## Sunday, 4 September 2011

### Factor Analysis..!!

• Factor analysis is a collection of methods used to examine how underlying constructs influence the responses on a number of measured variables.

• There are basically two types of factor analysis: exploratory and confirmatory.

O Exploratory factor analysis (EFA) attempts to discover the nature of the constructs influencing a set of responses.

O Confirmatory factor analysis (CFA) tests whether a specified set of constructs is influencing responses in a predicted way.

• Both types of factor analyses are based on the Common Factor Model. This model proposes that each observed response (measure 1 through measure 5) is influenced partially by underlying common factors (factor 1 and factor 2) and partially by underlying unique factors (E1 through E5). The strength of the link between each factor and each measure varies, such that a given factor influences some measures more than others. This is the same basic model as is used for LISREL analyses.

• Factor analyses are performed by examining the pattern of correlations (or covariance) between the observed measures. Measures that are highly correlated (either positively or negatively) are likely influenced by the same factors, while those that are relatively uncorrelated are likely influenced by different factors.

• Factor analysis was invented nearly 100 years ago by psychologist Charles Spearman, who hypothesized that the enormous variety of tests of mental ability--measures of mathematical skill, vocabulary, other verbal skills, artistic skills, logical reasoning ability, etc.--could all be explained by one underlying "factor" of general intelligence that he called g. He hypothesized that if g could be measured and you could select a subpopulation of people with the same score on g, in that subpopulation you would find no correlations among any tests of mental ability. In other words, he hypothesized that g was the only factor common to all those measures.

What Exactly Is A Factor – And What Is A Factor Analysis?

A factor can be thought of as an underlying concept that explains the variability in a given dataset.

To understand the basic theoretical idea behind what a factor analysis involves, take this picture of the Muppets from Sesame Street. Conceptually a factor analysis is like asking, “How can we explain the most about how these Muppets are different from each other while using the fewest adjectives possible?” Ideally, you’d want to use enough descriptors to be thorough without going overboard, perhaps focusing on 2-5 of the most crucial, defining differences. Individually describing every single Muppet wouldn’t be very helpful, nor would it be helpful to say, “Well, some of them are furry.” However, if you posit that the most important features to focus on are furriness, color, and clothing, you’ve done a pretty good job of briefly (yet thoroughly) summarizing the main ways in which the Muppets differ from each other – and those features could also be thought of as factors.

Behind all of the numbers, figures, and statistics, this is the conceptual basis of a factor analysis.

Written by: Ajvad Rehmani (13003)

Group: Marketing 1