Description Usage Arguments Details Value Examples
Estimate interval mean and variance accounting for missed arrival observations, by fitting the probability density function intervalpdf to the interval data.
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data 
A numeric list of intervals. 
mu 
Start value for the numeric optimization for the mean arrival interval. 
sigma 
Start value for the numeric optimization for the standard deviation of the arrival interval. 
p 
Start value for the numeric optimization for the probability to not observe an arrival. 
N 
Maximum number of missed observations to be taken into account (default N=5). 
fun 
Assumed distribution for the intervals, one of " 
trunc 
Use a truncated probability density function with range 
fpp 
Baseline proportion of intervals distributed as a random poisson process with mean arrival interval 
fpp.method 
A string equal to 'fixed' or 'auto'. When 'auto' 
p.method 
A string equal to 'fixed' or 'auto'. When 'auto' 
conf.level 
Confidence level for deviance test that checks whether model with nonzero missed event probability

group 
optional vector of equal length as data, indicating the group or subject in which the interval was observed 
sigma.within 
optional withinsubject standard deviation. When equal to default 'NA', assumes
no additional betweensubject effect, with 
iter 
maximum number of iterations in numerical iteration for 
tol 
tolerance in the iteration, when 
silent 
logical. When 
... 
Additional arguments to be passed to optim 
The probability density function for observed intervals intervalpdf
is fit to data
by maximization of the
associated loglikelihood using optim.
Withingroup variation sigma.within
may be separated from the total variation sigma
in an iterative fit of intervalpdf on the interval data.
In the iteration partition is used to (1) determine which intervals according to the fit are a fundamental interval at a confidence level conf.level
,
and (2) to partition the withingroup variation from the total variation in interval length.
Within and betweengroup variation is estimated on the subset of fundamental intervals with repeated measures only.
As the set of fundamental interval depends on the precise value of sigma.within
, the fit of intervalpdf and the subsequent estimation of
sigma.within
using partition is iterated until both converge to a stable solution. Parameters tol
and iter
set the threshold for convergence and the maximum number of iterations.
We note that an exponential interval model can be fitted by setting fpp=1
and fpp.method=fixed
.
This function returns an object of class intRvals
, which is a list containing the following:
data
the interval data
mu
the modelled mean interval
mu.se
the modelled mean interval standard error
sigma
the modelled interval standard deviation
p
the modelled probability to not observe an arrival
fpp
the modelled fraction of arrivals following a random poisson process, see intervalpdf
N
the highest number of consecutive missed arrivals taken into account, see intervalpdf
convergence
convergence field of optim
counts
counts field of optim
loglik
vector of length 2, with first element the loglikelihood of the fitted model, and second element the loglikelihood of the model without a missed event probability (i.e. p
=0)
df.residual
degrees of freedom, a 2vector (1, number of intervals  n.param
)
n.param
number of optimized model parameters
p.chisq
p value for a likelihoodratio test of a model including a miss probability relative against a model without a miss probability
distribution
assumed interval distribution, one of 'gamma' or 'normal'
trunc
interval range over which the interval pdf was truncated and normalized
fpp.method
A string equal to 'fixed' or 'auto'. When 'auto' fpp
has been optimized as a free model parameter
p.method
A string equal to 'fixed' or 'auto'. When 'auto' p
has been optimized as a free model parameter
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 28 29  data(goosedrop)
# calculate mean and standard deviation of arrival intervals, accounting for missed observations:
dr=estinterval(goosedrop$interval)
# plot some summary information
summary(dr)
# plot a histogram of the intervals and fit:
plot(dr)
# test whether the mean arrival interval is greater than 200 seconds:
ttest(dr,mu=200,alternative="greater")
# let's estimate mean and variance of dropping intervals by site
# (schiermonnikoog vs terschelling) for time period 5.
# first prepare the two datasets:
set1=goosedrop[goosedrop$site=="schiermonnikoog" & goosedrop$period == 5,]
set2=goosedrop[goosedrop$site=="terschelling" & goosedrop$period == 5,]
# allowing a fraction of intervals to be distributed randomly (fpp='auto')
dr1=estinterval(set1$interval,fpp.method='auto')
dr2=estinterval(set2$interval,fpp.method='auto')
# plot the fits:
plot(dr1,xlim=c(0,1000))
plot(dr2,xlim=c(0,1000))
# mean dropping interval are not significantly different
# at the two sites (on a 0.95 confidence level):
ttest(dr1,dr2)
# now compare this test with a ttest not accounting for unobserved intervals:
t.test(set1$interval,set2$interval)
# not accounting for missed observations leads to a (spurious)
# larger difference in means, which also increases
# the apparent statistical significance of the difference between means

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