The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Sufficient Statistics and Latent Trait Models
Abstract
For questionnaires with two answer categories, it has been proven in complete generality that if a minimal sufficient statistic exists for the individual parameter and if it is the same statistic for all values of the item parameters, then the raw score (or the number of correct answers) is the minimal sufficient statistic. It follows that the model must by of the Rasch type with logistic item characteristic curves and equal item-discriminating powers. This paper extends these results to multiple choice questionnaires. It is shown that the minimal sufficient statistic for the individual parameter is a function of the so-called score vector. It is also shown that the so-called equidistant scoring is the only scoring of a questionnaire that allows for a real valued sufficient statistic that is independent of the item parameters, if a certain ordering property for the sufficient statistic holds.
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Cites
Probabilistic Models for Some Intelligence and Attainment Tests
(1961) · Information and Control · doi:10.1016/s0019-9958(61)80061-2 · Cited by 6,939
Bock, R. D. (1972) · Psychometrika · doi:10.1007/bf02291411 · Cited by 1,228
Lord, F. M. (1952) · Cited by 494
Conditional Inference and Models for Measuring.
Williams, E. J., & Anderson, E. B. (1974) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2344962 · Cited by 240
CONDITIONAL INFERENCE FOR MULTIPLE‐CHOICE QUESTIONNAIRES
Andersen, E. B. (1973) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1973.tb00504.x · Cited by 196
Self-citationXXIII.—On Problems connected with Item Selection and Test Construction
Lawley, D. N. (1943) · Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences · doi:10.1017/s0080454100006282 · Cited by 137
Cited by
brms : An R Package for Bayesian Multilevel Models Using Stan
Bürkner, P.-C. (2017) · Journal of Statistical Software · doi:10.18637/jss.v080.i01 · Cited by 9,476
“Using threshold = "equidistant" forces the distance between two adjacent thresholds to be the same, that is for thresholds τ k and distance δ (see also Andrich 1978a; Andrich 1978b; Andersen 1977).”
BackgroundA Rasch model for partial credit scoring
Masters, G. N. (1982) · Psychometrika · doi:10.1007/bf02296272 · Cited by 3,782
Comorbidity: a network perspective
Cramer, A. O. J., Waldorp, L. J., van der Maas, H. L. J., & Borsboom, D. (2010) · Behavioral and Brain Sciences · doi:10.1017/s0140525x09991567 · Cited by 1,575
Ordinal Regression Models in Psychology: A Tutorial
Bürkner, P.-C., & Vuorre, M. (2019) · Advances in Methods and Practices in Psychological Science · doi:10.1177/2515245918823199 · Cited by 689
Measuring progressions: Assessment structures underlying a learning progression
Wilson, M. (2009) · Journal of Research in Science Teaching · doi:10.1002/tea.20318 · Cited by 329
Metadata
- Authors
- Andersen, E. B.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1977-03
- Volume
- 42
- Issue
- 1
- Pages
- 69-81
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2104351701
- Cited by
- 395
- References
- 6
- FWCI
- 5.59
- Type
- journal article
- Language
- en
- Open access
- closed
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