Construction of index based on the GSR-5 items using the graded response model

Abstract

This article is about building of the index for GSR-5 items (questions). They а measure general attitudes towards the general welfare state. The simplest way is to calculate an additive index (a total score of the respondent’s answers to GSR-5 items). Such an index is easy to interpret but it has some limitations. Firstly, it assumes that all the questions have the same weight. But it is logical to suppose that this is not always the case. Secondly, it is expected that the distances between the neighboring answer options are the same for each item. However, if we are dealing with variables that are measured on an ordinal scale this condition may not be fulfilled. Therefore, we need an appropriate tool allows us to construct an index that overcomes the limitations are mentioned above. One such a tool is a graded response model; it is designed to work with variables that are measured on an ordinal scale. First of all, it is found out is there appropriate to construct an additive index for GSR-5 items. After building the single factor CFA model (confirmatory factor analysis model) with the same factor loadings for each question it turned out that this model does not show an acceptable fit to the data. Thus, the calculation of the additive index for GSR-5 items is not appropriate. Therefore, there is a need for an alternative model. Since GSR-5 items are measured on an ordinal scale a unidimensional graded response model (GRM model) is applied. It shows a good fit to the data. With the GRM model it is possible to build the index which takes into account different weights of the questions and distances between the answer options for each item. The index is constructed with the graded response model shows more variability than the additive index. In addition the graded response model (in order to facilitate interpretation) allows us to represent values of the latent variable as the additive index values. This is the advantage of the graded response model compared to confirmatory factor analysis models. The latter can also be used as tools for constructing additive indices but they do not provide the transformation of latent variables from the one scale to another.