Fisher information over a grid of person locations, with the corresponding
standard error of measurement. Ordinary Rasch fits return one whole-test
curve; a fit with split items (split_items,
resolve_dif) returns one curve per test form, the unsplit
items with the copies a set of persons answered, since the copies of a
split item are answered by different persons and never inform one
measure together. EFRM fits return one curve per person group and per item
administration pattern actually observed within that group (in a linking
design, persons who took only the core set get a core-only curve, and the
linking subsample gets the pooled one). MFRM fits return one curve per
observed item-by-facet pattern for a person, so ratings that jointly
inform the same person measure are added and mutually exclusive designs
remain separate. Partly answered sets or facet conditions contribute only
their observed items; a missing response is not treated as an administered
item when defining these patterns. Where item nonresponse leaves nearly
every person a pattern of their own, that is what these fits return:
an unanswered item carries no information about the person who left it,
so no pattern is merged into a fuller one and no curve of theirs is
drawn over a design nobody was administered.
Arguments
- fit
A fitted object from
rasch.- grid
Logit grid over which to evaluate the information.
- items
Optional item selection: item names or indices. Every design block is restricted to the named items, so a restricted person-item map can carry the information of its own selection. The
designlabels are those of the restricted blocks, and blocks that differ only outside the selection are returned once.
Value
A data frame with theta, info, and sem. For
EFRM and MFRM fits it also contains a design column identifying
the administrable frame or facet design; for a fit with split items,
the test form, named by the copies it holds and by the split items it
holds no copy of.
Details
For an administrable block \(\mathcal A\), the information and standard
error of measurement are
$$I(\theta)=\sum_{i\in\mathcal A}d_i^2
\operatorname{Var}(X_i\mid\theta),\qquad
\operatorname{SEM}(\theta)=I(\theta)^{-1/2},$$
where \(d_i\) is the frame unit or discrimination multiplier. For an
ordinary Rasch fit, \(d_i=1\).
Information is returned only for a converged calibration. Comparative
Judgement designs use btl_information instead.
References
Andrich, D. and Marais, I. (2019). A Course in Rasch Measurement Theory: Measuring in the Educational, Social and Health Sciences. Springer.
See also
targeting_table and plot_tif.
Examples
set.seed(1)
d <- seq(-1.5, 1.5, length.out = 6)
X <- matrix(rbinom(300 * 6, 1, plogis(outer(rnorm(300), d, "-"))), 300, 6)
colnames(X) <- paste0("I", 1:6)
head(test_information(rasch(X)))
#> theta info sem
#> 1 -6.0 0.02364631 6.503068
#> 2 -5.9 0.02609577 6.190346
#> 3 -5.8 0.02879468 5.893101
#> 4 -5.7 0.03176749 5.610590
#> 5 -5.6 0.03504089 5.342105
#> 6 -5.5 0.03864388 5.086976