# Select Next Item Selects the next item in the question set to be administered to respondent based on the specified selection method. ```r selectItem(catObj) ``` ## Arguments - `catObj`: An object of class `Cat` ## Returns The function `selectItem` returns a list with three elements: `estimates`: a data frame with a row for each unasked question and three columns representing the item index number, the item name, and the item value (calculated by the specified selection method), and `next_item`: a numeric representing the index of the item that should be asked next. `next_item_name`: a string representing the unique identifier of the item that should be asked next. ## Details Selection approach is specified in the `selection` slot of the `Cat` object. The minimum expected posterior variance criterion is used when the `selection` slot is `"EPV"`. This method calls `expectedPV` for each unasked item. The maximum Fisher's information criterion is used when the `selection` slot is `"MFI"`. This method calls `fisherInf` for each unasked item. The maximum likelihood weighted information criterion is used when the `selection` slot is `"MLWI"`. Note that when no questions have been answered, likelihood evaluates to 1. This method involves integration. See Note for more information. The maximum posterior weighted information criterion is used when the `selection` slot is `"MPWI"`. Note that when no questions have been answered, likelihood evaluates to 1. This method involves integration. See Note for more information. The maximum expected information criterion is used when the `selection` slot is `"MEI"`. This method calls `expectedObsInf` for each unasked item. **Not implemented for three parameter model for binary data.** The maximum Kullback-Leibler information criterion is used when the `selection` slot is `"KL"`. This method calls `expectedKL` for each unasked item. See `expectedKL` for more information. The maximum likelihood weighted Kullback-Leibler information criterion is used when the `selection` slot is `"LKL"`. This method calls `likelihoodKL` for each unasked item. The maximum posterior weighted Kullback-Leibler information criterion is used when the `selection` slot is `"PKL"`. This method calls `posteriorKL` for each unasked item. The maximum Fisher interval information criterion is used when the `selection` slot is `"MFII"`. This method involves integration. See Note for more information. The bounds of integration are $\hat{\theta} \pm \delta$, where $\delta$ is qnorm($z$) times the square root of the Fisher test information and $z$ is specified in the `z` slot of the `Cat` object. A random number generator is used when the `selection` slot is `"RANDOM"`. ## Note This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled `C++` code. This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the `lowerBound` and `upperBound` slots of the `Cat` object unless otherwise noted. The `"RANDOM"` item selection criterion uses the package `RcppArmadillo` to randomly choose the next item among unasked questions. `RcppArmadillo` provides an exact reproduction of R's `sample` function that can be called from C++. In the rare instance that item parameters are identical, it may be that that `selectItem` must choose between two items with the same value calculated by the selection criterion. In such an instance, `selectItem` will choose the item with the lower question index. ## Examples ```r ## Loading ltm Cat object data(ltm_cat) ## Store example answers setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35)) ## Set different selection criterion and choose next item setSelection(ltm_cat) <- "EPV" selectItem(ltm_cat) setSelection(ltm_cat) <- "MFI" selectItem(ltm_cat) setSelection(ltm_cat) <- "MLWI" selectItem(ltm_cat) setSelection(ltm_cat) <- "MPWI" selectItem(ltm_cat) setSelection(ltm_cat) <- "MEI" selectItem(ltm_cat) setSelection(ltm_cat) <- "KL" selectItem(ltm_cat) setSelection(ltm_cat) <- "LKL" selectItem(ltm_cat) setSelection(ltm_cat) <- "PKL" selectItem(ltm_cat) setSelection(ltm_cat) <- "MFII" selectItem(ltm_cat) setSelection(ltm_cat) <- "RANDOM" selectItem(ltm_cat) ``` ## References van der Linden, Wim J. 1998. "Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216. Van der Linden, Wim J., and Peter J. Pashley. 2009. "Item Selection and Ability Estimation in Adaptive Testing." Elements of Adaptive Testing. Springer New York, 3-30. Veldkamp, B.P., 2003. Item Selection in Polytomous CAT. In New Developments in Psychometrics (pp. 207-214). Springer Japan. ## See Also `estimateTheta`, `expectedPV`, `fisherInf` ## Author(s) Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

selectItem function