Specification of the Reference Distribution
Specification of the asymptotic, approximative (Monte Carlo) and exact reference distribution.
asymptotic(maxpts = 25000, abseps = 0.001, releps = 0)
approximate(nresample = 10000L, parallel = c("no", "multicore", "snow"),
ncpus = 1L, cl = NULL, B)
exact(algorithm = c("auto", "shift", "split-up"), fact = NULL)maxpts |
an integer, the maximum number of function values. Defaults to
|
abseps |
a numeric, the absolute error tolerance. Defaults to |
releps |
a numeric, the relative error tolerance. Defaults to |
nresample |
a positive integer, the number of Monte Carlo replicates used for the
computation of the approximative reference distribution. Defaults to
|
parallel |
a character, the type of parallel operation: either |
ncpus |
an integer, the number of processes to be used in parallel operation.
Defaults to |
cl |
an object inheriting from class |
B |
deprecated, use |
algorithm |
a character, the algorithm used for the computation of the exact reference
distribution: either |
fact |
an integer to multiply the response values with. Defaults to |
asymptotic, approximate and exact can be supplied to the
distribution argument of, e.g., independence_test to
provide control of the specification of the asymptotic, approximative (Monte
Carlo) and exact reference distribution respectively.
The asymptotic reference distribution is computed using a randomised
quasi-Monte Carlo method (Genz and Bretz, 2009) and is applicable to arbitrary
covariance structures with dimensions up to 1000. See
GenzBretz in package mvtnorm for
details on maxpts, abseps and releps.
The approximative (Monte Carlo) reference distribution is obtained by a
conditional Monte Carlo procedure, i.e., by computing the test statistic for
nresample random samples from all admissible permutations of the
response Y within each block (Hothorn et al., 2008). By
default, the distribution is computed using serial operation
(parallel = "no"). The use of parallel operation is specified by
setting parallel to either "multicore" (not available for MS
Windows) or "snow". In the latter case, if cl = NULL (default)
a cluster with ncpus processes is created on the local machine unless a
default cluster has been registered (see
setDefaultCluster in package
parallel) in which case that gets used instead. Alternatively, the use
of an optional parallel or snow cluster can be specified by
cl. See ‘Examples’ and package parallel for details on
parallel operation.
The exact reference distribution, currently available for univariate
two-sample problems only, is computed using either the shift algorithm
(Streitberg and Röhmel, 1984, 1986, 1987) or the split-up
algorithm (van de Wiel, 2001). The shift algorithm handles blocks pertaining
to, e.g., pre- and post-stratification, but can only be used with positive
integer-valued scores h(Y). The split-up algorithm can be
used with non-integer scores, but does not handle blocks. By default, an
automatic choice is made (algorithm = "auto") but the shift and
split-up algorithms can be selected by setting algorithm to either
"shift" or "split-up" respectively.
Starting with coin version 1.1-0, the default for algorithm is
"auto", having identical behaviour to "shift" in previous
versions. In earlier versions of the package, algorithm = "shift"
silently switched to the split-up algorithm if non-integer scores were
detected, whereas the current version exits with a warning.
In versions of coin prior to 1.3-0, the number of Monte Carlo replicates
in approximate() was specified using the now deprecated B
argument. This will be made defunct and removed in a future release.
It has been replaced by the nresample argument (for conformity with the
libcoin, party and partykit packages).
Genz, A. and Bretz, F. (2009). Computation of Multivariate Normal and t Probabilities. Heidelberg: Springer-Verlag.
Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2008). Implementing a class of permutation tests: The coin package. Journal of Statistical Software 28(8), 1–23. doi: 10.18637/jss.v028.i08
Streitberg, B. and Röhmel, J. (1984). Exact nonparametrics in APL. APL Quote Quad 14(4), 313–325. doi: 10.1145/384283.801115
Streitberg, B. and Röhmel, J. (1986). Exact distributions for permutations and rank tests: an introduction to some recently published algorithms. Statistical Software Newsletter 12(1), 10–17.
Streitberg, B. and Röhmel, J. (1987). Exakte verteilungen für rang- und randomisierungstests im allgemeinen c-stichprobenfall. EDV in Medizin und Biologie 18(1), 12–19.
van de Wiel, M. A. (2001). The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics. Computational Statistics 16(4), 519–538. doi: 10.1007/s180-001-8328-6
## Approximative (Monte Carlo) Cochran-Mantel-Haenszel test
## Serial operation
set.seed(123)
cmh_test(disease ~ smoking | gender, data = alzheimer,
distribution = approximate(nresample = 100000))
## Not run:
## Multicore with 8 processes (not for MS Windows)
set.seed(123, kind = "L'Ecuyer-CMRG")
cmh_test(disease ~ smoking | gender, data = alzheimer,
distribution = approximate(nresample = 100000,
parallel = "multicore", ncpus = 8))
## Automatic PSOCK cluster with 4 processes
set.seed(123, kind = "L'Ecuyer-CMRG")
cmh_test(disease ~ smoking | gender, data = alzheimer,
distribution = approximate(nresample = 100000,
parallel = "snow", ncpus = 4))
## Registered FORK cluster with 12 processes (not for MS Windows)
fork12 <- parallel::makeCluster(12, "FORK") # set-up cluster
parallel::setDefaultCluster(fork12) # register default cluster
set.seed(123, kind = "L'Ecuyer-CMRG")
cmh_test(disease ~ smoking | gender, data = alzheimer,
distribution = approximate(nresample = 100000,
parallel = "snow"))
parallel::stopCluster(fork12) # clean-up
## User-specified PSOCK cluster with 8 processes
psock8 <- parallel::makeCluster(8, "PSOCK") # set-up cluster
set.seed(123, kind = "L'Ecuyer-CMRG")
cmh_test(disease ~ smoking | gender, data = alzheimer,
distribution = approximate(nresample = 100000,
parallel = "snow", cl = psock8))
parallel::stopCluster(psock8) # clean-up
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.