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Testing Equality of Functions Across Multiple Experimental Conditions for Different Ability Levels in the IRT Context: The Case of the IPRASE TLT 2016 Survey

Author

Listed:
  • Fabrizio Maturo

    (“G. d’ Annunzio” University)

  • Francesca Fortuna

    (“G. d’ Annunzio” University)

  • Tonio Di Battista

    (“G. d’ Annunzio” University)

Abstract

In the educational field, it is common to analyze test data through item response theory models. In this context, a key role is played by item characteristic curves (ICCs) and item information curves (IICs). In many real cases, practitioners are interested in understanding if some factors have a significant influence on the probability of correctly answering items. In the literature, this problem has been addressed by applying the standard analysis of variance model, which is based on the total scores or the proportion of correct responses. However, this method needs to meet some strong assumptions and may present some limitations because it does not consider useful information typical of the IRT, such as the shapes of the ICCs and IICs, which provide interesting insights for different ability levels. To overcome these issues, this research suggests the use of the functional analysis of variance approach and a novel functional tool in the IRT context. The main advantages of this approach are that it is distribution-free and allows us to check the degree of consistency with the hypothesis of equality among mean curves for different ability levels. Specifically, the proposed method is applied on ICCs and IICs for improving the existing techniques in the educational studies. A real dataset drawn from the IPRASE Trentino Language Testing Survey 2016 is considered. The final purpose of this study is to provide additional tools for scholars and practitioners in defining specific educational plans.

Suggested Citation

  • Fabrizio Maturo & Francesca Fortuna & Tonio Di Battista, 2019. "Testing Equality of Functions Across Multiple Experimental Conditions for Different Ability Levels in the IRT Context: The Case of the IPRASE TLT 2016 Survey," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 19-39, November.
    • Handle: RePEc:spr:soinre:v:146:y:2019:i:1:d:10.1007_s11205-018-1893-4
    DOI: 10.1007/s11205-018-1893-4
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Natasha Rossi & Xiaohui Wang & James O. Ramsay, 2002. "Nonparametric Item Response Function Estimates with the EM Algorithm," Journal of Educational and Behavioral Statistics, , vol. 27(3), pages 291-317, September.
    3. Ssu-Kuang Chen & Fang-Ming Hwang & Sunny Lin, 2013. "Satisfaction Ratings of QOLPAV: Psychometric Properties Based on the Graded Response Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(1), pages 367-383, January.
    4. Rizopoulos, Dimitris, 2006. "ltm: An R Package for Latent Variable Modeling and Item Response Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i05).
    5. Brian O’Connor & Maxine Crawford & Mark Holder, 2015. "An Item Response Theory Analysis of the Subjective Happiness Scale," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 124(1), pages 249-258, October.
    6. J. Ramsay, 1991. "Kernel smoothing approaches to nonparametric item characteristic curve estimation," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 611-630, December.
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    1. Ventre, Viviana & Martino, Roberta & Cruz Rambaud, Salvador & Maturo, Fabrizio & Porreca, Annamaria, 2024. "An original approach to anomalies in intertemporal choices through functional data analysis: Theory and application for the study of Hikikomori syndrome," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).

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    Keywords

    IRT; ICC; IIC; FANOVA; P-Statistic;
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