Title: Estimation of Speed-Accuracy Response Models: Positive Scoring Rules
for Easy Tests

Authors: Peter van Rijn (1), Usama Ali (2)

Affiliation: (1) ETS Global, (2) Educational Testing Service

Abstract: We develop an estimation routine to estimate item response models
that combine response accuracy and response time in a straightforward scoring
rule. This was proposed by Maris and van der Maas (2012), who focused on a
psychometric model for multiple choice items in which the scoring rule
resulted in positive scores for fast correct responses and negative scores for
fast incorrect responses. The resulting score is treated as a sufficient
statistic, and leads to an exponential family model. We will focus on a
scoring rule that results in positive scores only, and discuss model
estimation using minorization techniques (see e.g., de Leeuw, 2006). The
minorization is however different from that used in Maris and van der Maas
(2012). Finally, we discuss a method for assessing item fit based on residual
analysis following Haberman, Sinharay, and Chon (2013). The methods are
illustrated with simulations and an application to real data from a relatively
easy mathematics assessment. It is found that adding the response time can
lead to a considerable improvement in measurement precision.

References:

Haberman, S., Sinharay, S., & Chon, K. (2013). Assessing item fit for
unidimensional item response theory models using residuals from estimated item
response functions. Psychometrika, 78, 417-440.

de Leeuw, J. (2006). Some majorization techniques. Statistical Computing and
Graphics Newsletter, 17, 3-7.

Maris, G., & van der Maas, H. (2012). Speed-accuracy response models: Scoring
rules based on response time and accuracy. Psychometrika, 77, 615-633.