The Comparison of Item Parameters Estimated From Parametric and Nonparametric Item Response Theory Models in Case of The Violance of Local Independence Assumption

Abstract

Item response theory(IRT) has so many advantages than its precedent Classical Test Theory(CTT) such as non-changing item parameters, ability parameter estimations free from the items. However, in order to get these advantages, some assumptions should be met and they are; unidimensionality, normality and local independence. However, it is not always so easy to be met these assumptions by datasets. Especially when the normality of data is not provided, another approach for IRT can be applied, which is Non-Parametric Item Response Theory (NIRT). NIRT provides more flexible methods to scale datasets and it is used when the assumptions of Parametric Item Response Theory (PIRT) are not met at a satisfactory level. The assumption of local independence, is one of the situations in which NIRT can be used more effectively than PIRT. In this study, by using a real dataset, taken from TIMSS 2011, the effect of local dependence on the item parameters was investigated. With this goal, a dataset composed of 1,000 students was formed randomly from the TIMSS 2011 eight grade Mathematic test. Firstly, the item parameters were calculated from data set according to the two approaches without any manipulation. After that, two items were arranged as local dependent by changing the response patterns completely the same and the item parameters have been estimated from each sample by using R program, ltm and mokken packages. Two sets of item parameters estimated from data set were compared and the differences of the parameters were analyzed with statistical test. By this way, the effect of local independence has been analyzed on the item parameters have been decided.