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 -