Rasch fit statistics and sample size considerations for polytomous data

doi:10.1186/1471-2288-8-33

BMC Medical Research Methodology

Volume 8

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Rush R
Fallowfield LJ
Velikova G
Sharpe M

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Research article

Rasch fit statistics and sample size considerations for polytomous data

Adam B Smith¹^,2 , Robert Rush³ , Lesley J Fallowfield⁴ , Galina Velikova¹^* and Michael Sharpe⁵^*

¹Cancer Research UK – Clinical Centre, St. James's University Hospital, Leeds, UK

²Centre for Health & Social Care, University of Leeds, Leeds, UK

³Centre for Integrated Health Research, Queen Margaret University, Edinburgh, UK

⁴Psychosocial Oncology Group – Cancer Research UK, University of Sussex, UK

⁵School of Molecular & Clinical Medicine, University of Edinburgh, Edinburgh, UK

author email corresponding author email* Contributed equally

BMC Medical Research Methodology 2008, 8:33doi:10.1186/1471-2288-8-33


Published:	29 May 2008

Abstract

Background

Previous research on educational data has demonstrated that Rasch fit statistics (mean squares and t-statistics) are highly susceptible to sample size variation for dichotomously scored rating data, although little is known about this relationship for polytomous data. These statistics help inform researchers about how well items fit to a unidimensional latent trait, and are an important adjunct to modern psychometrics. Given the increasing use of Rasch models in health research the purpose of this study was therefore to explore the relationship between fit statistics and sample size for polytomous data.

Methods

Data were collated from a heterogeneous sample of cancer patients (n = 4072) who had completed both the Patient Health Questionnaire – 9 and the Hospital Anxiety and Depression Scale. Ten samples were drawn with replacement for each of eight sample sizes (n = 25 to n = 3200). The Rating and Partial Credit Models were applied and the mean square and t-fit statistics (infit/outfit) derived for each model.

Results

The results demonstrated that t-statistics were highly sensitive to sample size, whereas mean square statistics remained relatively stable for polytomous data.

Conclusion

It was concluded that mean square statistics were relatively independent of sample size for polytomous data and that misfit to the model could be identified using published recommended ranges.