A Rasch Hierarchical Measurement Model

Maier, Kimberly S.

doi:10.3102/10769986026003307

Cited by 57 publications

(41 citation statements)

References 23 publications

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“…interest, the efficient incorporation of prior information into empirical data analysis, model averaging, and model selection (Best, Spiegelhalter, Thomas, and Brayne, 1996;Maier, 2001;Rupp, Dey, and Zumbo, 2004;Western, 1999). Additionally, unlike the maximum likelihood estimation requiring large samples to approximate the sampling distribution of the MLE when making statistical inference, Bayesian inference can be considered a plausible way to deal with small sample size studies (Congdon, 2005;Lee and Wagenmakers, 2005;Zhang et al 2007).…”

Section: Objectives Of the Studymentioning

confidence: 99%

“…That is, unlike those of the frequentists, Bayesian methods provide a clear channel for us to incorporate prior information, which helps increase the statistical power of the analysis and contributes to the accumulation of scientific findings (Hsieh and Maier, 2009). Moreover, based on Bayes' law, whenever our prior is uniformly distributed in the region where the likelihood function is located, the posterior distribution for the Bayesian function is nearly proportional to the likelihood function (Gill, 2002;Maier, 2001;Rice, 1995).…”

Section: Specification Of Priorsmentioning

confidence: 99%

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The best of both worlds: a joint modeling approach for the assessment of change across repeated measurements

Hsieh

Eye

2010

Int. j. psychol. res.

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Lo mejor de ambos mundos: una propuesta de modelamiento combinado para la evaluación del cambio a lo largo de mediciones repetidas. Chueh-An Hsieh and Alexander von EyeMichigan State University, East Lansing, USA ABSTRACTThe usefulness of Bayesian methods in estimating complex statistical models is undeniable. From a Bayesian standpoint, this paper aims to demonstrate the capacity of Bayesian methods and propose a comprehensive model combining both a measurement model (e.g., an item response model, IRM) and a structural model (e.g., a latent variable model, LVM). That is, through the incorporation of the probit link and Bayesian estimation, the item response model can be introduced naturally into a latent variable model. The utility of this IRM-LVM comprehensive framework is investigated with a real data example and promising results are obtained, in which the data drawn from part of the British Social Attitudes Panel Survey 1983-1986 reveal the attitude toward abortion of a representative sample of adults aged 18 or older living in Great Britain. The application of IRMs to responses gathered from repeated assessments allows us to take the characteristics of both item responses and measurement error into consideration in the analysis of individual developmental trajectories, and helps resolve some difficult modeling issues commonly encountered in developmental research, such as small sample sizes, multiple discretely scaled items, many repeated assessments, and attrition over time Key words: Bayesian inference, item response model, latent growth curve analysis, simulation, generalized linear latent and mixed model RESUME La utilidad de los métodos Bayesianos en la estimación de modelos estadísticos complejos es innegable. Desde un punto de vista Bayesiano, el presente artículo busca demostrar la capacidad de los métodos Bayesianos y proponer un modelo exhaustivo que combina un modelo de medición y un modelo estructural. La utilidad de este método combinado se investiga usando datos reales tomados de una encuesta sobre actitudes sociales. El método combinado permite extraer las características de las respuestas a los ítems como de los errores en la medición para el análisis individual de trayectorias del desarrollo. Tales resultados permiten resolver asuntos que se presentan en investigación en psicología del desarrollo, e.g., tamaños de muestra pequeños, evaluaciones repetidas, etc.Palabras clave: Inferencia Bayesiana, modelo de respuesta al ítem, análisis de curva de crecimiento latente, simulación, modelo linear generalizado latente y mixto.

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Section: Objectives Of the Studymentioning

confidence: 99%

Section: Specification Of Priorsmentioning

confidence: 99%

The best of both worlds: a joint modeling approach for the assessment of change across repeated measurements

Hsieh

Eye

2010

Int. j. psychol. res.

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“…The latter approach results in multilevel IRT models (Fox & Glas, 2001;Kamata, 2001;Maier, 2001). Considering the standard case of a mixed logistic regression model with only a random intercept, and assuming normal distributions for the random effects on all levels, we obtain…”

Section: Multilevel Irt Modelsmentioning

confidence: 99%

A nonlinear mixed model framework for item response theory.

Rijmen¹,

Tuerlinckx²,

Boeck³

et al. 2003

Psychological Methods

196

180

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Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger.Mixed models (see, e.g., Diggle, Heagerty, Liang, & Zeger, 2002;Goldstein, 1995;Longford, 1993;Verbeke & Molenberghs, 2000) are a collection of statistical tools that are well suited for analyzing clustered data, such as, for example, data from students nested within schools or repeated measurement data (measurements nested within participants). Modeling clustered data under a model that assumes independent observations is inappropriate because the observations on the subunits (students, measurements) of the same unit (school, participant) tend to be more homogeneous than the observations on subunits of different units. The heterogeneity between units can be taken into account by assuming that (some of) the parameters of the model follow some random distribution over the population of units. Hence, (some of) the parameters of the model are random variables, and the model is a random effects model, or mixed model.The random effects represent the unit effects. The parameters that are not assumed to be random realizations from a distribution, and hence are not considered to be unit specific, are called fixed effects.Mixed models and related methods were first developed in the context of analysis of variance and regression analysis, leading to the linear mixed model. Other commonly used terms are multilevel models (Goldstein, 1995), hierarchical models (Raudenbush & Bryk, 2002), and random coefficient models (Longford, 1993). More recently, nonlinear mixed models were also developed. A nonlinear mixed model is a model with random coefficients in which the fixed and/or random effects enter the model nonlinearly (Davidian & Giltinan, 1995). As we explain below, a subset of nonlinear mixed models is the class of generalized linear mixed models (McCulloch & Searle, 2001).The main purpose of this article is to explain how item response theory (IRT) models can be conceptualized as nonlinear mixed models and to provide a framework for this conceptualization. There are four important assets of this approach. First, this conceptualization relates IRT to the broad statistical literature on mixed models. Second, applying the same framework to different IRT models can help in the understanding of their differences and commonalities. Third, using this framework, one can read...

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“…Some modeling approaches have been proposed for multilevel IRT models both for dichotomous and polytomous data (e.g., Fox 2001;Kamata, 1998;Maier, 2001;Williams, 2003). Among these, Kamata (1998) generalized the Rasch model as a multilevel model with a hierarchical generalized linear model (HGLM) framework.…”

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confidence: 99%

Parameter Recovery for the 1-P HGLLM with Non-Normally Distributed Level-3 Residuals*

2017

EDUC SCI-THEOR PRACT

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A Rasch Hierarchical Measurement Model

Cited by 57 publications

References 23 publications

The best of both worlds: a joint modeling approach for the assessment of change across repeated measurements

The best of both worlds: a joint modeling approach for the assessment of change across repeated measurements

A nonlinear mixed model framework for item response theory.

Parameter Recovery for the 1-P HGLLM with Non-Normally Distributed Level-3 Residuals*

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