th century) data(florida_hurr20) oldloc<-Sys.setlocale("LC_TIME", "C") fh_dates<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") fh_days<-as.numeric(fh_dates) fh_ints<-diff(fh_days) fh_counts<-tabulate(florida_hurr20$year[-1]-1899,nbins=100) EIplot(fh_days,main="Florida hurricanes, 1900-1999", xlab="Year",ylab="Interval between hurricanes (days)", xaxticks=as.Date(as.character(seq(1900,2000,by=20)),"%Y"), xaxlabs=seq(1900,2000,by=20)) Sys.setlocale("LC_TIME", oldloc)# Florida hurricane analysis (20th century) data(florida_hurr20) oldloc<-Sys.setlocale("LC_TIME", "C") fh_dates<- as.Date(paste(florida_hurr20$day,florida_hurr20$month, florida_hurr20$year,sep="-"),"%d-%B-%Y") fh_days<-as.numeric(fh_dates) fh_ints<-diff(fh_days) fh_counts<-tabulate(florida_hurr20$year[-1]-1899,nbins=100) EIplot(fh_days,main="Florida hurricanes, 1900-1999", xlab="Year",ylab="Interval between hurricanes (days)", xaxticks=as.Date(as.character(seq(1900,2000,by=20)),"%Y"), xaxlabs=seq(1900,2000,by=20)) Sys.setlocale("LC_TIME", oldloc)
Atlantic hurricanes recorded as affecting Florida, USA during the 20th century.
data(florida_hurr20)data(florida_hurr20)
Blake, E.S., Rappaport, E.N. & Landsea, C.W. (2007) The deadliest, costliest, and most intense United States tropical cyclones from 1851 to 2006 (and other frequently requested hurricane facts). NOAA Technical Memorandum NWS TPC-5, Miami: National Weather Service.
Average statewide temperatures in Florida, USA from 1900-1999.
data(florida_temp20)data(florida_temp20)
Florida Climate Center (2013) Florida statewide averaged temperature data (in degrees Fahrenheit). URL: http://climatecenter.fsu.edu/products-services/data/statewide-averages/temperature accessed 28/5/2013
Calculate the intervals between a series of times, spreading out equal times in one unit of time.
get_intervals(event_times)get_intervals(event_times)
event_times |
A numeric vector of times of occurrence of events. |
‘get_intervals’ calculates the intervals between the times passed in ‘event_times’, adding increments to spread out times that are exactly the same. This can be a problem when the times are integers, as in days. The spreading out of events avoids zero intervals. The rationale for this is that even if more than event occurred on the same day, it is extremely unlikely that the events occurred at exactly the same time of day. The best estimate of the times of day is a uniform distribution over one day.
a vector of intervals between the vector of times passed
Jim Lemon
event_times<-c(1,3,5,5,7,9,10,10,10,12) get_intervals(event_times)event_times<-c(1,3,5,5,7,9,10,10,10,12) get_intervals(event_times)
Scale a vector or matrix of numbers into a new range.
rescale(x,newrange)rescale(x,newrange)
x |
A numeric vector, matrix or data frame. |
newrange |
The minimum and maximum value of the range into which ‘x’ will be scaled. |
‘rescale’ performs a simple linear conversion of ‘x’ into the range specified by ‘newrange’. Only numeric vectors, matrices or data frames with some variation will be accepted. NAs are now preserved - formerly the function would fail.
On success, the rescaled object, otherwise the original object.
Jim Lemon
# scale one vector into the range of another normal.counts<-rnorm(100) normal.tab<-tabulate(cut(normal.counts,breaks=seq(-3,3,by=1))) normal.density<-rescale(dnorm(seq(-3,3,length=100)),range(normal.tab)) # now plot them plot(c(-2.5,-1.5,-0.5,0.5,1.5,2.5),normal.tab,xlab="X values", type="h",col="green") lines(seq(-3,3,length=100),normal.density,col="blue")# scale one vector into the range of another normal.counts<-rnorm(100) normal.tab<-tabulate(cut(normal.counts,breaks=seq(-3,3,by=1))) normal.density<-rescale(dnorm(seq(-3,3,length=100)),range(normal.tab)) # now plot them plot(c(-2.5,-1.5,-0.5,0.5,1.5,2.5),normal.tab,xlab="X values", type="h",col="green") lines(seq(-3,3,length=100),normal.density,col="blue")