## Sunday, 4 September 2011

Why do we do factor analysis?

Factor analysis is basically done for two reasons

· For the reduction of variables

· And then grouping of those variables

For example, data on fifty characteristics for 300 nations are unwieldy to handle, descriptively or analytically. The management, analysis, and understanding of such data are facilitated by reducing them to their common factor patterns. These factors concentrate and index the dispersed information in the original data and can therefore replace the fifty characteristics without much loss of information. Nations can be more easily discussed and compared on economic development, size, and politics dimensions, for example, than on the hundreds of characteristics each dimension involves.

Variables are reduced on the basis of correlation between them and Z-score is used as a method of standardization between the variables. All the variables converted into Z-score will have a Mean of zero and standard deviation of one. The distribution of Z-score values will remain the same as in the original values.

After all this is done SPSS does the data reduction for all the scale variables. Ordinal variables can also be used but nominal variables cannot be used.

In the output table, communalities table is one of the critical elements for factor analysis which shows the common variance which each component can extract from other components. Higher values mean the commonness is more and hence factor analysis can be used. The new variables now produced can be used in some other procedure. Higher the correlation between the variables, the better it is.

THUMB RULE: When a variable has lower extraction value (<0.5), it is to be removed from the analysis.

Rotation is another critical element for factor analysis. It is a method to equalize the variance among the variables in order to identify the dominant variables. The dominant variables which have the highest cumulative variance are the most important variables for the purpose of analysis as they are the only variables which will be considered for the future analysis purposes.

Scree Plot:

The plot looks like the side of a mountain, and "scree" refers to the debris fallen from a mountain and lying at its base. So the scree test proposes to stop analysis at the point the mountain ends and the debris (error) begins.

Thumb Rule: Consider only those with eigenvalues over 1. Another rule of thumb is to plot all the eigenvalues in their decreasing order.

Looking at the ‘Rotated Component Matrix’, the components with values greater than 0.5 can be identified and can be bundled into different groups and each group is now a new factor. Now in order to form clusters based on these factors, K- means clustering can be done.

Application of factor analysis in finance

Financial ratio analysis is a useful measure to provide a snapshot of a firm’s financial position at any particular moment of time or to provide a comprehensive idea about the financial performance of the company over a particular period of time. Use of financial ratios in finance is multi-dimensional. It is not only useful for judging the financial health or performance of a particular firm over time, it is also a useful tool for comparing a firm’s financial position and performance with respect to others in the same or different industry to pinpoint problem areas or to identify areas of further improvements.

Therefore, factor analysis can be used as a means of eliminating redundancy among financial ratios and/or reducing the number of ratios selected as a basis for further investigation to a limited but crucial subset.

Author: Ankita Agarwal (13008)

Group: Finance_6