lzstarMix
Sandip Sinharay · Applied Psychological Measurement · 2015
In a report for the Council of Chief State School Officers, Olson and Fremer (2013) recommended the use of person-fit assessment, in addition to other methods, to detect irregularities in answering behavior of the test takers.Mixed-format tests, which include both dichotomous and polytomous items, are becoming increasingly popular because of an increasing emphasis on performance tasks in the common-core assessments (e.g., Darling-Hammond & Adamson, 2010).However, there is a lack of research on person-fit assessment for mixed-format tests (Sinharay, 2015a; 2015b).One reason is that there exist few statistics and no publicly available software packages to assess person fit for mixed-format tests.lzstarMix is a function written in R (R Core Team, 2015) to compute the l z statistic for mixed-format tests (Drasgow, Levine, & Williams, 1985;Sinharay, 2015b).The function also computes the l à z statistic for mixed-format tests that was recently suggested by Sinharay (2015a).The null distribution of l à z is generally much closer than that of l z to the standard normal distribution for mixed-format tests.The function lzstarMix currently works when the dichotomous items are modeled using the three-parameter logistic (3PL) model, 1 and the polytomous items are modeled using the generalized partial credit model (GPCM; Muraki, 1992). 2 The input to the function consists of the item-parameter estimates, and the item scores and estimated abilities (maximum likelihood estimate or weighted likelihood estimates) of several examinees.The output are l z and l à z for the examinees.The function can be used for tests that include only dichotomous items, in which case l à z for mixed-format tests (Sinharay, 2015a) becomes identical to l à z for dichotomous items (Snijders, 2001), or only polytomous items.