Cluster-Rasch Models

Li and Hong (L&H, 2001) propose a multi-stage model for relating gene expression profiles to phenotypes. It estimates several Rasch measures associated with each tissue-sample ("person") based on its gene ("item") expression ("response") profile. These measures are used to predict the phenotypes (physical characteristics).

Stage 1: Each data-point is the frequency of a gene-indicator in a tissue sample. The frequencies are stratified into ordinal responses. L&H choose 4 strata, so that the ordinal responses become 0,1,2,3. In their examples, there are about 100 genes and 72 tissue-samples.

Stage 2: The genes are segmented into clusters. L&H use the original data-points, but better would be the residuals from a Rasch analysis of the entire dataset.

Stage 3. A Rasch Partial-Credit analysis is performed on each gene-cluster. This constructs a latent unidimensional variable on which each gene and each tissue-sample is located. The measure for each tissue-sample for each gene cluster is estimated. L&H model each gene to have its own rating-scale structure, but they note that their data are somewhat thin for this type of analysis. A Rasch-Andrich (or gene-grouped) model would be more robust.

Stage 4. The cluster-measures for each tissue-sample are regressed on its observed phenotype, producing a set of regression parameters.

Stage 5. The phenotype of a new tissue-sample is predicted based on its gene expression, the clustering of the genes, and the regression parameters. The predicted phenotype is compared with its observed phenotype to evaluate the success of the cluster-Rasch model.

The Figure cross-plots the measures (latent factors) for two groups of tissue-sample and two clusters of genes.

Li H. & Hong F. (2001). Cluster-Rasch models for microarray gene expression data. Genome Biology, 2(8): research0031.1-0031.13

Cluster-Rasch Models … H. Li & F. Hong, Rasch Measurement Transactions, 2008, 22:2 p. 1166

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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