Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: factoranalysis Description: performs factor analysis on the data using three different methods and extracts k factors

Reference(s):
Haerdle, W. and Simar, L. (2002). Applied Multivariate Statistical Analysis. Lecture Notes.

 Usage: {loadings,explained,communalities,specifics,pvalue}=factoranalysis(data,k{,method{,maxiter}}) Input: data n x p data matrix k scalar, number of factors to be extracted. Beware that it can be changed to a lower number so that all loadings can be computed. method optional string defining the method which should be used, "PFM" = Principal Factors Method; "PCM" = Principal Components Method (default); "MLM" = Maximum Likelihood Method maxiter optional integer, maximal number of iterations for PFM or MLM, default is 10. For MLM, 10 is recommended and sufficient since the method is computationally time consuming, for PFM, it can be much more but should not change the results. Output: loadings p x k matrix of estimated factor loadings explained 1 x k vector with proportion of explained variance of the k-th factor communalities p x 1 vector of estimated communalities specifics p x 1 vector; estimated specific variances pvalue optional, result of a likelihood test for H0: SIGMA=loadings*loadings'+diag(specifics), i.e., the model holds. It only works if k is sufficiently small compared to p. Otherwise you get an error warning.

Note:
The extracted number of factors does not necessarily equal the input - it is corrected so that the calculation is possible.

We recommend to perform varimax rotation on the result in order to improve the interpretation of the FA model.

Example:
```library("nummath")
library("xplore")
library("stats")
y=y[,1:10]
b=factoranalysis(y,3,"PFM",10)
b

```
Result:
```Contents of b.loadings
[ 1,]   0.8513 -0.37924 -0.10322
[ 2,]  0.67668  -0.2378   0.5339
[ 3,]  0.61571  0.03942  -0.2804
[ 4,]  0.57424  0.49455  0.037712
[ 5,]  0.80336 -0.37154  0.14977
[ 6,]  0.83119 -0.040257 -0.21215
[ 7,]  0.56891   0.4344  -0.2316
[ 8,]  0.55473  0.17172  0.22624
[ 9,]  0.42994  0.30881 -0.21547
[10,]  0.064053  0.50396  0.50722

Contents of b.explained
[1,]   0.4048  0.11537  0.085172

Contents of b.communalities
[ 1,]  0.87919
[ 2,]  0.79949
[ 3,]  0.45928
[ 4,]  0.57576
[ 5,]  0.80586
[ 6,]   0.7375
[ 7,]    0.566
[ 8,]  0.38839
[ 9,]  0.32664
[10,]  0.51535

Contents of b.specifics
[ 1,]  0.12081
[ 2,]  0.20051
[ 3,]  0.54072
[ 4,]  0.42424
[ 5,]  0.19414
[ 6,]   0.2625
[ 7,]    0.434
[ 8,]  0.61161
[ 9,]  0.67336
[10,]  0.48465

Contents of rotated
[ 1,]  0.90806 -0.095924  0.21312
[ 2,]  0.48177 -0.19221  0.72831
[ 3,]  0.61769   0.2782  0.018456
[ 4,]  0.30753  0.59669  0.35375
[ 5,]  0.77456  -0.1732  0.41944
[ 6,]  0.80842   0.2422  0.15904
[ 7,]  0.41936  0.61619  0.10218
[ 8,]  0.33903  0.24045  0.46436
[ 9,]  0.33813  0.45918  0.038189
[10,] -0.30297  0.33771  0.55634
```

Author: M. Hanek, 20020712 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006