Abstract
The Gifi system is a powerful and flexible framework for exploratory multivariate data analysis. It is especially attractive for categorical input data or, more general, input variables with mixed scale levels. At the core of Gifi is the idea of optimal scaling, introduced in the first part of this chapter. Subsequently, two of the most prominent Gifi models are presented. The first model is called Princals. In its basic form, it is a principal component analysis variant for ordinal input data. The second model is called Homals which performs multiple correspondence analyses. Both models can be extended in various directions. In this chapter we focus on a combined Homals-Princals strategy for input data with mixed scale levels. In the last part, another optimal scaling approach called Lineals is introduced which can be used as a preprocessing tool for factor analysis and structural equation models with categorical indicators.
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Notes
- 1.
We could argue that with ordinal Princals we did the “right thing”, since it is certainly safer to treat the data as ordinal.
- 2.
Note that in Homals the same issues apply as in single and multiple CA when it comes to interpreting distances between categories of different items (see Sect. 7.1.2 for details).
- 3.
A “copy” is literally a copy of a variable, achieved by adding it to the input matrix, as the function does internally.
- 4.
Of course, the multivariate normality assumption implies linearity.
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Mair, P. (2018). Gifi Methods. In: Modern Psychometrics with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-93177-7_8
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DOI: https://doi.org/10.1007/978-3-319-93177-7_8
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