Comparison of Kernel equating results according to properties of covariates

In this research, "What kind of covariate should we use in NEC design?" search for an answer to the question. For this purpose, the path model in which the mean score and equating errors equating with Kernel are internal, the covariates' properties are external, and the rate of variance explained in the regression model in equating is both internal and external variable. In the research, TIMSS 2019 mathematics 8th-grade in Turkey, France, Switzerland and America datasets (Phase-1); 4th-grade in Canadian dataset (Phase-2). The RStudio interface was used for all analyzes whose data were arranged with the IEA IDB Analysis Program. Hot-deck imputation has been made for coping with missing data. 114 equalizations were made in Phase 1 and 126 in Phase 2, and the results were used in the path analysis after removing the outliers. As a result of the research, standard errors were lower in the results of NEAT design in CTT, and the equating mean scores in IRT were higher. The results in NEC design, in which the common items are used as a covariate, are similar to NEAT design, especially when the anchor item has three or five categories. When phases are considered together, the difference between the frequency distributions is the absolute value of the relationship between the test scores and the covariate; The absolute value of the skewness and kurtosis of the covariate and the explained variance proportion of the regression model established with the covariate in the P and Q populations significantly affect the equating results.