The l-parameter could be specified to this theoretically # with four response-options, resulting in a 25% chance of guessing the # value of 0.25 (e.g., the test is composed of multiple-choice questions # Suppose you have good theoretical reasons to fix the l parameter at a # with the same mean and variance as the estimated true-score distribution. # alpha and beta parameters necessary to produce a Beta distribution # model, specifying the l and u parameters and estimating the # dealing with such an occurrence is to revert to a two-parameter # This example produced an l-value estimate less than 0. # is a four-parameter Beta distribution with location parameters l = 0.25, # where all items are equally difficult, and the true-score distribution Say 1000 individuals take a 100-item test How Accurate Are the STAR Scores for Individual Students? – An Interpretive Guide. A strong true-score theory, with applications.
American College Testing Research Report Series. Method of Moments Estimates for the Four-Parameter Beta Compound Binomial Model and the Calculation of Classification Consistency Indexes. "l" is the lower location-parameter, "u" the upper location-parameter, "alpha" the first shape-parameter, and "beta" the second shape-parameter. Option to specify true-score distribution moments as output if the value of the output argument does not equal "parameters".Ī list with the parameter values of a four-parameter Beta distribution. Default is NA (i.e., estimate the parameter). If failsafe = TRUE or true.model = "2P": The beta shape-parameter of the Beta distribution. If failsafe = TRUE or true.model = "2P": The alpha shape-parameter of the Beta distribution. Default is 1 (i.e., the upper-bound of the Standard, two-parameter Beta distribution). If failsafe = TRUE or true.model = "2P": The upper-bound of the Beta distribution. Default is 0 (i.e., the lower-bound of the Standard, two-parameter Beta distribution).
If failsafe = TRUE or true.model = "2P": The lower-bound of the Beta distribution. Whether to revert to a fail-safe two-parameter solution should the four-parameter solution contain invalid parameter estimates. Options are "4P" and "2P", where "4P" refers to the four-parameter (with the same mean, variance, skewness, and kurtosis), and "2P" the two-parameter solution where both location-parameters are specified (with the same mean and variance). The type of Beta distribution which is to be fit to the moments of the true-score distribution. If specified, overrides the input of the etl argument. Optional specification of the test-score reliability coefficient. Not necessary to specify if reliability is supplied to the reliability argument. The value of Livingston and Lewis' effective test length. The maximum possible score to attain on the test. The minimum possible score to attain on the test. Returns a list with entries representing the lower- and upper shape parameters (l and u), and the shape parameters (alpha and beta) of the four-parameters beta distribution. DescriptionĮstimator for the Beta true-score distribution shape-parameters from the observed-score distribution and Livingston and Lewis' effective test length. Estimate Beta true-score distribution based on observed-score raw-moments and the effective test length.