GROUP I Factor Analysis

Factor Analysis – SPSS

Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations

within a set of observed variables. Factor analysis is often used in data reduction to identify a small number

of factors that explain most of the variance observed in a much larger number of manifest variables. Factor

analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for

subsequent analysis (for example, to identify collinearity prior to performing a linear regression analysis).

Data. The variables should be quantitative at the interval or ratio level. Categorical data (such as religion or

country of origin) are not suitable for factor analysis. Data for which Pearson correlation coefficients can

sensibly be calculated should be suitable for factor analysis.

Assumptions. The data should have a bivariate normal distribution for each pair of variables, and

observations should be independent.

Extraction method. Allows you to specify the method of factor extraction.

Analyze. Allows you to specify either a correlation matrix or a covariance matrix.

Extract. You can either retain all factors whose eigenvalues exceed a specified value or retain a specific

number of factors.

Display. Allows you to request the unrotated factor solution and a scree plot of the eigenvalues.

Maximum Iterations for Convergence. Allows you to specify the maximum number of steps the

algorithm can take to estimate the solution.

Rotation method. Allows you to select the method of factor rotation.

Display factor score coefficient matrix. Shows the coefficients by which variables are multiplied to

obtain factor scores. Also shows the correlations between factor scores.

Missing Values. Allows you to specify how missing values are handled. The available alternatives are to

exclude cases listwise, exclude cases pairwise, or replace with mean.

Coefficient Display Format. Allows you to control aspects of the output matrices. You sort coefficients by

size and suppress coefficients with absolute values less than the specified value.

Communalities indicate the amount of variance in each variable that is accounted for.

                                     Communalities

	Initial	Extraction
4-year resale value	1.000	.906
Price in thousands	1.000	.931
Engine size	1.000	.805
Horsepower	1.000	.880
Wheelbase	1.000	.837
Width	1.000	.758
Length	1.000	.783
Curb weight	1.000	.870
Fuel capacity	1.000	.749
Fuel efficiency	1.000	.705

Extraction Method: Principal Component Analysis.

Each number represents the correlation between the item and the unrotated factor .These correlations can help you formulate an interpretation of the factors or components. This is done by looking for a common thread among the variables that have large loading for a particular factor or component.

It is possible to see items with large loadings on several of the unrotated factors, which can make

interpretation difficult. In these cases, it can be helpful to examine a rotated solution.

Rotation is a method used to simplify interpretation of a factor analysis.

                              

 Component Matrix(a)

 

	Component
	1	2
4-year resale value	.558	.771
Price in thousands	.681	.683
Engine size	.881	.169
Horsepower	.808	.476
Wheelbase	.652	-.642
Width	.800	-.345
Length	.712	-.525
Curb weight	.916	-.175
Fuel capacity	.839	-.215
Fuel efficiency	-.839	.024

Extraction Method: Principal Component Analysis.

a  2 components extracted.

When trying to interpret the first factor, we can see that all variables that measure in one way or

another (yellow) are highly correlated with this factor.

By

Sushilkumar Balvir (Group I)

www.cs.uu.nl/docs/vakken/arm/SPSS/spss7.pdf