DIF analysis using IRT three parameter logistic model of the State Level Achievement Survey data on Environment & Science for grade VII students in West Bengal, India

  • Ankita Dey
  • Rathindranath Dey
Keywords: Ability, Differential item functioning, Item characteristic curve, Item Response Theory, State Level Achievement Survey, Three parameter logistic model, z-scores


A three parameter Item Response Theory (IRT) model is applied to the data on “Utkarsha  Abhiyan”  (UA), a State Level Achievement Survey in school education of West Bengal, India.  The data set contains scores (correct or incorrect) of about

24,000 grade VII students on 40 multiple choice items in the discipline Environment and Science.  There are two sets of items viz.  Set A and Set B created by shuffling the  sequence  of  items.   The  relationship  between  the  ability  of  student  and  the chance  of  giving  correct  answer  to  an  item  is  modelled  probabilistically  through IRT three parameter logistic model.  Differential item functioning (DIF) analysis is performed separately in two different sets of items.  The focal and reference group for  detection  of  DIF  are  taken  to  be  the  rural  and  urban  learners  respectively.  A new methodology using Z-scores to measure the extent of DIF in items is described using  the  data  set.   The  DIF  as  visualised  from  the  Item  Characteristic  Curves (ICCs) are corroborated with the DIF statistic values.  The effect of item shuffling as  observed  in  the  varying  nature  of  DIF  is  discussed.   Probable  explanations  of presence of DIF in some of the items in both the sets are given in the light of item bias  and  multidimensionality  of  ability  space  and  are  considered  as  possible  areas of future research.  The analysis is done by using ltm package in R version 1.0.136.


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