# Accounting for Variable Task Discrimination in Divergent Thinking Fluency Measurement – An Example of the Benefits of a 2-Parameter Poisson Counts Model and its Bifactor Extension Over the Rasch Poisson Counts Model

By Nils Myszkowski in Psychometrics Poisson models Log-linear models Item-Response Theory

# What it’s about

In this paper, we introduce new psychometric models for count/fluency tasks (tasks in which individuals have to provide many instances). Notably, we extent the Rasch Poisson Counts Model (RPCM) to account for variable discrimination (2-Parameter Poisson Counts Model) and to account for local dependencies/nuisance factors (Bifactor 2-Parameter Poisson Counts Model).

# Abstract

Fluency tasks are among the most common item formats for the assessment of certain cognitive abilities, such as verbal fluency or divergent thinking. A typical approach to the psychometric modeling of such tasks (e.g., Intelligence, 2016, 57, 25) is the Rasch Poisson Counts Model (RPCM; Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research, 1960), in which, similarly to the assumption of (essential) \(\tau\)-equivalence in Classical Test Theory, tasks have equal discrimination – meaning that, beyond varying in difficulty, they do not vary in how strongly they are related to the latent variable. In this research, we question this assumption in the case of divergent thinking tasks, and propose instead to use a more flexible 2-Parameter Poisson Counts Model (2PPCM), which allows to characterize tasks by both difficulty and discrimination. We further propose a Bifactor 2PPCM (B2PPCM) to account for local dependencies (i.e., specific/nuisance factors) emerging from tasks sharing similarities (e.g., similar prompts and domains). We reanalyze a divergent thinking dataset (Psychology of Aesthetics, Creativity, and the Arts, 2008, 2, 68) and find the B2PPCM to significantly outperform the 2PPCM, both outperforming the RPCM. Further extensions and applications of these models are discussed.

# How to access the paper

You can access the full paper here.

- Posted on:
- December 12, 2021

- Length:
- 2 minute read, 264 words

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