Modelos complementarios al Análisis Factorial en la construcción de escalas ordinales: un ejemplo aplicado a la medida del Clima Social Aula

Abstract

It is well known that factor analysis (FA) by principal components is one of the statistical models more frequently used in educational research to study the properties of scales of measurement. The generalised use of FA extends also to non-metric scales (such as categorical and ordinal scales), yet the properties of such scales do not meet the requirements of factor analysis (such as normal distributions and linear relationships between variables). Several problems are thus generated, but there are a number of techniques for solving to some extent the imperfect application of the FA model to nonmetric data. Some of the most important models are briefly described: parallel analysis or factor analysis using item response theory. The joint use of multivariate models of interdependence for dimensionality reduction, such as non-linear principal component analysis (NLPCA), non-metric multidimensional scaling (NM-MDS) and cluster analysis (CA), is proposed as a possible solution, because all these models can be considered appropriate for use with ordinal scales. An example of the combined, complementary use of NM-MDS and CA is shown, together with FA by principal components, to study a Likert scale concerning classroom social climate that was prepared in a prior research project. The results show that the models are significantly more fit for the data, and the internal dimension solution is more parsimonious and consistent with the underlying idea that lay at the origin of the scale.