gDiscrim {ShinyItemAnalysis}

Compute generalized item discrimination

Description

Generalized version of discrimination index ULI. The function enumerates the ability of an item to distinguish between individuals from upper (U) vs. lower (L) ability groups, i.e. between respondents with high vs. low overall score on the test. Number of groups, as well as upper and lower groups can be specified by user. You can also manually supply the maximal and minimal scores when the theoretical range of item score is known. Note that if the observed item range is zero NaN is returned.

Usage

gDiscrim(Data, k = 3, l = 1, u = 3, maxscore, minscore, x, ...)

Arguments

Data

matrix or data.frame of items to be examined. Rows represent respondents, columns represent items.

k

numeric: number of groups to which may be Data divided by the total score. Default value is 3. See Details.

l

numeric: lower group. Default value is 1. See Details.

u

numeric: upper group. Default value is 3. See Details.

maxscore

numeric: maximal score in ordinal items. If missing, vector of obtained maximal scores is imputed. See Details.

minscore

numeric: minimal score in ordinal items. If missing, vector of obtained minimal scores is imputed. See Details.

x

deprecated. Use argument Data instead.

...

Arguments passed on to base::findInterval

rightmost.closed

logical; if true, the rightmost interval, vec[N-1] .. vec[N] is treated as closed, see below.

all.inside

logical; if true, the returned indices are coerced into 1,...,N-1, i.e., 0 is mapped to 1 and N to N-1.

left.open

logical; if true all the intervals are open at left and closed at right; in the formulas below, \le should be swapped with < (and > with \ge), and rightmost.closed means ‘leftmost is closed’. This may be useful, e.g., in survival analysis computations.

Details

The function computes total test scores for all respondents and then divides the respondents into k groups. The lower and upper groups are determined by l and u parameters, i.e., l-th and u-th group where the ordering is defined by increasing total score.

In ordinal items, difficulty is calculated as difference of average score divided by range (maximal possible score maxscore minus minimal possible score minscore for given item).

Discrimination is calculated as difference in difficulty between upper and lower group.

Note

gDiscrim is used by DDplot() function.

Author(s)

Adela Hladka
Institute of Computer Science of the Czech Academy of Sciences
[e-mail]

Lubomir Stepanek
Institute of Computer Science of the Czech Academy of Sciences

Jana Vorlickova
Institute of Computer Science of the Czech Academy of Sciences

Patricia Martinkova
Institute of Computer Science of the Czech Academy of Sciences
[e-mail]

Jan Netik
Institute of Computer Science of the Czech Academy of Sciences
[e-mail]

References

Martinkova, P., Stepanek, L., Drabinova, A., Houdek, J., Vejrazka, M., & Stuka, C. (2017). Semi-real-time analyses of item characteristics for medical school admission tests. In: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems. https://doi.org/10.15439/2017F380

See Also

DDplot()

Examples

# binary dataset
dataBin <- dataMedical[, 1:100]
# ordinal dataset
dataOrd <- dataMedicalgraded[, 1:100]

# ULI for the first 5 items of binary dataset
# compare to psychometric::discrim(dataBin)
gDiscrim(dataBin)[1:5]
# generalized ULI using 5 groups, compare 4th and 5th for binary dataset
gDiscrim(dataBin, k = 5, l = 4, u = 5)[1:5]

# ULI for first 5 items for ordinal dataset
gDiscrim(dataOrd)[1:5]
# generalized ULI using 5 groups, compare 4th and 5th for binary dataset
gDiscrim(dataOrd, k = 5, l = 4, u = 5)[1:5]
# maximum (4) and minimum (0) score are same for all items
gDiscrim(dataOrd, k = 5, l = 4, u = 5, maxscore = 4, minscore = 0)[1:5]