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\f0\fs24 \cf0 Four different functions are provided.\
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1) method_of_successive_dichotomization.m implements the \'93Method of Successive Dichotomizations\'94 or MSD. The input is a matrix of non-negative numbers with all missing entries labeled as NaN. The output includes estimated person and item measures, estimated thresholds, the index of persons and items whose measures could be estimated, and standard errors. Person and item measures that could not be estimated are labeled NaN.\
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2) demo.m simulates ordered thresholds across N persons, M items and L thresholds (with L+1 rating categories) with a specified percent of missing data such that each threshold has a specified distribution across all trials (in our case a normal distribution). The function demo.m can be run without any input. Parameters can be changed within the script. The output includes simulated person measures, item measures, thresholds and a ratings matrix that can be used as input to method_of_successive_dichotomization.m.\
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For example, one can run:\
D = demo()\
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and then run:\
M = method_of_successive_dichotomization(D.ratings_matrix)\
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to get MSD estimated parameters on a simulated dataset.\
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3) probability_curves.m generates rating category probability curves for either the Andrich model or MSD given a dataset simulated using demo.m. \
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Example:\
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After running:\
D = demo()\
M = method_of_successive_dichotomization(D.ratings_matrix)\
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Then, define:\
true_P = D.person_measures;\
true_I = D.item_measures;\
rMatrix = D.ratings_matrix;\
model_P = M.person_measures;\
model_I = M.item_measures;\
model_T = M.average_thresholds;\
modelType = 'MSD'\
hEdges = -4:0.2:4;\
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Now we can call:\
P = probability_curves(true_P, true_I, rMatrix, model_P, model_I, model_T, modelType, hEdges)\
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Note that modelType can be modelType = 'Andrich', but Andrich model estimated parameters must be provided from another program such as Winsteps. Note the dimensions of model_P and model_I. model_P is a column vector while model_I is a row vector.
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4) misfit_statistics.m generates infit and outfit statistics for all persons and items.\
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Example:\
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After running:
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\f0 D = demo()\
M = method_of_successive_dichotomization(D.ratings_matrix)\
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Then, define:\
rMatrix = D.ratings_matrix;\
model_P = M.person_measures;\
model_I = M.item_measures;\
model_T = M.average_thresholds;\
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Then call:\
Q = misfit_statistics(rMatrix, model_P, model_I, model_T)}
