Modeling Responses and Response Times in Personality Tests with Rating Scales

By Ranger, Jochen | Psychological Test and Assessment Modeling, October 1, 2013 | Go to article overview

Modeling Responses and Response Times in Personality Tests with Rating Scales


Ranger, Jochen, Psychological Test and Assessment Modeling


Abstract

In this article several latent trait models for the joint distribution of the responses and response times in rating scales are compared. Among these models are two generalizations of established models for binary items, namely a generalization of the approach of Ferrando and Lorenzo-Seva (2007a) and a generalization of the approach of Ranger and Ortner (2011). Two new models and a variant of the hierarchical model of van der Linden (2007) are also considered. All these models combine the graded response model with a response time model based on the log-normal distribu-tion. The models differ in the assumed relationship between the expected log response time and the underlying latent traits. Although the proposed models have different interpretations and implica-tions they can all be calibrated within the same general framework using marginal maximum likeli-hood estimation and an application of the ECM-algorithm. The models are used for the analysis of an empirical data set. According to the AIC index, the generalization of the model of Ranger and Ortner (2011) can represent the data best.

Keywords: response time, log-normal distribution, inverted U-shaped relationship, rating scale

(ProQuest: ... denotes formulae omitted.)

The analysis of response times in psychological tests has a long history (Thurstone, 1937; Furneaux, 1952). The focus of psychological research has thereby been on achievement tests, and substantial progress has been made in this area. A major step forward was the development of latent trait models that can be used for the joint analysis of the responses and response times in a test. In comparison to the simple indices, which have formerly been used in order to combine the accuracy and speed of a respondent, the usage of a latent trait model has several advantages. First, some latent trait models have an epistemological foundation as these models can be derived from the principle of spe- cific objectivity, which states that the result of a comparison of two individuals must not depend on the specific item used for the comparison (Fischer, 1989). And second, latent trait models allow for more sophisticated research questions and applications. Latent trait models have been used for item selection in adaptive testing (van der Linden, 2008), the detection of collusion between test takers (van der Linden, 2009a) and the detection of aberrant responses (van der Linden & van Krimpen-Stoop, 2003).

Much progress has been made in the field of achievement testing, where a large number of different models for responses and response times has been proposed. For an overview over the different models proposed so far see van der Linden (2009b) as well as Lee and Chen (2011). Some of these models explicitly refer to the concept of specific objectivity and have a sound measurement theoretic foundation. See for example Scheiblechner (1979) who proposed a response time model based on the exponential distribution. In this model the total test time has a similar function as the sum score in the Rasch model, being a sufficient statistic for the speed of a test taker. Other models have been derived from assumptions about the response process. The components of such process models are closely related to psychological concepts, such that these models go beyond the usual measurement models of item response theory (Tuerlinckx & De Boeck, 2005; van der Maas, Molenaar, Maris, Kievit, & Boorsboom, 2011; Vandekerckhove, Tuerlinckx, & Lee, 2011).

Less progress has been made in the area of attitudinal scales and personality tests. The latent trait models devised for the responses and response times in achievement tests can not simply be transferred to this area of application. This is due to a different relation between the time needed to give a response and the trait that is intended to be measured with the test. In personality and attitudinal scales the individuals located at either end of the trait continuum usually respond fast, a data pattern that is described as an inverted-U relationship (Kuiper, 1981; Ferrando, 2006; Akrami, Hedlund, & Ekehammar, 2007). …

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