Description Usage Arguments Details Value References See Also Examples
Generators for efpFunctional
objects suitable for aggregating
empirical fluctuation processes to test statistics along (ordinal)
categorical variables.
1 2 3 
freq 
object specifying the category frequencies for the
categorical variable to be used for aggregation: either a

nproc 
numeric. Number of processes used for simulating
from the asymptotic distribution (passed to 
nrep 
numeric. Number of replications used for simulating
from the asymptotic distribution (passed to 
probs 
numeric vector specifying for which probabilities critical values should be tabulated. 
... 
further arguments passed to 
algorithm 
algorithm specification passed to 
Merkle, Fan, and Zeileis (2014) discuss three functionals that are
suitable for aggregating empirical fluctuation processes along categorical
variables, especially ordinal variables. The functions catL2BB
,
ordL2BB
, and ordwmax
all require a specification of the
relative frequencies within each category (which can be computed from
various specifications, see arguments). All of them employ
efpFunctional
(Zeileis 2006) internally to set up an
object that can be employed with gefp
fluctuation
processes.
catL2BB
results in a chisquared test. This is essentially
the LM test counterpart to the likelihood ratio test that assesses
a split into unordered categories.
ordL2BB
is the ordinal counterpart to supLM
where aggregation is done along the ordered categories (rather than
continuously). The asymptotic distribution is nonstandard and needs
to be simulated for every combination of frequencies and number of
processes. Hence, this is somewhat more timeconsuming compared to
the closedform solution employed in catL2BB
. It is also
possible to store the result of ordL2BB
in case it needs to
be applied several gefp
fluctuation processes.
ordwmax
is a weighted double maximum test based on ideas
previously suggested by Hothorn and Zeileis (2008) in the context of
maximally selected statistics. The asymptotic distribution is
(multivariate) normal and computed by means of pmvnorm
.
An object of class efpFunctional
.
Hothorn T., Zeileis A. (2008), Generalized Maximally Selected Statistics. Biometrics, 64, 1263–1269.
Merkle E.C., Fan J., Zeileis A. (2014), Testing for Measurement Invariance with Respect to an Ordinal Variable. Psychometrika, 79(4), 569–584. doi:10.1007/S1133601393767.
Zeileis A. (2006), Implementing a Class of Structural Change Tests: An Econometric Computing Approach. Computational Statistics & Data Analysis, 50, 2987–3008. doi:10.1016/j.csda.2005.07.001.
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  ## artificial data
set.seed(1)
d < data.frame(
x = runif(200, 1, 1),
z = factor(rep(1:4, each = 50)),
err = rnorm(200)
)
d$y < rep(c(0.5, 0.5), c(150, 50)) * d$x + d$err
## empirical fluctuation process
scus < gefp(y ~ x, data = d, fit = lm, order.by = ~ z)
## chisquaredtype test (unordered LMtype test)
LMuo < catL2BB(scus)
plot(scus, functional = LMuo)
sctest(scus, functional = LMuo)
## ordinal maxLM test (with few replications only to save time)
maxLMo < ordL2BB(scus, nrep = 10000)
plot(scus, functional = maxLMo)
sctest(scus, functional = maxLMo)
## ordinal weighted double maximum test
WDM < ordwmax(scus)
plot(scus, functional = WDM)
sctest(scus, functional = WDM)

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