피험자 표준화 적합도 지수를 이용한 무선추측 문항반응 유형분석

초록

The purpose of this study is to compare the relative power of five person-fit indicies UWZ, Uz, Lz, ECI2, ECI4, under the one selected type of aberrant response patterns, namely random guessing using the Rasch model. The procedures utilized in this study involve simulated data. First, to conduct a simulation study person/item generation program called the SIMTEST(Luppescu,1993) was used to create random response patterns. And then, to compute the probabilities of observed scores, the ability and difficulty parameters were estimated by the BIGSTEPS computer program (Linacre & Wright,1993) for each examinee and item. Second, the IRT parameters were used to calculate unweighted/weighted standardized fit index using BIGSTEPS computer program, standardized likelihood index, ECI2z and ECI4z using RASCHFIT computer program (Walker & Seol,1997). In order to compare the power of the five fit indices when random guessing are introduced, responses were simulated to fit the model by SIMTEST computer program. Two equal-size groups (reference vs focal) were designated in which the number of persons in the reference and focal group were set at 500 each. The total number of items was also set at 50 The distribution of person abilities in the reference and focal group was assumed to be normal, with a standard deviation of 1 logit. The item difficulties for the reference and focal group had uniform distribution with a standard deviation of 1 logit. To simulate guessing problem, the probability of a correct response was set to 0.25. This value usually occurs the difference between person abilities and item difficulties was less than -1.0 logit. Responses for the focal group were generated with item difficulties 0.5 logits more difficult than the item difficulties used with the reference group. The two groups were then combined for the analysis. To increase the amount of guessing in the data the mean ability of the focal group was decreased from 0.0 to -1.0 logits in 0.5 logit steps while the mean ability of the reference group was held constant at 0.0 logits. The findings of this study indicates that the five person-related fit indices are reasonably sensitive with respect to their capability for detecting responses with guessing problems. The seeming lack of absolute power in the five standardized fit indices may be due to the fact that even for the person affected by the random measurement disturbances, their responses generated from SIMTEST computer program appeared to fit the model. Nonetheless, the ECI2z and ECI4z indices appear somewhat more sensitive to the presence off guessing compared to the other three indicies. These findings also partially support the results of Birenbaum (1985) and Seol (1998). In the light of the findings of this study, the following recommendations may be useful in carrying out similar studies. First, it is recommended that this study be replicated to investigate the properties of fit indicies based on polytomous model because the distributional properties, power and interpretation of fit indices for polytomous model is a recent development. Second, With respect to the ECI2z and EC!4z indices, the natures of these two indices should be taken into consideration when a choice of one of them to be used in a specific situation is to be made. With regard to this, for example, Tatuoka & Linn (1983) suggested the ECI4z index can be useful index for diagnosing purpose. Additional work is needed in selecting the appropriate index that fits the specific needs for the person fit measure.