TY - JOUR

T1 - A note on monotone likelihood ratio of the total score variable in unidimensional item response theory

AU - Ünlü, Ali

PY - 2008/5

Y1 - 2008/5

N2 - This note provides a direct, elementary proof of the fundamental result on monotone likelihood ratio of the total score variable in unidimensional item response theory (IRT). This result is very important for practical measurement in IRT, because it justifies the use of the total score variable to order participants on the latent trait. The proof relies on a basic inequality for elementary symmetric functions which is proved by means of few purely algebraic, straightforward transformations. In particular, flaws in a proof of this result by Huynh [(1994). A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59, 77-79] are pointed out and corrected, and a natural generalization of the fundamental result to non-linear (quasi-ordered) latent trait spaces is presented. This may be useful for multidimensional IRT or knowledge space theory, in which the latent 'ability' spaces are partially ordered with respect to, for instance, coordinate-wise vector-ordering or set-inclusion, respectively.

AB - This note provides a direct, elementary proof of the fundamental result on monotone likelihood ratio of the total score variable in unidimensional item response theory (IRT). This result is very important for practical measurement in IRT, because it justifies the use of the total score variable to order participants on the latent trait. The proof relies on a basic inequality for elementary symmetric functions which is proved by means of few purely algebraic, straightforward transformations. In particular, flaws in a proof of this result by Huynh [(1994). A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59, 77-79] are pointed out and corrected, and a natural generalization of the fundamental result to non-linear (quasi-ordered) latent trait spaces is presented. This may be useful for multidimensional IRT or knowledge space theory, in which the latent 'ability' spaces are partially ordered with respect to, for instance, coordinate-wise vector-ordering or set-inclusion, respectively.

UR - http://www.scopus.com/inward/record.url?scp=44349178625&partnerID=8YFLogxK

U2 - 10.1348/000711007X173391

DO - 10.1348/000711007X173391

M3 - Article

C2 - 17535477

AN - SCOPUS:44349178625

SN - 0007-1102

VL - 61

SP - 179

EP - 187

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

IS - 1

ER -