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 Publications
Rasch Measurement Transactions (free, online)	Rasch Measurement research papers (free, online)	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Applying the Rasch Model 3rd. Ed., Bond & Fox	Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters	Introduction to Rasch Measurement, E. Smith & R. Smith	Introduction to Many-Facet Rasch Measurement, Thomas Eckes	Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.	Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Journal of Applied Measurement	Rasch models for measurement, David Andrich	Constructing Measures, Mark Wilson	Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish:	Análisis de Rasch para todos, Agustín Tristán		Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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