Assessing unidimensionality: A comparison of Rasch modeling, Parallel analysis, and TETRAD

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Testing Rating Scale Unidimensionality Using the Principal Component Analysis (PCA)/t-Test Protocol with the Rasch Model: The Primacy of Theory over Statistics (2014, background): “Instead, assessment of dimensionality requires a good deal of judgment and the importance of prioritizing a theory driven approach over a data driven one in order to achieve interpretable and useful rating scale derived measures cannot be under emphasized [13].”
An application of item response theory to psychological test development (2016, neutral): “Other new recommended techniques, although not very often used, to evaluate unidimensionality are the Tetrad analysis and the Hull method (Yu et al. 2007; Lorenzo-Seva et al. 2011).”
Current Methodological Considerations in Exploratory and Confirmatory Factor Analysis (2011, methodology): “Because over- or under-factoring (e.g., selecting too few/many factors) can result in significant modeling error, with underfactoring generally considered to be more detrimental of the two, appropriate methods must be used when determining the number of factors.”