Conditions leading to the observation of a difficulty effect and its consequence for confirmatory factor analysis

Schweizer, Karl; Di Stefano, Christine; Troche, Stefan (2021). Conditions leading to the observation of a difficulty effect and its consequence for confirmatory factor analysis. Psychological test and assessment modeling, 63(4), pp. 469-483. Pabst Science Publishers

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Psychometric research has posited that difficulty effects related to item-level input for factor analysis serves as the precondition for observing a difficulty factor. Two studies are reported that investigated and confirmed this hypothesis. First, it was demonstrated that extreme and same-sized extreme difficulty levels of items resulted in deviations of the input to factor analysis from the expected systematic variation. Difficulty levels, as defined by McDonald and Ahlawat (1974), that were close to the upper limit for such levels were used for this purpose. Subsequently, it was demonstrated that data with this effect were likely to show model misfit in structural investigations by the one-factor CFA model. According to these results the difficulty effect is a method effect caused by the difficult factor condition of data. This condition is the source of additional systematic variation that is not accounted for by the intended latent variable. This additional variation means model misfit unless it is captured by a difficulty factor.

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