Le Bras (1974) has given the following (artificial) data from neuropsychology concerning certain functions which are hypothetically performed in specific areas of the brain's right hemisphere:
To discover if a function is not performed, presumably due to a tumor, hemmorhage, and so on, individuals are given 25 tests where "pass" = 0 and "fail" = 1. The areas where the functions are performed however are not known-all we have are the outcomes of the tests. Assuming the right hemishpere consists of 25 specific connected areas located on a grid, we wish to assign each of the 25 tests to a location on the grid.
(a) Using principal components estimate the underlying grid structure of the p = 25 variables. How many dimensions are required to estimate the structure? Confirm by plotting the variables in the common factor space.
(b) Using principal axes (Section 8.5) repeat the exercise of part a. Plot the variables and individuals in the common factor space.