INVESTIGATION OF MEASUREMENT PRECISION OF LATENT VARIABLE DEPENDING ON THE RANGE OF VARIATION OF INDICATORS SET - Maslak, A. A.; Moiseev, S. I.; Osipov, S. A.; Pozdnyakov, S. A. (Radio Electronics, Computer Science, Control, 2017)
Context. An important practical aspect of measurement of a latent variable is precision because the efficacy of accepted decisions depends on it. One of possible ways of increasing precision of measurement of latent variables is the choice of best location of a set of indicators. Objective. The objective is the investigation of precision of measurement of a latent variable depending on location of a set of indicators. In order to achieve this goal it is necessary to generate matrices of data based on Rasch model, to obtain estimations of latent variable, and to compare the obtained estimations of a latent variable to those values which were used for modelling. Method. Taking into account that the model of measurement of latent variable is nonlinear, the analytical decision is complicated. Therefore, research was conducted through the simulation experiment within the framework of the theory of measurement of latent variables. Data from the simulation experiment was described by Rasch model for dichotomic indicators and processed using the dialogue system «Measurement of latent variables». Results. Investigation of precision of measurement of latent variable depending on location of a set of indicators was carried out within the framework of the theory of latent variables based on simulation experiment. The analysis of variance has shown that narrowing the range of indicators compared to variation of latent variable raises precision of its measurement with other things being equal. Precision of measurement of latent variable is higher at its center of variation than on the edges irrespective of range of variation of indicators. Conclusions. The technique of the analysis of precision of measurement of latent variable depending on location of indicators is presented. Unlike the existing point of view, that the range of variation of indicators should cover range of variation of latent variable, it is shown that the greatest precision of measurement of latent variable is reached at location of indicators in the middle of range of latent variable with other things being equal. The obtained results are used for the choice of optimum algorithm of adaptive testing. It is of interest to expand research and to estimate influence of other ranges of variation of latent variable and location of set of indicators on precision of measurement.