Investigation of the effect of assigning data of missing data at different rates with different assignment methods on differential item functioning with methods based on item response theory

In this study, it was aimed to examine the effects of regression imputation (RI), multiple imputation (MI) and k-nearest neighbor (kNN) methods on the differential item functioning (DIF), which are missing data assignment methods. In this direction, the data sets used in the research were created by deleting the data under the missing completely at random (MCAR) mechanism on the complete data sets obtained from 600 students in Turkey, the United Kingdom, the USA, New Zealand and Australia who answered the booklet numbered 14 and 15 from the PISA2018 science literacy test. Data were assigned to the datasets with missing data by RI, MI and kNN methods, and to all datasets, Lord's   method, Raju's field measurements method and item response theory probability Ratio (IRT-LR) DIF analysis was performed according to language and gender variables using the method. The DIF results obtained in the full datasets were taken as reference and compared with the results obtained from other datasets. As a result of the research, in the RI assignment method, in accordance with the DIF analysis made according to the language variable, 10% better results were obtained compared to the other rates, and determinations were made close to the correct result. While it was seen that relatively accurate results were obtained at the rate of 5%, 20% and 30%, poor results were obtained at the rates of 20% and 30%. Although values close to the correct result were obtained at a rate of 10% according to the gender variable with the RI method, wrong results were obtained at other rates. In MI and kNN methods, according to the language variable, the closest results to the full data set were obtained at 5% missing data rate, while it was seen that more accurate estimations were made at 20% missing data rate than 10% and 30% missing data rates. In the MI method, it was determined that wrong results were obtained in all missing data rates according to the gender variable. According to the gender variable, according to the DIF analysis, it was seen that the kNN method gave correct results at 5% and 10% missing data rates, but wrong estimations were made at 20% and 30% rates. It has been revealed that RI, MI and kNN methods, and 5% missing data rate, in determining DIF according to the language variable, findings close to the full data set of MI and kNN methods were reached, while the RI method gave erroneous results compared to other methods. While the closest result to the full data set was obtained in the RI method according to the language variable at 10% missing value, it was determined that erroneous findings were obtained in the MI and kNN methods. As a result of 20% of the DIF analysis according to the language variable, although MI and kNN methods yielded the same results, they did not provide sufficient estimation to detect DIF, while more inaccurate values were determined in the RI method compared to these methods. Although similar results were obtained for the three methods according to the language variable at the rate of 30% missing value, correct answers could not be obtained. As a result of the DIF analysis for the gender variable at the rate of 5%, DIF could not be determined in any item in the CA and RA methods, while the same result was obtained with the full data set in the kNN method. While erroneous results were obtained in the MI method at a rate of 10% according to the gender variable, correct estimations were made in the RI and kNN methods. Accurate results could not be obtained in all three methods (RI, MI, kNN) according to the gender variable at 20% and 30% undervalued rates. Keywords: Differential item functioning, missing data, item response theory, Raju's Area Measurement, Likelihood ratio