Generators for efpFunctionals along Categorical Variables
Generators for efpFunctional objects suitable for aggregating
empirical fluctuation processes to test statistics along (ordinal)
categorical variables.
catL2BB(freq) ordL2BB(freq, nproc = NULL, nrep = 1e5, probs = c(0:84/100, 850:1000/1000), ...) ordwmax(freq, algorithm = mvtnorm::GenzBretz(), ...)
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 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 for every combination of frequencies and number of
processes. Hence, this is somewhat more time-consuming compared to
the closed-form 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/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.
## 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)
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