What are the minimal sample size requirements for Mokken scaling? An empirical example with the Warwick- Edinburgh Mental Well-Being Scale

Purpose: Sample size in Mokken scales is mostly studied on simulated data, reflected in the lack of consideration of sample size in most Mokken scaling studies. Recently, [Straat, J. H., van der Ark, L. A., & Sijtsma, K. (2014). Minimum sample size requirements for Mokken scale analysis. Educational and Psychological Measurement, 74, 809–822] provided minimum sample size requirements for Mokken scale analysis based on simulation. Our study uses real data from the Warwick-Edinburgh Mental Well-Being Scale (N = 8463) to assess whether these hold.
Methods: We use per element accuracy to evaluate the impact of sample size, with scaling coefficients and confidence intervals around scale, item and item pair scalability coefficients.
Results: Per element accuracy, scalability coefficients, and confidence intervals around scalability coefficients are sensitive to sample size. The results from Straat et al. were not replicated; depending on the main goal of the research, sample sizes ranging from > 250 to > 1000 are needed.
Conclusions: Using our pragmatic approach, some practical recommendations are made regarding sample sizes for studies of Mokken scaling.