Many types of models are available to assess psychological abilities such as skill. These models often present questions or tasks (called items) to an individual and then an estimate (preferably, a measure) of an individual’s ability can be calculated from the sum-score of the item responses. In item response theory (IRT) models, estimates of item difficulty and consistency of responses across people and items are central.

The original Rasch model [101] is a type of IRT model by which skill can be measured. The ability of a person j is denoted βj , and the difficulty of an item i is denoted δi. Xij is a random variable with values 0 and 1 such that Xij = 1 if the response is correct and Xij = 0 if the response is incorrect when person j solves item i. The probability of a correct response is:

The Rasch model typically uses some form of maximum likelihood function when estimating β and δ.

The model uses an interval-logit scale as the unit of measurement. A logit is the logarithmic transformation of the odds. Humphry and Andrich [70] discuss the use of this unit of measurement in the context of the Rasch model.

The original Rasch model is classified as a unidimensional model; that is, ability is measured along only one dimension. Furthermore, the model is called the dichotomous Rasch model because only two score categories are available (e.g., incorrect and correct).

Andrich derived the polytomous Rasch model [7] as a generalization of the dichotomous model. The polytomous model permits multiple score categories 0, . . . , Mi, where Mi is the maximum score for an item i. Each higher score category indicates a higher ability (and therefore also an increased difficulty in solving correctly), which enables evaluations of partially correct solutions. This is an attractive feature for our work and we therefore used the polytomous Rasch model.

A requirement of the polytomous, unidimensional Rasch model is that score categories must be structured according to a Guttman-structured response subspace [8]. For example, a response awarded a score of “2” for an item i indicates that the requirements for scores 0, 1, and 2 are met and that the requirements for scores 3 to Mi are not met.

The Rasch model has been used in many large-scale educational testing programmes, such as OECD’s Programme for International Student Assessment [20]. The Rasch model has also been used to measure programming ability in C [128], Lisp [98], and Pascal [122], and to explain software engineering practices that are based on CMM [44].

Referensi : Gunnar R. Bergersen, Dag I. K. Sjøberg, Member, IEEE, and Tore Dyb° a, Member, IEEE “Construction and Validation of an Instrument for measuring programming skill”