%Candace Metoyer
%Stat 135
%Chapter 9 Demos

%EXAMPLE 9.9
%Rotated Loadings for the Consumer-Preference Data

clear;
clc;
format compact;
format short g;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Example 9.9
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

p = 5;

%Enter the correlation matrix

R1 = [1 .02 .96 .42 .01];
R2 = [.02 1 .13 .71 .85];
R3 = [.96 .13 1 .5 .11];
R4 = [.42 .71 .50 1 .79];
R5 = [.01 .85 .11 .79 1];

R = [R1;R2;R3;R4;R5];

[ellV, psiV]  = factoran(R,2,'xtype', 'cov','rotate', 'varimax')

%compute the communalities

hV = 1 - psiV

%obtain the MLEs for the eigenvalues using the fact on page 487
lambdaMLE(1) = (norm(ellV(:,1)))^2;
lambdaMLE(2) = (norm(ellV(:,2)))^2;

%compute cumulative proportion total standardized sample variance explained

cpercentMLE(1) = lambdaMLE(1)/p;
cpercentMLE(2) = sum(lambdaMLE(1:2))/p;
cpercentMLE