Mixture Models

Fieuws, Steffen; Spiessens, Bart; Draney, Karen

doi:10.1007/978-1-4757-3990-9_11

Cited by 12 publications

(9 citation statements)

References 21 publications

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“…The results reported in this work clearly show the need for alternative approaches to the analysis of non‐Gaussian longitudinal data. A plausible choice would be to replace the normal random‐effects distribution by nonparametric distribution (Butler and Louis, 1992; Aitkin, 1999), a semiparametric distribution (Chen et al, 2002), or a finite mixture of normals (i.e., a heterogeneity model; Fieuws, Spiessens, and Draney, 2004). However, Agresti et al (2004) reported that there can be some loss of efficiency, when using a nonparametric approach, compared to a parametric assumption close to the real distribution.…”

Section: Discussionmentioning

confidence: 99%

Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

2007

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Generalized linear mixed models (GLMMs) have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based. In the present work we have used simulations with a logistic random-intercept model to study the impact of misspecifying the random-effects distribution on the type I and II errors of the tests for the mean structure in GLMMs. We found that the misspecification can either increase or decrease the power of the tests, depending on the shape of the underlying random-effects distribution, and it can considerably inflate the type I error rate. Additionally, we have found a theoretical result which states that whenever a subset of fixed-effects parameters, not included in the random-effects structure equals zero, the corresponding maximum likelihood estimator will consistently estimate zero. This implies that under certain conditions a significant effect could be considered as a reliable result, even if the random-effects distribution is misspecified.

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Section: Discussionmentioning

confidence: 99%

Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

2007

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“…This model was previously termed as no variability within classes mixture model (Fieuws, Spiessens, and Draney 2004), and we will refer to this model as a mixture GLM model. The mixture GLM model is still not identifiable, because a constant can be added to all abilities (θ k ) and reduced from all difficulty parameters (β kj ), a problem it shares with the dichotomous Rasch model.…”

Section: Possible Solutions To Non-identifiabilitymentioning

confidence: 99%

“…Second, it seems reasonable to believe that all groups share similar variability from the main group ability. A similar modeling approach has been discussed by Fieuws, Spiessens, and Draney (2004) and by Rijmen and De Boeck (2003); however, both manuscripts did not follow with a full Bayesian analysis, and relied on maximum likelihood estimation and asymptotic variance approximation. Bayesian sampling also allows estimation of the posterior predictive distributions of different test statistics described in Section 3.…”

Section: Mixed Generalized Linear Mixed Model (Mglmm)mentioning

confidence: 99%

Rasch Model and Its Extensions for Analysis of Aphasic Deficits in Syntactic Comprehension

Gutman

DeDe

Caplan

et al. 2011

Journal of the American Statistical Association

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Aphasia is the loss of the ability to produce and/or comprehend language, due to injury to brain areas responsible for these functions. Aphasic patients' performance on comprehension tests has traditionally been related both to the patient's individual ability and to the difficulty of the test questions. The natural choice for analysis of these test results is the Rasch model. It assumes that the probability of a patient responding correctly to a question is the inverse-logit function of the difference between the individual patient's ability and the difficulty of the test question. This study first modeled the way aphasic patients process different sentence types, as well as their ability to accomplish tasks using Rasch models. However, several scientifically important features of the data, such as the correlation of correct responses between two different comprehension tasks, and the association between response patterns in control sentences and response patterns in experimental sentences, were found to be inadequately captured by such models. Alternatively, we used a full Bayesian approach, exploring a mixture of generalized linear mixed models that clustered patients into similar response patterns and abilities. The mixture model was found to better describe the experimental results than any other model examined. The mixture model also expresses the hypothesis that aphasic patients can be classified into different ability and response profile groups, and that patients utilize different cognitive resources in different comprehension tasks. These results are scientifically important and could not have been discovered by using the simple Rasch model. This article has supplementary material online.

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“…Latent DIF using mixture item response models is applied to an empirical data set, following our recommended steps for latent DIF analysis. A verbal aggression data set (Vansteelandt, ) was selected because it is available to freely download from https://bearcenter.berkeley.edu/page/materials-explanatory-item-response-models, has well‐structured item designs, and has been widely used for item response modeling (e.g., De Boeck & Wilson, ), including mixture item response modeling (Choi & Wilson, ; Fieuws, Spiessens, & Draney, ; Rijmen & De Boeck, ).…”

Section: Applicationmentioning

confidence: 99%

An NCME Instructional Module on Latent DIF Analysis Using Mixture Item Response Models

Cho

Suh

Lee

2015

Educational Measurement

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The purpose of this ITEMS module is to provide an introduction to differential item functioning (DIF) analysis using mixture item response models. The mixture item response models for DIF analysis involve comparing item profiles across latent groups, instead of manifest groups. First, an overview of DIF analysis based on latent groups, called latent DIF analysis, is provided and its applications in the literature are surveyed. Then, the methodological issues pertaining to latent DIF analysis are described, including mixture item response models, parameter estimation, and latent DIF detection methods. Finally, recommended steps for latent DIF analysis are illustrated using empirical data.

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Mixture Models

Cited by 12 publications

References 21 publications

Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

Rasch Model and Its Extensions for Analysis of Aphasic Deficits in Syntactic Comprehension

An NCME Instructional Module on Latent DIF Analysis Using Mixture Item Response Models

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