ItemAnalysis: Compute traditional item analysis indices
In netique/ShinyItemAnalysis: Test and Item Analysis via Shiny

Description Usage Arguments Details Value Author(s) References See Also Examples

ItemAnalysis function computes various traditional item analysis indices including difficulty, discrimination and item validity. For ordinal items the difficulty and discrimination indices take into account minimal item score as well as range.

ItemAnalysis(
  Data,
  criterion = "none",
  k = 3,
  l = 1,
  u = 3,
  maxscore = NULL,
  minscore = NULL,
  cutscore = NULL,
  bin = FALSE,
  data,
  y,
  add.bin
)

`Data`	matrix or data.frame of items to be examined. Rows represent respondents, columns represent items.
`criterion`	vector of criterion values.
`k`	numeric: number of groups to which may be data.frame x 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 or vector: maximal score in ordinal items. If missing, vector of obtained maximal scores is imputed. See Details.
`minscore`	numeric or vector: minimal score in ordinal items. If missing, vector of obtained minimal scores is imputed. See Details.
`cutscore`	numeric or vector: cut-score used for binarization of ordinal data. If missing, vector of maximal scores is imputed. See Details.
`bin`	logical: If TRUE, indices are printed also for binarized data. See Details.
`data`	deprecated. Use argument `Data` instead.
`y`	deprecated. Use argument `criterion` instead.
`add.bin`	deprecated. Use argument `bin` instead.

For ordinal items the difficulty and discrimination indices take into account minimal item score as well as range.

For calculation of discrimination ULI index, it is possible to specify the number of groups k, and which two groups l and u are to be compared.

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

If bin is set to TRUE, item analysis of binarized data is included in the output table. In such a case, cutscore is used for binarization. When binarizing the Data, values greater or equal to cut-score are set to 1, other values are set to 0.

ItemAnalysis function computes various traditional item analysis indices. Output is a data.frame with following columns:

`Difficulty`	average score of the item divided by its range.
`Mean`	average item score.
`SD`	standard deviation of the item score.
`SD.bin`	standard deviation of the item score for binarized data.
`Prop.max.score`	proportion of maximal scores.
`Min.score`	minimal score specified in `minscore`; if not provided, observed minimal score.
`Max.score`	maximal score specified in `maxscore`; if not provided, observed maximal score.
`obs.min`	observed minimal score.
`obs.max`	observed maximal score.
`Cut.Score`	cut-score specified in `cutscore`.
`gULI`	generalized ULI.
`gULI.bin`	generalized ULI for binarized data.
`ULI`	discrimination with ULI using the usual parameters (3 groups, comparing 1st and 3rd).
`ULI.bin`	discrimination with ULI using the usual parameters for binarized data (3 groups, comparing 1st and 3rd).
`RIT`	item-total correlation (correlation between item score and overall test score).
`RIT.bin`	item-total correlation for binarized data.
`RIR`	item-rest correlation (correlation between item score and overall test score without the given item).
`RIR.bin`	item-rest correlation for binarized data.
`Corr.criterion`	correlation between item score and criterion `criterion`.
`Corr.criterion.bin`	correlation between item score and criterion `criterion` for binarized data.
`Index.val`	item validity index calculated as `cor(item, criterion) * sqrt(((N - 1) / N) * var(item))`, see Allen and Yen (1979, Ch.6.4).
`Index.val.bin`	item validity index for binarized data.
`Index.rel`	item reliability index calculated as `cor(item, test) * sqrt(((N - 1) / N) * var(item))`, see Allen and Yen (1979, Ch.6.4).
`Index.rel.bin`	item reliability index for binarized data.
`Index.rel.drop`	item reliability index 'drop' (scored without item).
`Index.rel.drop.bin`	item reliability index 'drop' (scored without item) for binarized data.
`Alpha.drop`	Cronbach's alpha without given item. In case of two-item dataset, `NA`s are returned.
`Alpha.drop.bin`	Cronbach's alpha without given item, for binarized data. In case of two-item dataset, `NA`s are returned.
`Perc.miss`	Percentage of missed responses on the particular item.
`Perc.nr`	Percentage of respondents that did not reached the item nor the subsequent ones, see `recode_nr` function for further details.

With bin = TRUE, indices based on binarized dataset are also provided and marked with bin suffix.

Patricia Martinkova
Institute of Computer Science of the Czech Academy of Sciences
martinkova@cs.cas.cz

Jan Netik
Institute of Computer Science of the Czech Academy of Sciences
Charles University
netik@cs.cas.cz

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

Adela Hladka
Institute of Computer Science of the Czech Academy of Sciences
hladka@cs.cas.cz

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

Allen, M. J. & Yen, W. M. (1979). Introduction to measurement theory. Monterey, CA: Brooks/Cole.

DDplot, gDiscrim, recode_nr

## Not run: 
# loading 100-item medical admission test datasets
data(dataMedical, dataMedicalgraded)
# binary dataset
dataBin <- dataMedical[, 1:100]
# ordinal dataset
dataOrd <- dataMedicalgraded[, 1:100]
# study success is the same for both data sets
StudySuccess <- dataMedical[, 102]

# item analysis for binary data
head(ItemAnalysis(dataBin))
# item analysis for binary data using also study success
head(ItemAnalysis(dataBin, criterion = StudySuccess))

# item analysis for binary data
head(ItemAnalysis(dataOrd))
# item analysis for binary data using also study success
head(ItemAnalysis(dataOrd, criterion = StudySuccess))
# including also item analysis for binarized data
head(ItemAnalysis(dataOrd,
  criterion = StudySuccess, k = 5, l = 4, u = 5,
  maxscore = 4, minscore = 0, cutscore = 4, bin = TRUE
))

## End(Not run)