R: Generators for efpFunctionals along Categorical Variables
catL2BB
R Documentation
Generators for efpFunctionals along Categorical Variables
Description
Generators for efpFunctional objects suitable for aggregating
empirical fluctuation processes to test statistics along (ordinal)
categorical variables.
object specifying the category frequencies for the
categorical variable to be used for aggregation: either a
gefp object, a factor, or a numeric
vector with either absolute or relative category frequencies.
nproc
numeric. Number of processes used for simulating
from the asymptotic distribution (passed to efpFunctional).
If feq is a gefp object, then its number of
processes is used by default.
nrep
numeric. Number of replications used for simulating
from the asymptotic distribution (passed to efpFunctional).
probs
numeric vector specifying for which probabilities
critical values should be tabulated.
...
further arguments passed to efpFunctional.
algorithm
algorithm specification passed to pmvnorm
for computing the asymptotic distribution.
Details
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 chi-squared 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 non-standard and needs
to be simulated via rmvnorm for every combination
of frequencies and number of processes. This can be somewhat
time-consuming, hence it is recommended 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.
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/S11336-013-9376-7.
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.
See Also
efpFunctional, gefp
Examples
## 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)
## chi-squared-type test (unordered LM-type 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)