Mh. Lin et Ca. Hsiung, EMPIRICAL BAYES ESTIMATES OF DOMAIN SCORES UNDER BINOMIAL AND HYPERGEOMETRIC DISTRIBUTIONS FOR TEST-SCORES, Psychometrika, 59(3), 1994, pp. 331-359
Citations number
23
Categorie Soggetti
Social Sciences, Mathematical Methods","Psychologym Experimental","Mathematical, Methods, Social Sciences
We introduce two simple empirical approximate Bayes estimators (EABEs)
-d(N)(x) and delta(N)(x)-for estimating domain scores under binomial a
nd hypergeometric distributions, respectively. Both EABEs (derived fro
m corresponding marginal distributions of observed test score x withou
t relying on knowledge of prior domain score distributions) have been
proven to hold DELTA-asymptotic optimality in Robbins' sense of conver
gence in mean. We found that, where d(N) and delta(N)* are the monoto
nized versions of d(N) and delta(N) under Van Houwelingen's monotoniza
tion method, respectively, the convergence rate of the overall expecte
d loss of Bayes risk in either d(N) or delta(N)* depends on test leng
th, sample size, and ratio of test length to size of domain items. In
terms of conditional Bayes risk, d(N) and delta(N)* outperform their
maximum likelihood counterparts over the middle range of domain scales
. In terms of mean-squared error, we also found that: (a) given a unim
odal prior distribution of domain scores, delta(N) performs better th
an both d(N) and a linear EBE of the beta-binomial model when domain
item size is small or when test items reflect a high degree of heterog
eneity; (b) d(N) performs as well as delta(N)* when prior distributio
n is bimodal and test items are homogeneous; and (c) the linear EBE is
extremely robust when a large pool of homogeneous items plus a unimod
al prior distribution exists.