Model-Data Fit using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and The Sample-Size-Adjusted BIC

The study determined if the 1PL, 2PL, 3PL and 4PL item response theory models best fit the data from the 2016 NECO Mathematics objective tests. Ex-post facto design was adopted for the study. The population for the study comprised 1,022,474 candidates who enrolled and sat for June/July SSCE 2016 NECO Mathematics Examination. The sample comprised 276,338 candidates who sat for the examination in three purposively Geo political zones in Nigeria (i.e., S/West, S/East and N/West). The research instruments used for the study were Optical Marks Record Sheets for the National Examination Council (NECO) June/July 2016 SSCE Mathematics objectives items. The responses of the tests were scored dichotomously. Data collected were analyzed using 2loglikelihood chi-square. The results of the likelihood ratio test revealed that 2PL fitted the data better than 1PL was statistically significant (χ2 (59) = 820636.1, p 0.05); the 2PL model fitted the data better than the 1PL model; 3PL model fitted the data better than the 2PL model and the result showed that the 4PL model fitted the data better than the 3PL model and the Likelihood ratio test that 4PL model fitted the data better than 3PL model was statistically significant, (χ2(60)=216159.2, p0.05). The study concluded that four-parameter logistic model fitted the 2016 NECO Mathematics test items.Keywords: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), one parameter model, two parameter model, three parameter model, four parameter model.