Correlation matrix for Thurstone's 26 hypothetical box attributes.
Correlation matrix for Thurstone's 26 hypothetical box attributes. The so-called Thurstone invariant box problem contains measurements on the following 26 functions of length, width, and height. Box26 variables:
x^2 * y
x * y^2
x^2 * z
x * z^ 2
y^2 * z
y * z^2
2x + 2y
2x + 2z
2y + 2z
sqrt(x^2 + y^2)
sqrt(x^2 + z^2)
sqrt(y^2 + z^2)
sqrt(x^2 + y^2 + z^2)
x Box length
y Box width
z Box height
Two data sets have been described in the literature as Thurstone's Box Data (or Thurstone's Box Problem). The first consists of 20 measurements on a set of 20 hypothetical boxes (i.e., Thurstone made up the data). Those data are available in Box20. The second data set, which is described in this help file, was collected by Thurstone to provide an illustration of the invariance of simple structure factor loadings. In his classic textbook on multiple factor analysis (Thurstone, 1947), Thurstone states that “[m]easurements of a random collection of thirty boxes were actually made in the Psychometric Laboratory and recorded for this numerical example. The three dimensions, x, y, and z, were recorded for each box. A list of 26 arbitrary score functions was then prepared” (p. 369). The raw data for this example were not published. Rather, Thurstone reported a correlation matrix for the 26 score functions (Thurstone, 1947, p. 370). Note that, presumably due to rounding error in the reported correlations, the correlation matrix for this example is non positive definite.
Thurstone, L. L. (1947). Multiple factor analysis. Chicago: University of Chicago Press.
Other Factor Analysis Routines:
data(Box26) fout <- faMain(R = Box26, numFactors = 3, facMethod = "faregLS", rotate = "varimax", bootstrapSE = FALSE, rotateControl = list( numberStarts = 100, standardize = "none"), Seed = 123) summary(fout) # We now choose Cureton-Mulaik row standardization to reveal # the underlying factor structure. fout <- faMain(R = Box26, numFactors = 3, facMethod = "faregLS", rotate = "varimax", bootstrapSE = FALSE, rotateControl = list( numberStarts = 100, standardize = "CM"), Seed = 123) summary(fout)
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