The currently implemented methods (following Ponocny's notation of \(T\)-statistics) and their options are:
- \(T_1\):
method = "T1"
Checks for local dependence via increased inter-item correlations.
For all item pairs, cases are counted with equal responses on both items.
- \(T_{1m}\):
method = "T1m"
Checks for multidimensionality via decreased inter-item correlations.
For all item pairs, cases are counted with equal responses on both items.
- \(T_{1l}\):
method = "T1l"
Checks for learning.
For all item pairs, cases are counted with response pattern (1,1).
- \(T_{md}\):
method = "Tmd", idx1, idx2
idx1 and idx2 are vectors of indices specifying items which define two subscales, e.g., idx1 = c(1, 5, 7) and idx2 = c(3, 4, 6)
Checks for multidimensionality based on correlations of person raw scores for the subscales.
- \(T_2\):
method = "T2", idx = NULL, stat = "var"
idx is a vector of indices specifying items which define a subscale, e.g., idx = c(1, 5, 7)
stat defines the used statistic as a character object which can be: "var" (variance), "mad1" (mean absolute deviation), "mad2" (median absolute deviation), or "range" (range)
Checks for local dependence within model deviating subscales via increased dispersion of subscale person rawscores.
- \(T_{2m}\):
method = "T2m", idx = NULL, stat = "var"
idx is a vector of indices specifying items which define a subscale, e.g., idx = c(1, 5, 7)
stat defines the used statistic as a character object which can be: "var" (variance), "mad1" (mean absolute deviation), "mad2" (median absolute deviation), "range" (range)
Checks for multidimensionality within model deviating subscales via decreased dispersion of subscale person rawscores.
- \(T_4\):
method = "T4", idx = NULL, group = NULL, alternative = "high"
idx is a vector of indices specifying items which define a subscale, e.g., idx = c(1, 5, 7)
group is a logical vector defining a subject group, e.g., group = ((age >= 20) & (age < 30))
alternative specifies the alternative hypothesis and can be: "high" or "low".
Checks for group anomalies (DIF) via too high (low) raw scores on item(s) for specified group.
% removed in version 0.14-5
% \item{\bold{T7:}}{\code{method = "T7", idx = NULL}}\cr
% \code{idx} \ldots vector of indices specifying items which define a subscale, e.g., \code{idx = c(1, 5, 7)}\cr
% Checks for lower discrimination (2PL) in item subscale via counting cases with response 1 on more
% difficult and 0 on easier items. The test is global for the subscale, i.e. all subscale items are evaluated
% using a single statistic.
%
% \item{\bold{T7a:}}{\code{method = "T7a", idx = NULL}}\cr
% \code{idx} \ldots vector of indices specifying items to investigate, e.g., \code{idx = c(1, 5, 7)}\cr
% Checks for lower discrimination (2PL) of an item compared to another item via counting cases with response 1 on more
% difficult and 0 on easier item. The test is performed pairwise, i.e. a statistic is calculated for each item pair.
% # Examples
% ##---- T7, T7a --------------------------------------------------
% # simultaenous test for all items in subscale
% t7<-NPtest(rmat,method="T7",idx=1:3)
% t7
%
% # test for item-pairs
% t7a<-NPtest(rmat,method="T7a",idx=c(1,3,5)) # test for item-pairs
% t7a
- \(T_{10}\):
method = "T10", splitcr = "median"
splitcr defines the split criterion for subject raw score splitting.
"median" uses the median as split criterion, "mean" performs a mean-split.
Optionally, splitcr can also be a vector which assigns each person to one of two subgroups (e.g., following an external criterion).
This vector can be numeric, character, logical, or a factor.
Global test for subgroup-invariance.
Checks for different item difficulties in two subgroups (for details see Ponocny, 2001).
- \(T_{11}\):
method = "T11"
Global test for local dependence.
The statistic calculates the sum of absolute deviations between the observed inter-item correlations and the expected correlations.
- \(T_{pbis}\):
method = "Tpbis", idxt, idxs
Test for discrimination.
The statistic calculates a point-biserial correlation for a test item (specified via idxt) with the person row scores for a subscale of the test sum (specified via idxs).
If the correlation is too low, the test item shows different discrimination compared to the items of the subscale.
- Martin-Löf
The ‘exact’ version of the Martin-Löf statistic is specified via method = "MLoef" and optionally splitcr (see MLoef).
% added in version 0.16-3
- \(Q_{3h}\):
method = "Q3h"
Checks for local dependence by detecting an increased correlation of inter-item residuals. Low p-values correspond to a high ("h") correlation between two items.
- \(Q_{3l}\):
method = "Q3l"
Checks for local dependence by detecting a decreased correlation of inter-item residuals. Low p-values correspond to a low ("l") correlation between two items.