Generalized partial credit and graded response models in polytomous mathematics achievement test items in ability estimation in Lagos State
The study examined the difficulty and discrimination indices of polytomous items using dichotomous scoring. It determined the effect of the systematic increase in the response levels of polytomous items on ability estimates in Generalized Partial Credit Model (GPCM) and Graded Response Model (GRM). It further compared the scores of GPCM and GRM on the accuracy of ability estimates and investigated which of the scoring formats was more effective in estimating ability. These were with a view to providing information on the ability of GPCM and GRM in improving the accuracy of scores in polytomous Mathematics achievement test items. The study adopted the survey research design. The population for the study consisted of students who registered for the Senior School Certificate Examination (SSCE) in Lagos State in 2015. A sample of 1015 students was selected. Two Education Districts (EDs) were selected using purposive sampling technique from the six EDs in the State based on availability of federal schools for an inclusive representation of schools. Three schools were selected from each of the EDs using stratified random sampling technique with school ownership as stratum for selection. One intact SS III class from each of the schools was selected using purposive sampling technique based on students’ ability groups. The instrument used in the study was an adapted version of May/June (2006-2014) SSCE General Mathematics Paper 1 titled Mathematics Achievement Test (MAT). Data collected were analysed using ANOVA and Pearson-r. Furthermore, BILOG and IRTPRO were used to generate item parameters of difficulty, discrimination and guessing. The results showed the difficulty and discrimination indices of polytomous items using two different formats. Using dichotomous scoring in the first format difficulty and discrimination indices were high (-0.73 to 1.95 and 0.38 to 1.72 respectively) while they were higher in the second format (0.09 to 3.33 and 0.43 to 1.85 respectively). The results also showed that there was a significant effect of the systematic increase in the response levels of the items in GPCM on Mathematics ability estimates (F= 3.98, p<0.05) in the first format, while there was no significant effect in the second format (F=3.16, p>0.05). The results further showed that there was a significant effect of the systematic increase in the response levels of the items in GRM on Mathematics ability estimates (F= 22.46, p<0.05 and F = 31.55, p<0.05) in the first and second formats respectively. Furthermore, GPCM estimated ability more accurately than GRM (r = 0.22, p<0.05). Finally, the results indicated that the first format which contained items with one partially correct answer, one full correct answer and two distracters was more effective in estimating ability (r = 0.22, p<0.05). The study concluded that Generalized Partial Credit Model had greater ability than Graded Response Model in improving the accuracy of scores in polytomous Mathematics achievement test items.