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## Interdisciplinaria

*On-line version* ISSN 1668-7027

#### Abstract

ATTORRESI, Horacio Félix et al. Application of the Graded Response Model to a Will-to-Work Scale.* Interdisciplinaria* [online].
2011,
vol.28, n.2, pp. 231-244.
ISSN 1668-7027.

This study aims to present the findings obtained from the application of an Item ResponseTheory model (IRT) to the reactive of a Will-to-Work Measuring Test (WW). WW is defined as the individuals' tendency to generate efficient volatile processes that allow them to commit themselves to starting a task and to persisting in its execution by overcoming obstacles until they achieve its materialization with precision and without procrastination. WW is a personality trait that describes the predisposition of an individual to assume duties in a responsible, self-motivated and prompt manner even when such duties may be unappealing. The scale measuring the WW comprises 9 items in polychromous response format (four-point rating scale), with the response options graded. Accordingly, one of the IRT most widely used models was applied for the monetization of ordered polychromous responses: Samejima's Graded Response Model (GRM). The GRM is a generalization of the Two Parameter Logistic Model of Birnbaum. In GRM, a person's probability of responding in category j to a specific item i, Pij(θ), is obtained by subtracting the probability of responding in or below category j-1 from the probability of responding in or below category j.Through the Item Response Category Curves, the GRM allows for the representation of an individual's likelihood to choose each of the item categories based on the level of the latent trait measured. The data from this psychometric test was obtained from a sample of 1,141 university students. The one-dimensional assumption required by the GRM was corroborated through an exploratory analysis of the data factor structure. The local independence assumption was considered to be satisfied after proving the scale one-dimensionality. All analyses based on the IRT were performed by operating the MULTILOG software program. The GRM parameters estimation was carried out through marginal maximum likelihood procedures. A discrimination parameter (a) and three location parameters (b_{1}, b_{2} and b_{3}) corresponding to thresholds separating the 4 response categories were estimated for each item. The model's goodness-of-fit was studied on an item basis by examining the residue of observed and expected proportions for each of the ordered response categories. The residue obtained was the same as or lower than .01, which led to the conclusion that the model adjustment to the data was satisfactory for all reactive. Despite this, one of the items showed inappropriate behavior. The value of its location parameters turned out to be very different from the expected one and showed high estimation errors when compared against the values obtained for the rest of the items. Most of the location parameters showed midlow WW values and discrimination parameters showed mid-high values (0.73 - 1.73). The instrument's reliability was acceptable if we consider the.75 marginal reliability coefficient obtained from IRT. However, local accuracy measures showed that the test is less reliable when measuring the WW highest levels. In other words, the measure error increases as we attempt to discriminate strongly willful individuals. This means that the WW scale is useful to measure mid-low levels of WW, but less accurate when it comes to individuals whose trait level is higher. It is therefore concluded that it is necessary to raise the number of WW scale items to optimize the instrument quality. It is particularly important to identify construct indicators allowing for a more accurate detection of the highest trait levels. The shortage of the application of IRT models to personality tests as well as the difficulty that the achievement of their exigent assumptions were discussed. The findings showed the problems posed by the WW scale and allowed us to obtain useful information to guide the building of new items.

**Keywords
:
**Graded response model; Samejima´s model; Will-to-work; Item response theory.