The Academic Events Group, 6th INTERNATIONAL CONFERENCE ON EDUCATION

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The Comparison of Dimensionality Estimation Methods in Terms of Correlation Matrix, Item Number, Sample Size and Mean Factor Loading
Abdullah Faruk Kilic, Ibrahim Uysal

Last modified: 2017-05-06

Abstract


The aim of this study is to compare the methods which are produced for estimating test dimensionality in terms of correlation matrix, item number, sample size and mean factor loading. Binary (1-0) and unidimensional simulated data were used in this study. The replication number was determined as 20 for each condition. Sample size (500, 1000, 3000 and 7000), item number (20, 30 and 40), mean factor loading (0,50 and 0,70) and correlation matrix (Pearson and tetracoric) were designated as preconditions for simulation. Dimensionality methods of parallel analysis, MAP analysis, CNG index, Bartlet, Anderson and Lawley coefficients, DIMTEST and DETECT methods were compared with each other. Data was produced through Psych package of the R program and analyzed with Pscyh and nFactor packages. However, MAP test was done with the use of Factor 10.4. According to the findings, MAP test was the one which has yielded 100% correct result under all conditions. When a paralel analysis was carried out with tetracoric correlation matrix, 500-people-sample showed 75% correct result in the tests with 20, 30 and 40 items with an average factor loading of 0,5. A paralel analysis has given 75% correct result with a data set of 20 items with an average factor load of 0,8. Three dimensions were identified in CNG coefficient under all conditions and it has yielded 0% accuracy. It has been observed that Bartlet and Anderson indexes have had an average accuracy of 25% and Lawley index has had an average accuracy of 19% under all conditions. DIMTEST has yielded a mean accuracy of 12% while DETECT has shown 0,19%. Since the DETECT value is around 0,1, the data set is thought to be as a unidimensional one. Thus, when the value is analysed accordingly, it has been observed that it has 45% accuracy and it has the tendency to be accurate as the size of the sample increases. According to the findings of the study, it is suggested that MAP test can be used primarily to designate the dimensionality of data and than the results of the paralel analysis could be relied on. Considering the conditions utilized in this research,  the authors do not recommend the use of DIMTEST, Bartlet, Anderson, Lawley and CNG coefficients.