A multilevel finite mixture item response model to cluster examinees and schools

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• 作者：Michela Gnaldi ; Silvia Bacci…
• 关键词：EM algorithm ; INVALSI Tests ; Latent class model ; Multilevel multidimensional item response models ; Two ; parameter logistic model
• 刊名：Advances in Data Analysis and Classification
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：10
• 期：1
• 页码：53-70
• 全文大小：486 KB
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• 作者单位：Michela Gnaldi (1)
  Silvia Bacci (2)
  Francesco Bartolucci (2)
  
  1. Department of Political Sciences, University of Perugia, via A. Pascoli, 20, 06123, Perugia, Italy
  2. Department of Economics, University of Perugia, via A. Pascoli, 20, 06123, Perugia, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistical Theory and Methods
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Statistics for Life Sciences, Medicine and Health Sciences
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Statistics for Social Science, Behavorial Science, Education, Public Policy and Law
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1862-5355

文摘

Within the educational context, a key goal is to assess students’ acquired skills and to cluster students according to their ability level. In this regard, a relevant element to be accounted for is the possible effect of the school students come from. For this aim, we provide a methodological tool which takes into account the multilevel structure of the data (i.e., students in schools) and allows us to cluster both students and schools into homogeneous classes of ability and effectiveness, and to assess the effect of certain students’ and school characteristics on the probability to belong to such classes. The proposed approach relies on an extended class of multidimensional latent class IRT models characterised by: (i) latent traits defined at student and school level, (ii) latent traits represented through random vectors with a discrete distribution, (iii) the inclusion of covariates at student and school level, and (iv) a two-parameter logistic parametrisation for the conditional probability of a correct response given the ability. The approach is applied for the analysis of data collected by two national tests administered in Italy to middle school students in June 2009: the INVALSI Language Test and the Mathematics Test.