## [Statistics]Factor analysis – R

Purpose of Factor Analysis

There are two basic reasons if you consider using Factor Analysis:

• Simplify a set of data by reducing a large number of measures for a set of respondents to a smaller manageable number of factors that still retain most of the information found in the original data set. In some cases, it also helps us to determine some variables/factors that cannot be measurable directly like intelligence for instance.
• Identify the underlying structure of the data in which a large number of variables may really be measuring a small number of basic characteristics of our sample.

Basic Principles of Factor Analysis

Factor Analysis will group together those variables that are highly correlated. Then, from those groups we can select a variable that is representative of the common concept that factor purports to measure.

Result interpretation

• Factor loadings: it presents the relationship between the observed variables and the newly produced factors. In case the are calculated from a data matrix of correlation coefficients, its value’s range is from -1.0 to +1.0.
• Communalities: the percentage of total variance summarized by the common factors, h2. It is calculated by summing all squared factor loadings of a variable across all factors.
• Eigenvalue: the sum of the squared factor loadings for each factor. The rule of thumb in choosing common factors is its eigenvalue is greater than 1.
• Total variance summarized: the total original variance of all nine variables is represented by all factor, or in other words, sum of all communalities and then divided by number of variables.

We will group all variables into a few common factors and name these factors based on the general characteristics of variables that constitute them.

Reference from Marketing Research, 7th Edition of David J.Luck and Ronald S.Robin
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