renewalTestPlot: Non-Parametric Tests for Renewal Processes
In STAR: Spike Train Analysis with R

Description Usage Arguments Details Value Note Author(s) See Also Examples

Performs and displays rank based tests checking if a spike train is a renewal process

renewalTestPlot(spikeTrain, lag.max = NULL,
                d=max(c(2,sqrt(length(spikeTrain)) %/% 5)),
                orderPlotPch=ifelse(length(spikeTrain)<=600,1,"."),
                ...)

`spikeTrain`	a `spikeTrain` object or a vector which can be coerced to such an object.
`lag.max`	argument passed to `acf.spikeTrain`.
`d`	an integer >= 2, the number of divisions used for the Chi 2 test. The default value is such that under the null hypothesis at least 25 events should fall in each division.
`orderPlotPch`	`pch` argument for the order plots.
`...`	additional arguments passed to function `chisq.test`.

renewalTestPlot generates a 4 panel plot. The 2 graphs making the top row are qualitative and display the rank of inter-spike interval (ISI) k+1 versus the rank of ISI k (left graph) and the rank of ISI k+2 versus the one of ISI k (right graph). The bottom left graph displays the autocorrelation function of the ISIs and is generated by a call to acf.spikeTrain. The bottom right graph display the result of a Chi square test performed on the ranks at different lags. More precisely, for each considered lag j (from 1 to lag.max) the square within which the rank of ISI k+1 vs the one of ISI k is found is splited in d^2 cells. This decomposition into cells is shown on the two graphs of the top row. Under the renewal process hypothesis the points should be uniformly distributed with a density N/d^2, where N is the number of ISIs. The sum other rows and other columns is moreover exactly N/d. The upper graphs are therefore graphical displays of two-dimensional contingency tables. A chi square test for two-dimensional contingency tables (function chisq.test) is performed on the table generated at each lag j. The resulting Chi 2 value is displayed vs the lag. The 95% confidence region appears as a clear grey rectangle, the value falling within this region appear as black dots and the ones falling out appear as dark grey triangles.

Nothing is returned, the function is used for its side effect: a plot is generated.

You should not use a too large value for d otherwise the Chi 2 values will be too approximative and warnings will be printed. If your process is a renewal process you should have on average 5% of the points on the bottom right graph appearing as dark triangles.

Christophe Pouzat christophe.pouzat@gmail.com

acf, varianceTime, acf.spikeTrain

## Not run: 
## Apply the test of Ogata (1988) shallow shock data
data(ShallowShocks)
renewalTestPlot(ShallowShocks$Date,d=3)

## Apply the test to the second and third neurons of the cockroachAlSpont
## data set
## load spontaneous data of 4 putative projection neurons
## simultaneously recorded from the cockroach (Periplaneta
## americana) antennal lobe
data(CAL1S)
## convert data into spikeTrain objects
CAL1S <- lapply(CAL1S,as.spikeTrain)
## look at the individual trains
## first the "raw" data
CAL1S[["neuron 1"]]
## next some summary information
summary(CAL1S[["neuron 1"]])
## next the renewal tests
renewalTestPlot(CAL1S[["neuron 1"]])

## Simulate a renewal log normal train with 500 isi
isi.nb <- 500
train1 <- c(cumsum(rlnorm(isi.nb+1,log(0.01),0.25)))
## make the test
renewalTestPlot(train1)

## Simulate a (non renewal) 2 states train
myTransition <- matrix(c(0.9,0.1,0.1,0.9),2,2,byrow=TRUE)
states2 <- numeric(isi.nb+1) + 1
for (i in 1:isi.nb) states2[i+1] <- rbinom(1,1,prob=1-myTransition[states2[i],])+1
myLnormPara2 <- matrix(c(log(0.01),0.25,log(0.05),0.25),2,2,byrow=TRUE)
train2 <-
cumsum(rlnorm(isi.nb+1,myLnormPara2[states2,1],myLnormPara2[states2,2]))
## make the test
renewalTestPlot(train2)
## End(Not run)