Thalasar Ventures

Factor Analysis is an excellent technique which is widely used in analytics and market research industry for quantitative analysis in surveys. Mainly it is used for reduction in variables, detecting relationships between variables, data summarization, identifying factors that are uncorrelated to each other and exploratory analysis to determine how many factors are there. Generally prior to apply any statistical technique like cluster, CHAID, segmentation etc you need to reduce the size of unmanageable data.

I would like to give you few examples where this technique is applicable:
The product marketing manager handling the market research / analytics division wants to determine whether or not relation exists between patriotism and consumers attitudes about domestic and foreign products.
Head Market Research / Analytics Team of a company want to measure a firms image.
Now we will proceed towards some general terminologies which are integral part of Factor Analysis. To identify the relation between factors we look at various types of variance such as Common variance i.e. variance shared with other variables, Specific variation i.e. variance of each variable unique to itself, not explained or associated with other variables and Error i.e. variance due to error in data collection.

For e.g . M = 0.80 I + A i , F = 0.60I + A f

Here M is the score in Mathematics which is dependent on Intelligence level and aptitude. The common link between indicator variable such as M and F is intelligence level. So we call it as common factor or latent factor (as not observable quantity)

Pattern Loading: Correlation between any indicator and the latent factor (unobservable quantity) is called as pattern loading

Communality: Variance that is common with general Intelligence level I, is given by the square of pattern loading. It measures the degree to which an indicator is good or reliable measure of factor.

Tip: If pattern loading is zero for any indicator than the correlation of this indicator with other indicator/variable is zero.
There are 2 types of Factor Analysis:

Principal Component Analysis (we will deal with it seperately in another aricle)
Looks at variance (common, specific and error) amongst variables
Solution has as many factors as variables
Common factor Analysis
Normally factor analysis is referred when we say common factor analysis
It takes only common variance into account not specific and error variance
Number of factors derived is one less than variables
The factor Analysis process includes following steps:

Nature of Data

(To identify are the Data is appropriate for Factor Analysis?)

Appropriateness of Factor Analysis
oBartletts Test of Sphericity (Sig) : High correlation among the variables indicates that the variables can be grouped into homogenous sets of variables such that each set of variables measures the same underlying dimensions.
oSecond one can examine the partial correlations controlling for all other variables. These correlations should be small for correlation matrix to be appropriate for factor analysis
oThe KMO (Kaiser-Meyer-Olkin) Measure of Sampling Adequacy
Range : 0-1
Critical value : >=0.6 and >=0.90 – marvelous
Below 0.5 – unacceptable
How to determine Number of factors
Using Kaiser-Guttman rule (Eigen Value > 1)
Using Percent variance explained (% variance > 5%)
Effectiveness of the Factor solutions
The residual correlation matrix can be used for this purpose. The RMSR should be vary small to indicate that the final solution explains most of the correlation
For a good factor solution the resulting partial correlation after the effect of the factors has been paralleled out should be close to zero.

SAS code to perform Factor Analysis

Data CORRMATR (TYPE = CORR);
INPUT A B C D E F;
_TYP_ = CORR;
CARDS;
Insert correlation matrix here;
PROC FACTOR METHOD = PRINT ROTATE=V CORR MSA SCREE
RESIDUALS PREPLOT PLOT;
VAR A B C D E F;
The METHOD= option specifies the method for extracting factors.
The default is METHOD=PRINCIPAL unless the DATA= data set is TYPE=FACTOR, in which case the default is METHOD=PATTERN. PRINIT used here yields iterated principal factor analysis
The ROTATE= option specifies the rotation method.
FACTOR procedure: EQUAMAX, ORTHOMAX, QUARTIMAX, PARSIMAX, and VARIMAX
In the VARIMAX rotation the major objective is to have a factor structure in which each variable loads highly on one and only one factor
The CORR option displays the correlation matrix and The MSA option produces the partial correlations between each pair of variables controlling for all other variables (the negative anti-image correlations) partial correlation matrix
The SCREE option displays a scree plot of the eigen values.
The RESIDUALS option displays the residual correlation matrix and the associated partial correlation matrix
The PREPLOT option plots the factor pattern before rotation.
The PLOT option plots the factor pattern after rotation.
The VAR statement specifies the numeric variables to be analyzed.

Related Bing Analytics Articles