Abstract
Item response theory (IRT) is a framework for modeling and analyzing item response data. Item-level modeling gives IRT advantages over classical test theory. The fit of an item score pattern to an item response theory (IRT) models is a necessary condition that must be assessed for further use of item and models that best fit the data. The study investigated item level diagnostic statistics and model- data fit with one-and two- parameter models using IRTPROV3.0 and BILOG- MG V3.0. Ex-post facto design was adopted. The population for the study consisted of 11,538 candidates’ responses who took Type L 2014 Unified Tertiary Matriculation Examination (UTME) Mathematics paper in Akwa Ibom State, Nigeria. The sample of 5,192(45%) responses was randomly selected through stratified sampling technique. BILOG-MG V3.0 and IRTPROV3.0 computer software was used to calibrate the candidates’ responses. Two research questions were raised to guide the study. Pearson’s χ2 and S - χ2 statistics as an item fit index for dichotomous item response theory models were used. The outputs from the two computer software were used to answer the questions. The findings revealed that only 1 item fitted 1- parameter model in BILOG- MG V3.0 and IRTPRO V3.0. Furthermore, the findings revealed that 26 items fitted 2-parameter models when using BILOG-MG V3.0. Five items fitted 2-parameter models in IRTPRO. It was recommended that the use of more than one IRT software programme offers more useful information for the choice of model that fit the data.KEYWORDS: Item Level, Diagnostics, Statistics, Model - Data Fit, Item Response Theory (IRT).
Highlights
The crucial benefits of item response theory (IRT) models are realized to the degree that the data fit the different models, 1, 2, and 3 parameters
There is an argument that the evaluation of fit in IRT modeling has been challenging, the use of item response theory model checking and item fit statistics serve crucial factors to effective IRT use in psychometrics for information on items and model selections (Reise, 1990; Embretson & Reise, 2000)
The results from research question 1 revealed that IRTPRO V 3.0 and BILOG MG 3.0, exhibited different degrees in the use of S-X2 and X2 diagnostic indices of each item at different IRT models
Summary
The crucial benefits of IRT models are realized to the degree that the data fit the different models, 1-, 2-, and 3 parameters. Model-data fit is a major concern when applying item response theory (IRT) models to real test data. Obtaining evidence of model-data- fit when an IRT model is used to make inferences from a data set is recommended as the standards for educational and psychological testing by the American Association of Educational Research, American Psychological Association, and National Council on Measurement in Education (2014). Failure to meet this requirement invalidates the application of IRT in real data set evaluation. Researches (Orlando and Thissen, 2000, 2003) indicated that model checking
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