Unidimensionality in the Rasch model: how to detect and interpret


  • Eugenio Brentani Università degli Studi di Brescia
  • Silvia Golia Università degli Studi di Brescia




Unidimensionality, that is the items in a questionnaire measure only a single construct, is a fundamental requirement for the Rasch model. The paper deals with the detection of unidimensionality making use of principal components analysis of residuals and item fit statistics. Simulated bi-dimensional data sets are analized in order to find regolarities in the behavoiur of these statistical tools. The results are applied to a real database coming from the satisfaction section of the first national survey concerning the social services sector carried out in Italy


D. ANDRICH, (1978), A rating formulation for ordered response categories, “Psychometrika”, 43, pp. 561-573.

T.G. BOND, C.M. FOX, (2007), Applying the Rasch Model. Fundamental measurement in the human sciences, snd Edition, Erlbaum, Mhawah NJ.

C. BORZAGA, M. MUSELLA, (2003), Produttività ed efficienza nelle organizzazioni nonprofit. Il ruolo dei lavoratori e delle relazioni di lavoro, Edizioni31, Trento.

E. BRENTARI, S. GOLIA, (2008), Measuring Job Satisfaction in the Social Services Sector with the Rasch Model, “Journal of Applied Measurement”, 9 (1), pp. 45-56.

K.B. CHRISTENSEN, J.B. BJOMER, S. KREINER, J.H. PETERSEN, (2002), Testing unidimensionality in polytomous Rasch models, “Psychometrika”, 67 (4), pp. 563-574.

C.A.W. GLAS, N.D. VERHELST, (1995), Testing the Rasch model, in G.H. FISCHER, I.W. MOLENAAR (Eds.), Rasch models - foundations, recent developments, and applications, Springer-Verlag.

J.E. GUSTAFSSON, (1980), Testing and obtaining fit of data to the Rasch model, “British Journal of Mathematical and Statistical Psychology”, 33, pp. 205-233.

J. HATTIE (1985), Methodology review: assessing unidimensionality of tests and items, “Applied Psychological Measurement”, 9 (2), pp. 139-164.

J.M. LINACRE (2006), WINSTEPS Rasch measurement computer program, Chicago: Winsteps.com.

P. MARTIN-LÖF, (1973), Statistiska modeller [Statistical models.] Anteckningar från seminarier lasåret 1969-1970, utarbetade av Rolf Sundberg. Obetydligt ändrat nytryck, October 1973. Stockholm: Institütet för Försäkringsmatemetik ochMatematisk Statistisk vid Stockholms Universitet.

G. RASCH, (1960), Probabilistic models for some intelligence and attainment tests, Copenhagen, The Danish Institute of Educational Research.

R.M. SMITH, (1996), A comparison of methods for determining dimensionality in Rasch measurement, “Structural Equation Modeling”, 3, pp. 25-40.

JR. E.V. SMITH, (2002), Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals, “Journal of Applied Measurement”, 3, pp. 205-231.

W.F. STOUT, (1987), A nonparametric approach for assessing latent trait unidimensionality, “Psychometrika”, 52, pp. 293-325.

B.D WRIGHT, G.N. MASTERS, (1982), Rating Scale Analysis, MESA Press, Chicago.




How to Cite

Brentani, E., & Golia, S. (2007). Unidimensionality in the Rasch model: how to detect and interpret. Statistica, 67(3), 253–261. https://doi.org/10.6092/issn.1973-2201/3508