Residual Analysis with Missing Data

I was finally able to run a principle component analysis of Rasch residuals on a large dataset of about 4000 people and 457 items. However, the output look very strange. It produced 3 factors: factor 1 has explained 68.48 of 457 variance units, factor 2 has explained -56.11, and factor 3 has explained -107.27. I am not sure what is the main cause of the negative (and huge) eigenvalues. The data have the weakness that nobody took every item. I also tried to factor analyze the original data with SPSS, but it stopped because there were not enough subjects to analyze. What do you recommend?

Surintorn Suanthong

Missing data always pose a problem in factor analysis because the basis of the methodology is the decomposition of correlations or covariances. There are two main approaches to the problem. Listwise deletion removes from the data every case with a missing data value. A drawback, apparently observed in your SPSS run, is that a large proportion of the cases may be omitted, skewing the results or preventing successful completion of the analysis.

Pairwise deletion skips over individual computations involving missing values. So correlations between pairs of items are computed based on all cases for which data is present for both items. Pairwise deletion can lead to contradictory results:

Inconsistent matrices of correlations produce negative eigenvalues.

In the analysis of Rasch residuals, there is a useful solution. For each missing residual, impute its expected value of zero. This will force the correlations to be consistent. The zero residuals will dampen the size of factors in the residuals, but will have little effect on the factor structure.

From a small data set, I randomly eliminated 54% of the responses of each respondent. In the residuals from the original data, factors 1 and 2 had eigenvalues of 3.0 and 2.4. Listwise deletion would have eliminated the entire data set. Using pairwise deletion, the eigenvalues were -6.0 and -11.1 with a meaningless factor structure. After imputing zero residuals, the eigenvalues climbed back to 2.0 and 1.5, with a weaker, but still recognizable, factor structure.

John Michael Linacre

Residual Analysis with Missing Data Linacre, J.M. … Rasch Measurement Transactions, 1999, 13:1 p. 679

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

Forum

Rasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

The URL of this page is www.rasch.org/rmt/rmt131b.htm

Website: www.rasch.org/rmt/contents.htm