Yarı Karışık Yapılı Çok Boyutlu Yapıların Tek Boyutlu Olarak Ele Alınması Durumunda Kestirilen Parametrelerin İncelenmesi

Abstract

This study investigates the errors resulted from unidimensional estimation of multidimensional semi-mixed structured tests. To this end, a research design was prepared to include various conditions such as test structure, number of dimensions, interdimensional correlation, test difficulty and different distributions. The research design involves 168 cells and additionally, unidimensional estimation of unidimensional data was conducted with the purpose of evaluating the errors emerged in case of unidimensional estimation of multidimensional structured tests. Parameters of multidimensional structures were used to form a unidimensional test. Under all conditions, values were fixed to 30 for test length and 5000 for sample size. BILOG program, which relies on unidimensionality assumption, was used for parameter estimation. RMSE (Root Mean Square Error) statistic was used for the evaluation of errors associated with the estimated parameters. The lowest errors were obtained from 0.45 correlation for parameters a1 and a2 in two-dimensional tests. Errors of MDISC which is equivalent to discrimination parameter of unidimensional IRT were relatively higher than other discrimination parameters, yet the pattern was similar with the results reported in the literature. While mean item discrimination had a similar pattern as parameters a1 and a2, it was estimated with less errors compared to both of the parameters. Under conditions where the number of complex items was more than the number of approximately simple items, errors obtained for a1 and a2 and MDISC were generally lower. In cases when the number of approximately simple items was higher, the effect of distributions was greater while this effect decreased as the number of complex items increased. In general terms, it can be said that high or medium test difficulty did not affect discrimination parameters. A particular distribution which was differentiated for parameter b related to ability had no importance while degree of differentiating the distribution came into prominence. As interdimensional correlation increased, effect of distributions decreased. RMSE values of difficulty parameter decreased as interdimensional correlation increased under most of the conditions. In general, as the number of complex items increased, errors associated with estimates of parameter b decreased. It was found that errors obtained from high-difficulty test were much higher than those in medium-difficulty test. In addition, it can be said that errors estimated for medium or high difficulty tests closed up as interdimensional correlation increased. The obtained errors were found larger under conditions where distribution differentiated more for ability parameter in two-dimensional tests. As interdimensional correlation increased, errors of ability parameters decreased. No pattern related to the increased number of complex items in two-dimensional tests was observed to be generalized for all ability parameters. Errors of θavg. calculated through the mean values of θ1 and θ2 were found smaller than the errors of these two parameters. In general it can be said that the difficulty of the test impacted the ability parameters, the errors obtained for difficult test were higher than those in medium-difficulty tests. RMSE values associated with parameters a1, a2, a3 and a mean increased as interdimensional correlation increased in three dimensional tests. aavg. calculated based on the mean values of three other parameters was estimated with the smallest error. Under conditions where interdimensional correlation was 0.90, errors increased as the number of complex items increased; while errors decreased in other correlations. In addition, patterns related to the number of complex items in MDISC and for other discrimination parameters were just opposite to each other. In general terms, it can be said that different distributions and high or medium test difficulty did not affect discrimination parameters. The most remarkable factor in parameter b in three-dimensional structures was the effect of factor distributions as in two-dimensional structures. At this point, which distribution is differentiated was not important while errors of parameter b increased based on the degree of change in mean values. As the number of complex items increased, errors of parameter b decreased except for the conditions where distributions were standard normal. Similarly, when the test was difficult, a sudden increase emerged in the errors associated with parameter b under conditions where especially distributions were standard normal. In general, it can be said that RMSE values of difficulty parameter decreased as interdimensional correlation increased. As interdimensional correlation increased, errors decreased for ability parameter in three-dimensional structures. No regular pattern was obtained related to the increase in the number of complex items in all ability parameters. RMSE values of the dimension whose distribution was differentiated were estimated high as in two-dimensional structures and a slight decrease was observed in the other. It was found that errors of θavg. were smaller than those of three other abilities.