Fisher information over a grid of person locations, with the corresponding standard error of measurement. Ordinary Rasch fits return one whole-test curve. 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.
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