Higher-order factor analysis
Encyclopedia
Higher-order factor analysis is a statistical method consisting of repeating steps factor analysis
– oblique rotation – factor analysis of rotated factors... Its merit is to enable the researcher to see the hierarchical structure of studied phenomena. To interpret the results, one proceeds either by post-multiplying
the primary factor pattern matrix by the higher-order factor pattern matrices (Gorsuch, 1983) and perhaps applying a Varimax rotation
to the result (Thompson, 1990) or by using a Schmid-Leiman solution (SLS, Schmid & Leiman, 1957, also known as Schmid-Leiman transformation) which attributes the variation
from the primary factors to the second-order factors.
Factor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
– oblique rotation – factor analysis of rotated factors... Its merit is to enable the researcher to see the hierarchical structure of studied phenomena. To interpret the results, one proceeds either by post-multiplying
Matrix multiplication
In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. If A is an n-by-m matrix and B is an m-by-p matrix, the result AB of their multiplication is an n-by-p matrix defined only if the number of columns m of the left matrix A is the...
the primary factor pattern matrix by the higher-order factor pattern matrices (Gorsuch, 1983) and perhaps applying a Varimax rotation
Varimax rotation
In statistics, a varimax rotation is a change of coordinates used in principal component analysis and factor analysis that maximizes the sum of the variances of the squared loadings...
to the result (Thompson, 1990) or by using a Schmid-Leiman solution (SLS, Schmid & Leiman, 1957, also known as Schmid-Leiman transformation) which attributes the variation
Variation
- Physics :* Magnetic variation, difference between magnetic north and true north, measured as an angle* Variation , any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon- Mathematics :* Bounded variation...
from the primary factors to the second-order factors.
Literature
- http://eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/16/8c/6d.pdf B.T. Gray: Higher-Order Factor Analysis
- Hans-Georg Wolff, Katja Preising: Exploring item and higher order factor structure with the schmid-leiman solution : Syntax codes for SPSS and SAS