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Educational and Psychological Measurement
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Modeling Nonignorable Missing Data in Speeded Tests

Cees A. W. Glas

University of Twente, c.a.w.glas{at}gw.utwente.nl

Jonald L. Pimentel

University of Twente

In tests with time limits, items at the end are often not reached. Usually, the pattern of missing responses depends on the ability level of the respondents; therefore, missing data are not ignorable in statistical inference. This study models data using a combination of two item response theory (IRT) models: one for the observed response data and one for the missing data indicator. The missing data indicator is modeled using a sequential model with linear restrictions on the item parameters. The models are connected by the assumption that the respondents' latent proficiency parameters have a joint multivariate normal distribution. Model parameters are estimated by maximum marginal likelihood. Simulations show that treating missing data as ignorable can lead to considerable bias in parameter estimates. Including an IRT model for the missing data indicator removes this bias. The method is illustrated with data from an intelligence test with a time limit.

Key Words: ignorability • item response theory • maximum marginal likelihood • missing data • nonignorable missing data • sequential model • steps model

This version was published on December 1, 2008

Educational and Psychological Measurement, Vol. 68, No. 6, 907-922 (2008)
DOI: 10.1177/0013164408315262
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