Statistical Descriptions of Item and Test Functioning

  • Mark D. Reckase
Part of the Statistics for Social and Behavioral Sciences book series (SSBS)


The MIRT models in Chap. 4 provide mathematical descriptions of the interactions of persons and test items. Although the parameters of these models summarize the characteristics of the items, the vectors of item parameters sometimes lack intuitive meaning. This chapter provides other statistical ways of describing the functioning of test items that may more clearly indicate the value of the test items for determining the location of individuals in the multidimensional θ-space. The ways of describing test item characteristics given here are direct extensions of the descriptive information for UIRT models described in Chap. 2.


Steep Slope Test Item Item Parameter Maximum Slope Information Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Ackerman TA (1996) Graphical representation of multidimensional item response theory analyses. Applied Psychological Measurement 20:311–329CrossRefGoogle Scholar
  2. Ackerman TA, Gierl MJ, Walker CM (2003) Using multidimensional item response theory to evaluate educational and psychological tests. Educational Measurement: Issues and Practice 22:37–51CrossRefGoogle Scholar
  3. Davey TC, Ackerman TA, Reckase MD, Spray JA (1989) Interpreting score differences when item difficulty and discrimination are confounded. Paper presented at the meeting of the Psychometric Society, Los AngelesGoogle Scholar
  4. Muraki E, Carlson JE (1993) Full-information factor analysis for polytomous item responses. Paper presented at the annual meeting of the American Educational Research Association, AtlantaGoogle Scholar
  5. Reckase MD, Ackerman TA, Carlson JE (1988) Building a unidimensional test using multidimensional items. Journal of Educational Measurement 25:193–204CrossRefGoogle Scholar
  6. Reckase MD, McKinley RL (1991) The discriminating power of items that measure more than one dimension. Applied Psychological Measurement 15:361–373CrossRefGoogle Scholar
  7. Wang M (1985) Fitting a unidimensional model to multidimensional item response data: The effect of latent space misspecification on the application of IRT (Research Report MW: 6-24-85). University of Iowa, Iowa City, IAGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Counseling, Educational, Psychology, and Special Education DepartmentMichigan State UniversityEast LansingUSA

Personalised recommendations