Thursday, February 07, 2013

Journal Alert: Web of Knowledge Alert - PSYCHOMETRIKA

For my quantoid readers
In memoriam, J. Douglas Carroll 1939-2011

Heiser, WJ

*PSYCHOMETRIKA*, 78 (1):5-13; JAN 2013


*Pages: 14-36 (Article)
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A Multicomponent Latent Trait Model for Diagnosis

Embretson, SE; Yang, XD

*PSYCHOMETRIKA*, 78 (1):14-36; JAN 2013

This paper presents a noncompensatory latent trait model, the
multicomponent latent trait model for diagnosis (MLTM-D), for cognitive
diagnosis. In MLTM-D, a hierarchical relationship between components and
attributes is specified to be applicable to permit diagnosis at two
levels. MLTM-D is a generalization of the multicomponent latent trait
model (MLTM; Whitely in Psychometrika, 45:479-494, 1980; Embretson in
Psychometrika, 49:175-186, 1984) to be applicable to measures of broad
traits, such as achievement tests, in which component structure varies
between items. Conditions for model identification are described and
marginal maximum likelihood estimators are presented, along with
simulation data to demonstrate parameter recovery. To illustrate how
MLTM-D can be used for diagnosis, an application to a large-scale test
of mathematics achievement is presented. An advantage of MLTM-D for
diagnosis is that it may be more applicable to large-scale assessments
with more heterogeneous items than are latent class models.


*Pages: 37-58 (Article)
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A Procedure for Dimensionality Analyses of Response Data from Various Test Designs

Zhang, JM

*PSYCHOMETRIKA*, 78 (1):37-58; JAN 2013

In some popular test designs (including computerized adaptive testing
and multistage testing), many item pairs are not administered to any
test takers, which may result in some complications during
dimensionality analyses. In this paper, a modified DETECT index is
proposed in order to perform dimensionality analyses for response data
from such designs. It is proven in this paper that under certain
conditions, the modified DETECT can successfully find the
dimensionality-based partition of items. Furthermore, the modified
DETECT index is decomposed into two parts, which can serve as indices of
the reliability of results from the DETECT procedure when response data
are judged to be multidimensional. A simulation study shows that the
modified DETECT can successfully recover the dimensional structure of
response data under reasonable specifications. Finally, the modified
DETECT procedure is applied to real response data from two-stage tests
to demonstrate how to utilize these indices and interpret their values
in dimensionality analyses.


*Pages: 59-82 (Article)
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Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods

Merkle, EC; Zeileis, A

*PSYCHOMETRIKA*, 78 (1):59-82; JAN 2013

The issue of measurement invariance commonly arises in factor-analytic
contexts, with methods for assessment including likelihood ratio tests,
Lagrange multiplier tests, and Wald tests. These tests all require
advance definition of the number of groups, group membership, and
offending model parameters. In this paper, we study tests of measurement
invariance based on stochastic processes of casewise derivatives of the
likelihood function. These tests can be viewed as generalizations of the
Lagrange multiplier test, and they are especially useful for: (i)
identifying subgroups of individuals that violate measurement invariance
along a continuous auxiliary variable without prespecified thresholds,
and (ii) identifying specific parameters impacted by measurement
invariance violations. The tests are presented and illustrated in
detail, including an application to a study of stereotype threat and
simulations examining the tests' abilities in controlled conditions.


*Pages: 83-97 (Article)
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Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

Tijmstra, J; Hessen, DJ; van der Heijden, PGM; Sijtsma, K

*PSYCHOMETRIKA*, 78 (1):83-97; JAN 2013

Most dichotomous item response models share the assumption of latent
monotonicity, which states that the probability of a positive response
to an item is a nondecreasing function of a latent variable intended to
be measured. Latent monotonicity cannot be evaluated directly, but it
implies manifest monotonicity across a variety of observed scores, such
as the restscore, a single item score, and in some cases the total
score. In this study, we show that manifest monotonicity can be tested
by means of the order-constrained statistical inference framework. We
propose a procedure that uses this framework to determine whether
manifest monotonicity should be rejected for specific items. This
approach provides a likelihood ratio test for which the p-value can be
approximated through simulation. A simulation study is presented that
evaluates the Type I error rate and power of the test, and the procedure
is applied to empirical data.


*Pages: 98-115 (Article)
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Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models

Doebler, A; Doebler, P; Holling, H

*PSYCHOMETRIKA*, 78 (1):98-115; JAN 2013

The common way to calculate confidence intervals for item response
theory models is to assume that the standardized maximum likelihood
estimator for the person parameter theta is normally distributed.
However, this approximation is often inadequate for short and medium
test lengths. As a result, the coverage probabilities fall below the
given level of significance in many cases; and, therefore, the
corresponding intervals are no longer confidence intervals in terms of
the actual definition. In the present work, confidence intervals are
defined more precisely by utilizing the relationship between confidence
intervals and hypothesis testing. Two approaches to confidence interval
construction are explored that are optimal with respect to criteria of
smallness and consistency with the standard approach.


*Pages: 116-133 (Article)
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How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis

Maydeu-Olivares, A; Montano, R

*PSYCHOMETRIKA*, 78 (1):116-133; JAN 2013

We investigate the performance of three statistics, R (1), R (2) (Glas
in Psychometrika 53:525-546, 1988), and M (2) (Maydeu-Olivares & Joe in
J. Am. Stat. Assoc. 100:1009-1020, 2005, Psychometrika 71:713-732, 2006)
to assess the overall fit of a one-parameter logistic model (1PL)
estimated by (marginal) maximum likelihood (ML). R (1) and R (2) were
specifically designed to target specific assumptions of Rasch models,
whereas M (2) is a general purpose test statistic. We report asymptotic
power rates under some interesting violations of model assumptions
(different item discrimination, presence of guessing, and
multidimensionality) as well as empirical rejection rates for correctly
specified models and some misspecified models. All three statistics were
found to be more powerful than Pearson's X (2) against two- and
three-parameter logistic alternatives (2PL and 3PL), and against
multidimensional 1PL models. The results suggest that there is no clear
advantage in using goodness-of-fit statistics specifically designed for
Rasch-type models to test these models when marginal ML estimation is


*Pages: 134-153 (Article)
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Global Convergence of the EM Algorithm for Unconstrained Latent Variable Models with Categorical Indicators

Weissman, A

*PSYCHOMETRIKA*, 78 (1):134-153; JAN 2013

Convergence of the expectation-maximization (EM) algorithm to a global
optimum of the marginal log likelihood function for unconstrained latent
variable models with categorical indicators is presented. The sufficient
conditions under which global convergence of the EM algorithm is
attainable are provided in an information-theoretic context by
interpreting the EM algorithm as alternating minimization of the
Kullback-Leibler divergence between two convex sets. It is shown that
these conditions are satisfied by an unconstrained latent class model,
yielding an optimal bound against which more highly constrained models
may be compared.


*Pages: 154-184 (Article)
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Methods for Mediation Analysis with Missing Data

Zhang, ZY; Wang, LJ

*PSYCHOMETRIKA*, 78 (1):154-184; JAN 2013

Despite wide applications of both mediation models and missing data
techniques, formal discussion of mediation analysis with missing data is
still rare. We introduce and compare four approaches to dealing with
missing data in mediation analysis including listwise deletion, pairwise
deletion, multiple imputation (MI), and a two-stage maximum likelihood
(TS-ML) method. An R package bmem is developed to implement the four
methods for mediation analysis with missing data in the structural
equation modeling framework, and two real examples are used to
illustrate the application of the four methods. The four methods are
evaluated and compared under MCAR, MAR, and MNAR missing data mechanisms
through simulation studies. Both MI and TS-ML perform well for MCAR and
MAR data regardless of the inclusion of auxiliary variables and for
AV-MNAR data with auxiliary variables. Although listwise deletion and
pairwise deletion have low power and large parameter estimation bias in
many studied conditions, they may provide useful information for
exploring missing mechanisms.


*Pages: 185-187 (Book Review)
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Statistical Models for Test Equating, Scaling, and Linking

Wiberg, M

*PSYCHOMETRIKA*, 78 (1):185-187; JAN 2013


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