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On the Contextual Conditions Driving a Difficulty Factor

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Listed:
  • Karl Schweizer
  • Siegbert Reiß

Abstract

This paper reports three simulation studies conducted to identify the contextual conditions leading to the observation of a difficulty factor in confirmatory factor analysis. The data of each study were generated to show one underlying source of responding only whereas the difficulties of the simulated items constituting the contextual condition were varied. The first study showed that a broad range of difficulties of items was insufficient for driving a difficulty factor. The second study revealed that very large and small difficulties of the same size could lead to a difficulty factor if the confirmatory factor model included two correlated factors. In the third study a subgroup of simulated items showed very large difficulties of the same size while the difficulties of the other simulated item were varied. In this study almost all combinations of difficulties led to the observation of a difficulty factor that was correlated or uncorrelated with the genuine factor.

Suggested Citation

  • Karl Schweizer & Siegbert Reiß, 2019. "On the Contextual Conditions Driving a Difficulty Factor," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 1-12, September.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:5:p:1
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    References listed on IDEAS

    as
    1. George Ferguson, 1941. "The factorial interpretation of test difficulty," Psychometrika, Springer;The Psychometric Society, vol. 6(5), pages 323-329, October.
    2. W. Gibson, 1960. "Nonlinear factors in two dimensions," Psychometrika, Springer;The Psychometric Society, vol. 25(4), pages 381-392, December.
    3. J. Guilford, 1941. "The difficulty of a test and its factor composition," Psychometrika, Springer;The Psychometric Society, vol. 6(2), pages 67-77, April.
    4. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
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    More about this item

    Keywords

    difficulty factor; simulation; binary data; difficulty; variance scaling;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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