Statistics Toolbox

Predicting Factor Scores

Sometimes, it is useful to be able to classify an observation based on its factor scores. For example, if you accepted the three-factor model and the interpretation of the rotated factors, you might want to categorize each week in terms of how favorable it was for each of the three stock sectors, based on the data from the ten observed stocks.

Since the data in this example are the raw stock price changes, and not just their correlation matrix, you can have factoran return estimates of the value of each of the three rotated common factors for each week. You can then plot the estimated scores to see how the different stock sectors were affected during each week.

• [LoadingsPM,specVarPM,TPM,stats,F] = factoran(stocks, 3,...
                                       'rotate','promax');
  subplot(1,1,1); 
  plot3(F(:,1),F(:,2),F(:,3),'b.');
  line([-4 4 NaN 0 0 NaN 0 0], [0 0 NaN -4 4 NaN 0 0],...
       [0 0 NaN 0 0 NaN -4 4], 'Color','black');
  xlabel('Financial Sector'); 
  ylabel('Retail Sector'); 
  zlabel('Technology Sector');
  grid on; 
  axis square;
  view(-22.5, 8);
  
  
  

Oblique rotation often creates factors that are correlated. This plot shows some evidence of correlation between the first and third factors, and you can investigate further by computing the estimated factor correlation matrix.

• inv(TPM'*TPM)
  ans =
         1.0000    0.1559    0.4082
         0.1559    1.0000   -0.0559
         0.4082   -0.0559    1.0000
  

Factor Rotation

Comparison of Factor Analysis and Principal Components Analysis