Academic journal article Psychological Test and Assessment Modeling

Pairwise Rasch Model Item Parameter Recovery under Sparse Data Conditions

Academic journal article Psychological Test and Assessment Modeling

Pairwise Rasch Model Item Parameter Recovery under Sparse Data Conditions

Article excerpt

Introduction

The objective of this paper is twofold. First, a short overview of different approaches to item parameter recovery in the framework of Item Response Theory (IRT) is given placing an emphasis on parameter estimation in the presence of missing data. Also an alternative approach to identifying the item parameters is introduced. This approach is the explicit calculation of item parameters on the basis of conditional item category frequencies, which are obtained through a pairwise comparison task. For better understanding the historical background of the method is briefly outlined as well as its relation to the fundamental assumptions of the Rasch model.

Secondly, the pairwise method is tested in comparison with other methods of item parameter recovery. For this a dataset comprising of n = 620 students answering to eight items of one personality facet from the German NEO-PI-R inventory (Ostendorf, 2004) is analyzed. To demonstrate the performance of the pairwise method in the context of missing values a minimal simulation scenario, based on the empirical dataset is constructed. The computations following the pairwise comparison approach were conducted using the R (R Development Core Team, 2014) package pairwise (Heine, 2014) and two other standalone software packages commonly used for estimation of the Rasch model in social sciences.

According to these two objectives, this article is organized as follows. The first section gives a general overview including some theoretical and historical aspects of methods of parameter estimation in the framework of Item Response Theory (IRT). As a rejoinder the principles of applying pairwise comparisons are derived from the basic equations given by Rasch (1960) following an approach first formalized by Choppin (1968). Further a minimal example is illustrated to demonstrate the basic principles of pairwise item parameter recovery from a practical perspective.

An "empirical section" covers the second objective in order to test the pairwise method under practical and simulated conditions. Thus the item parameters in the framework of IRT are recovered for empirical data containing no missing values at baseline first, using different methods of estimation. Thereupon artificial missing values are added to the complete baseline dataset in several steps, estimating the item parameters at every stage of missing data percentage.

Theoretical framework and history of pairwise comparisons

Since the basic formulation of the probabilistic test model by the Danish mathematician Georg Rash and its extension to multi-level, ordinal response formats by Masters (1982), several estimation methods for parameter recovery have been developed and proposed. With regard to the practical application of the model, each of these different methods have certain advantages and disadvantages. As a consequence each method must be carefully considered in each case of application, depending on the different objectives of empirical studies, their designs and the kind of inference to draw from their results. Next, a short outline to several estimation methods in the framework of Item Response Theory (IRT) is given, that are most prevalent in current applications in social sciences. The article then goes on to discuss some issues about the structure of the data matrices in general and the missing data problem in particular, concerning the choice of either method of parameter estimation in IRT. Lastly the method of pairwise comparisons as a non-iterative method of item parameter recovery is introduced, beginning with some remarks on the historical origins of this method and its parallels to measurement according to the Rasch model.

Methods of parameter estimation in Rasch models

As stated by Johnson (2007) there are basically four estimation methods for (item) parameter recovery in the framework of IRT, commonly used in social sciences. The Joint Maximum Likelihood (JML), Conditional Maximum Likelihood (CML), Marginal Maximum Likelihood (MML) and bayesian estimation with Markov Chain Monte Carlo algorithm (MCMC). …

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