Analysis of Test Result Data with non-Random Missingness
Author
Simonsen, Mikkel Runason
Term
4. term
Education
Publication year
2022
Submitted on
2022-05-31
Pages
149
Abstract
Specialet undersøger statistisk inferens for speedede testdata med ikke-tilfældig manglendehed. Udgangspunktet er Rasch-modellen for de fulde data og en trinmodel (steps model) til at beskrive frafald, og der sammenlignes fælles, betingede og marginale maksimum-likelihood-estimatorer. Rasch-modellen formuleres som en generaliseret lineær mixed model, hvor den marginale likelihood beregnes ved hjælp af Laplace-approksimation og Gauss–Hermite-kvadratur. De asymptotiske egenskaber af estimatorerne udledes og vurderes via simulationsstudier, og metoderne anvendes på et datasæt med 663 danske skoleelever (10–12 år) der besvarer 36 opgaver om brøker under tidsbegrænsning, hvor manglende svar tiltager mod slutningen af testen. Analysen peger på en sammenhæng mellem tidspunktet for frafald og elevens evneniveau, hvilket gør eksplicit modellering af frafaldet nødvendig; antagelser om ignorerbar manglendehed kan være utilstrækkelige. Arbejdet omfatter desuden en praktisk implementering i R samt diskussion af modeltilpasning og estimatorernes anvendelighed i denne kontekst.
This thesis investigates statistical inference for speeded test data with non-random missingness. The complete-data responses are modeled with the Rasch model and dropout is represented by a steps model, while joint, conditional, and marginal maximum likelihood estimators are derived and compared. The Rasch model is cast as a generalized linear mixed model, with marginal likelihoods computed using the Laplace approximation and Gauss–Hermite quadrature. Asymptotic properties of the estimators are established and examined through simulation studies, and the methods are applied to responses from 663 Danish school students (ages 10–12) on 36 fraction items under a time limit, where missingness increases toward later items. The analysis indicates a correlation between the timing of dropout and subject ability, making explicit modeling of dropout essential; ignorability assumptions may be inadequate. The work includes a practical R implementation and discusses goodness-of-fit and the suitability of the estimators in this setting.
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