Principal component analysis (PCA)

 

PCA is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. This transformation is defined in such a way that the first principal component has as high a variance as possible (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it be orthogonal to (uncorrelated with) the preceding components. Principal components are guaranteed to be independent only if the data set is jointly normally distributed.

Factor Analysis or Principal Components Analysis

If your purpose is to reduce the information in many variables into a set of weighted linear combinations of those variables, use Principal Components Analysis (PCA), which does not differentiate between common and unique variance.

If your purpose is to identify the latent variables which are contributing to the common variance in a set of measured variables, use Factor Analysis (FA), which will attempt to exclude unique variance from the analysis.

Scores

 

If subjects’ ID variable is specified, score for each subject will be saved to a tab delimited text file.

 

Below is the sample input window

 

 

 

Below is the sample output of the above model:

 

Principal component analysis

Call:

princomp(x = tmp.xx, scores = TRUE)

 

Standard deviations:

   Comp.1    Comp.2    Comp.3    Comp.4    Comp.5    Comp.6    Comp.7

22.415761 11.387252  9.686490  9.077332  6.296622  4.988263  4.589976

 

 7  variables and  30 observations.

Importance of components:

                          Comp.1     Comp.2    Comp.3     Comp.4     Comp.5

Standard deviation     22.415761 11.3872521 9.6864899 9.07733239 6.29662167

Proportion of Variance  0.562068  0.1450507 0.1049578 0.09217187 0.04435036

Cumulative Proportion   0.562068  0.7071187 0.8120765 0.90424841 0.94859877

                           Comp.6     Comp.7

Standard deviation     4.98826289 4.58997585

Proportion of Variance 0.02783432 0.02356691

Cumulative Proportion  0.97643309 1.00000000

 

Loadings:

           Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7

RATING     -0.447  0.422 -0.240  0.126  0.201 -0.472  0.534

COMPLAINTS -0.521  0.372 -0.143 -0.108 -0.372        -0.647

PRIVILEGES -0.376         0.651 -0.626                0.173

LEARNING   -0.421 -0.146  0.186  0.485  0.621  0.302 -0.235

RAISES     -0.376 -0.233 -0.224  0.104 -0.447  0.593  0.437

CRITICAL   -0.130 -0.398 -0.633 -0.517  0.378        -0.115

ADVANCE    -0.229 -0.666  0.110  0.258 -0.295 -0.577      

 

               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7

SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000

Proportion Var  0.143  0.143  0.143  0.143  0.143  0.143  0.143

Cumulative Var  0.143  0.286  0.429  0.571  0.714  0.857  1.000

 

Scores for each ID will be saved into an .xls file:

 

Empower also output following biplot of component 1 versus 2, and a scree plot.