Estimates each person separately on two item subsets and compares the two
estimates with a per-person t-test (Smith 2002). By default the subsets
are defined by the sign of a residual-component loading (the first by
default; any leading component may be chosen); they can also be nominated
manually (for example, by content). Under
unidimensionality and local independence the two subset estimates are
independent given the person location, so
t = (theta_A - theta_B) / sqrt(se_A^2 + se_B^2) is approximately
standard normal and about alpha of the tests should reach
significance. Persons with an extreme score on either subset are excluded
(their weighted-likelihood estimates are most biased there). The
proportion of significant tests is reported with an exact
(Clopper-Pearson) binomial confidence interval; a lower bound above
alpha signals multidimensionality.
Usage
dimensionality_test(
fit,
alpha = 0.05,
items_positive = NULL,
items_negative = NULL,
component = 1
)Arguments
- fit
A fitted object from
rasch.- alpha
Nominal significance level for the per-person t-tests.
- items_positive, items_negative
Optional character vectors naming the two item subsets; both must be given (disjoint, at least two items each), otherwise the sign of a residual component defines the split.
- component
Which residual principal component's loading sign defines the default split (ignored when subsets are named). Default the first component.
Value
A list with the proportion of significant tests, its exact
confidence interval, the sample sizes (n used,
n_excluded_extreme), the item split and its source, a
multidimensional verdict, and paired_t, the paired t-test
of the two subset means (the group-level comparison, which requires
pairing because both estimates come from the same persons).