The hierarchical generalized linear model (HGLM) is presented as an explicit, two‐level formulation of a multilevel item response model. In this paper, it is shown that the HGLM is equivalent to the Rasch model and that, characteristic of the HGLM, person ability can be expressed in the form of random effects rather than parameters. The two‐level item analysis model is presented as a latent regression model with person‐characteristic variables. Furthermore, it is shown that the two‐level HGLM model can be extended to a three‐level latent regression model that permits investigation of the variation of students' performance across groups, such as is found in classrooms and schools, and of the interactive effect of person‐and group‐characteristic variables.

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surgeons. Clearer understanding of the facets of competence valued by the profession will hopefully contribute to refinement of curricula and assessment tools. References 1. Hamdorf JM. Critical evaluation. What makes a competent surgeon? ANZ J. Surg. 2010; 80: 656. 2. Arora S, Sevdalis N, Suliman I, Athanasiou T, Kneebone R, Darzi A.What makes a competent surgeon? Experts' and trainees' perceptions of the roles of a surgeon.

The Individual Zone of Optimal Functioning (IZOF) model postulates the functional relationship between emotions and optimal performance, and aims to predict the quality of upcoming performance with respect to the pre-performance emotional state of the performer. Several limitations associated with the traditional method of determining the IZOF are outlined and a new probabilistic approach is introduced instead. To reliably determine the boundaries of the IZOF and their associated probabilistic curve thresholds, performance outcomes that vary in quality, as well as the emotional intensity associated with them, are taken into account. Several probabilistic models of varying complexity are presented, along with hypothetical and real data to illustrate the concept. The traditional and the new methods are contrasted in one actual set and two hypothetical sets of data. In all cases the proposed probabilistic method was found to show greater sensitivity and to more accurately represent the data than the traditional method. The development of the method is a first stage toward developing models that take into account the interactive nature and multidimensionality of the emotional construct, as well as the fluctuations in emotional intensity and performance throughout the competition phases (i.e., momentum).

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