# Factor Analysis

Factor analysis in SPSS means exploratory factor analysis: One or more "factors" are extracted according to a predefined criterion, the solution may be "rotated", and factor values may be added to your data set.

*Example*:

FACTOR | |

/ VARIABLES environ1 environ2 environ3 environ4 environ5 | |

/ PRINT INITIAL EXTRACTION ROTATION KMO AIC CORR REPR | |

/ PLOT EIGEN | |

/ CRITERIA MINEIGEN(1) | |

/ EXTRACTION PC | |

/ ROTATION VARIMAX | |

/ SAVE REG(ALL). |

The above example does the following: It computes the Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett's test of sphericity (these are requested with keyword `KMO`

in the `PRINT`

line). Also, the anti-image covariance and correlation matrices are computed (keyword `AIC`

) which help to judge the "factorabiliy" of the correlation matrix. Keyword `CORR`

prints the initial correlation matrix and `REPR`

the correlation matrix as reproduced by the factor solution. The other keywords in the `PRINT`

subcommand request SPSS to show the initial communalities, the matrix of exctracted factor loadings and the matrix of rotated factor loadings. (These are all default values; but as additional elements are added to the `PRINT`

subcommand, these keywords are necessary; they may be replaced by the keyword `DEFAULT`

).

Then it performs a *principal component* factor analysis (sucommand `EXTRACTION PC`

- other methods of extraction are available, like `PAF`

for [principal] factor analysis), with the number of factors determined by the eigenvalue of the factors (the number of factors extracted will be equal to the number of factors with an eigenvalue of at least 1; again, other criteria are available, for instance a pre-set number of factors, determined, e.g., by a Scree plot or by theoretical considerations). Finally, a varimax rotation is performed and (standardized) factor values as determined by a regression equation are added to the data set (line `SAVE`

. . .). In addition, a Scree plot is requested with line `PLOT EIGEN`

.

The subcommand /FORMAT SORT (not shown in the example above) is a useful option facilitating work with the rotated factor matrix. The variables in the rotated factor matrix are sorted according to their factor loadings for the factors extracted.

Note that the subcommand lines `CRITERIA `

and `EXTRACTION`

are not necessary in this example, as they only give the default values (that is, the respective subcommands are executed anyway). They may remind you, however, that other criteria and other extraction methods are available, even though in practice they are used less frequently.

© W. Ludwig-Mayerhofer, IGSW | Last update: 31 May 2004