# Make a list object containing information required for analysis of choice data. The list object `dataList` contains 22 objects that supply all of the information required to analyze the data. Initial values of the score indices in object `theta` and the bin boundaries and centres in object `thetaQnt`. The returned named list object contains 22 named members, which are described in the value section below. ```r make_dataList(chcemat, scoreList, noption, sumscr_rng=NULL, titlestr=NULL, itemlabvec=NULL, optlabList=NULL, nbin=nbinDefault(N), NumBasis=7, jitterwrd=TRUE, PcntMarkers=c( 5, 25, 50, 75, 95), verbose=FALSE) ``` ## Arguments - `chcemat`: An N by n matrix. Column `i` must contain the integers from 1 to `M_i`, where `M_i` is the number of options for item `i`. If missing or illegitimate responses exist for item `i`, the column must also contain an integer greater than `M_i` that is used to identify such responoses. Alternatively, the column use `NA` for this purpose. Because missing and illegible responses are normally rare, they are given a different and simpler estimation procedure for their surprisal values. - `scoreList`: Either a list of length n, each containing a vector of length `M_i` that assigns numeric weights to the options for that item. In the special case of multiple choice items where the correct option has weight 1 and all others weight 0, a single integer can identify the correct answer. If all the items are of the multiple type, scoreList may be a numeric vector of length n containing the right answer indices. List object scoreList is mandatory because these weights define the person scores for the surprisal curve estimation process. - `noption`: A numeric vector of length `n`containing the number of choices for each item. These should not count missing or illegal choices. Although this object might seem redundant, it is needed for checking the consistencies among other objects and as an aid for detecting missing and illegal choices. - `sumscr_rng`: A numeric vector of length two containing the initial and final values for the interval over which test scores are to be plotted. Default is minimum and maximum sum score. - `titlestr`: A title string for the data and their analyses. Default is NULL. - `itemlabvec`: A character value containing labels for the items. Default is NULL and item position numbers are used. - `optlabList`: A list vector of length `n`, each element `i` of which is a character vector of length `M_i`. Default is NULL, and option numbers are used. - `nbin`: The number of bins for containing proportions of examinees choosing options. The default is computed by a function that uses the number of examinees. - `NumBasis`: The number of spline basis functions used to represent surprisal curves. The default is computed by a function that uses the number of examinees. - `jitterwrd`: A boolian constant: TRUE implies adding a small random value to each sum score value prior to computing percent rank values. - `PcntMarkers`: Used in plots of curves to display marker or reference percentage points for abscissa values in plots. - `verbose`: If TRUE details of calculations are displayed. ## Details The score range defined `scrrng` should contain all of the sum score values, but can go beyond their boundaries if desired. For example, it may be that no examinee gets a zero sum score, but for reporting and display purposes using zero as the lower limit seems desirable. The number of bins is chosen so that a minimum of at least about 25 initial percentage ranks fall within a bin. For larger samples, the number per bin is also larger, making the proportions of choice more accurate. The number bins can be set by the user, or by a simple algorithm used to adjust the number of bins to the number `N` or examinees. The number of spline basis functions used to represent a surprisal curve should be small for small sample sizes, but can be larger when larger samples are involved. There must be at least two basis functions, corresponding to two straight lines. The norder of this simple spline would not exceed 1, corresponding to taking only a single derivative of the resulting spline. But this rule is bent here to allow higher higher derivatives, which will autmatically have values of zero, in order to allow these simple linear basis functions to be used. This permits direct comparisons of TestGardener models with the many classic item response models that use two or less parameters per item response curve. Adding a small value to discrete values before computing ranks is considered a useful way of avoiding any biasses that might arise from the way the data are stored. The small values used leave the rounded jittered values fixed, but break up ties for sum scores. It can be helpful to see in a plot where special marker percentages 5, 25, 50, 75 and 95 percent of the interval [0,100] are located. The median abscissa value is at 50 per cent for initial percent rank values, for example, but may not be located at the center of the interval after iterations of the analysis cycle. ## Returns A named list with named members as follows: - **chcemat:**: A matrix of response data with N rows and n columns where N is number of examinees or respondents and n is number of items. Entries in the matrices are the indices of the options chosen. Column i of chcemat is expected to contain only the integers `1,...,noption`. - **optList:**: A list vector containing the numerical score values assigned to the options for this question. - **key:**: If the data are from a test of the multiple choices type where the right answer is scored 1 and the wrong answers 0, this is a numeric vector of length n containing the indices the right answers. Otherwise, it is NULL. - **Sfd:**: A fd object for the defining the surprisal curves. - **noption:**: A numeric vector of length n containing the numbers of options for each item. - **nbin:**: The number of bins for binning the data. - **scrrng:**: A vector of length 2 containing the limits of observed sum scores. - **scrfine:**: A fine mesh of test score values for plotting. - **scrvec:**: A vector of length N containing the examinee or respondent sum scores. - **itemvec:**: A vector of length n containing the question or item sum scores. - **percntrnk:**: A vector length N containing the sum score percentile ranks. - **thetaQnt:**: A numeric vector of length 2*nbin + 1 containing the bin boundaries alternating with the bin centers. These are initially defined as `seq(0,100,len=2*nbin+1)`. - **Sdim:**: The total dimension of the surprisal scores. - **PcntMarkers:**: The marker percentages for plotting: 5, 25, 50, 75 and 95. - **grbg:**: A logical vector of length number of questions. TRUE for an item indicates that a garbage option must be added to the score values, and FALSE indicates that there are no illegal or missing responses and the number of options is equal to number of score values. ## References Ramsay, J. O., Li J. and Wiberg, M. (2020) Full information optimal scoring. Journal of Educational and Behavioral Statistics, 45, 297-315. Ramsay, J. O., Li J. and Wiberg, M. (2020) Better rating scale scores with information-based psychometrics. Psych, 2, 347-360. ## Author(s) Juan Li and James Ramsay ## See Also `TG_analysis, Analyze, index_distn, index2info, index_fun, Sbinsmth` ## Examples ```r # Example 1: Input choice data and key for the short version of the # SweSAT quantitative multiple choice test with 24 items and 1000 examinees # input the choice data as 1000 strings of length 24 # set up index and key data chcemat <- Quant_13B_problem_chcemat key <- Quant_13B_problem_key # number of examinees and of items N <- nrow(chcemat) n <- ncol(chcemat) # number of options per item and option weights noption <- rep(0,n) for (i in 1:n) noption[i] <- 4 scoreList <- list() # option scores for (item in 1:n){ scorei <- rep(0,noption[item]) scorei[Quant_13B_problem_key[item]] <- 1 scoreList[[item]] <- scorei } # Use the input information to define the # big three list object containing info about the input data dataList <- make_dataList(chcemat, scoreList, noption) ```

make_dataList function