factorm.m

function [hatH, hatB, hmu] = factorm(X, q, centeredX)
%----------------------------------------------------------------------------------
% Author:       Liu Wei
% Maintainer:    Liu Wei <weiliu@smail.swufe.edu.cn>
% Date:         Jan. 13, 2018
% Copyright (c) 2018, Liu Wei
% All rights reserved.
% Linear factor model to estimate latent factor matrix and loading matrix.

if(~exist('centeredX', 'var'))
    centeredX = 1;
end

n = size(X, 1);
hmu = zeros(size(X,2),1);
if(~centeredX)
   hmu = mean(X);
   X = X - repmat(hmu, n, 1);
   hmu = hmu';
end
[evec,~] = eig(X*X');
hatH = evec(:, end:-1:end-q+1)* sqrt(n);
hatB = X'*hatH/n; % ensure B'B is a diagonal matrix with decreasing order 
sB = sign(hatB(1,:));
hatB = hatB * diag(sB);
hatH = hatH * diag(sB); % ensure F is unqiue (A2) condition
cF = cov(hatH, 0);
hatH = (hatH - repmat(mean(hatH),n,1))*cF^(-1/2);
end