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"Theory and Methods"
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Item Complexity: A Neglected Psychometric Feature of Test Items?
Despite its frequent consideration in test development, item complexity receives little attention in the psychometric modeling of item response data. In this address, I consider how variability in item complexity can be expected to emerge in the form of item characteristic curve (ICC) asymmetry, and how such effects may significantly influence applications of item response theory, especially those that assume interval-level properties of the latent proficiency metric and groups that vary substantially in mean proficiency. One application is the score gain deceleration phenomenon often observed in vertical scaling contexts, especially in subject areas like math or second language acquisition. It is demonstrated how the application of symmetric IRT models in the presence of complexity-induced positive ICC asymmetry can be a likely cause. A second application concerns the positive correlation between DIF and difficulty commonly seen in verbal proficiency (and other subject area) tests where problem-solving complexity is minimal and proficiency-related guessing effects are likely pronounced. Here we suggest negative ICC asymmetry as a probable cause and apply sensitivity analyses to demonstrate the ease with which such correlations disappear when allowing for negative ICC asymmetry. Unfortunately, the presence of systematic forms of ICC asymmetry is easily missed due to the considerable flexibility afforded by latent trait metrics in IRT. Speculation is provided regarding other applications for which attending to ICC asymmetry may prove useful.
Journal Article
Identifiability of Latent Class Models with Covariates
Latent class models with covariates are widely used for psychological, social, and educational research. Yet the fundamental identifiability issue of these models has not been fully addressed. Among the previous research on the identifiability of latent class models with covariates, Huang and Bandeen-Roche (Psychometrika 69:5–32, 2004) studied the local identifiability conditions. However, motivated by recent advances in the identifiability of the restricted latent class models, particularly cognitive diagnosis models (CDMs), we show in this work that the conditions in Huang and Bandeen-Roche (Psychometrika 69:5–32, 2004) are only necessary but not sufficient to determine the local identifiability of the model parameters. To address the open identifiability issue for latent class models with covariates, this work establishes conditions to ensure the global identifiability of the model parameters in both strict and generic sense. Moreover, our results extend to the polytomous-response CDMs with covariates, which generalizes the existing identifiability results for CDMs.
Journal Article
Social Network Mediation Analysis: A Latent Space Approach
A social network comprises both actors and the social connections among them. Such connections reflect the dependence among social actors, which is essential for individuals’ mental health and social development. In this article, we propose a mediation model with a social network as a mediator to investigate the potential mediation role of a social network. In the model, the dependence among actors is accounted for by a few mutually orthogonal latent dimensions which form a social space. The individuals’ positions in such a latent social space are directly involved in the mediation process between an independent and dependent variable. After showing that all the latent dimensions are equivalent in terms of their relationship to the social network and the meaning of each dimension is arbitrary, we propose to measure the whole mediation effect of a network. Although individuals’ positions in the latent space are not unique, we rigorously articulate that the proposed network mediation effect is still well defined. We use a Bayesian estimation method to estimate the model and evaluate its performance through an extensive simulation study under representative conditions. The usefulness of the network mediation model is demonstrated through an application to a college friendship network.
Journal Article
Everything is predictable : how Bayes' remarkable theorem explains the world
Thomas Bayes was an eighteenth-century Presbyterian minister and amateur mathematician whose obscure life belied the profound impact of his work. Like most research into probability at the time, his theorem was mainly seen as relevant to games of chance, like dice and cards. But its implications soon became clear, affecting fields as diverse as medicine, law and artificial intelligence. Bayes' theorem helps explain why highly accurate screening tests can lead to false positives, causing unnecessary anxiety for patients. A failure to account for it in court has put innocent people in jail. But its influence goes far beyond practical applications. Fusing biography, razor-sharp science communication and intellectual history, 'Everything Is Predictable' is a captivating tour of Bayes' theorem and its impact on modern life.
BOOK
Robust Inference for Mediated Effects in Partially Linear Models
We consider mediated effects of an exposure,
X
on an outcome,
Y
, via a mediator,
M
, under no unmeasured confounding assumptions in the setting where models for the conditional expectation of the mediator and outcome are partially linear. We propose G-estimators for the direct and indirect effects and demonstrate consistent asymptotic normality for indirect effects when models for the conditional means of
M
, or
X
and
Y
are correctly specified, and for direct effects, when models for the conditional means of
Y
, or
X
and
M
are correct. This marks an improvement, in this particular setting, over previous ‘triple’ robust methods, which do not assume partially linear mean models. Testing of the no-mediation hypothesis is inherently problematic due to the composite nature of the test (either
X
has no effect on
M
or
M
no effect on
Y
), leading to low power when both effect sizes are small. We use generalized methods of moments (GMM) results to construct a new score testing framework, which includes as special cases the no-mediation and the no-direct-effect hypotheses. The proposed tests rely on an orthogonal estimation strategy for estimating nuisance parameters. Simulations show that the GMM-based tests perform better in terms of power and small sample performance compared with traditional tests in the partially linear setting, with drastic improvement under model misspecification. New methods are illustrated in a mediation analysis of data from the COPERS trial, a randomized trial investigating the effect of a non-pharmacological intervention of patients suffering from chronic pain. An accompanying R package implementing these methods can be found at github.com/ohines/plmed.
Journal Article
The magic circle : principles of gaming & simulation
\"The purpose of this unique book is to outline the core of game science by presenting principles underlying the design and use of games and simulations\"--Page 4 of cover.
Book
Psychometric network models from time-series and panel data
Researchers in the field of network psychometrics often focus on the estimation of Gaussian graphical models (GGMs)—an undirected network model of partial correlations—between observed variables of cross-sectional data or single-subject time-series data. This assumes that all variables are measured without measurement error, which may be implausible. In addition, cross-sectional data cannot distinguish between within-subject and between-subject effects. This paper provides a general framework that extends GGM modeling with latent variables, including relationships over time. These relationships can be estimated from time-series data or panel data featuring at least three waves of measurement. The model takes the form of a graphical vector-autoregression model between latent variables and is termed the
ts-lvgvar
when estimated from time-series data and the
panel-lvgvar
when estimated from panel data. These methods have been implemented in the software package
psychonetrics
, which is exemplified in two empirical examples, one using time-series data and one using panel data, and evaluated in two large-scale simulation studies. The paper concludes with a discussion on ergodicity and generalizability. Although within-subject effects may in principle be separated from between-subject effects, the interpretation of these results rests on the intensity and the time interval of measurement and on the plausibility of the assumption of stationarity.
Journal Article