Factor Analysis – An introduction
Factor analysis is the name given to a group of statistical
techniques that can be used to analyze interrelationships among a large number
of variables and to explain these variables in terms of their common underlying
dimensions (factors). The approach involves condensing the information
contained in a number of original variables into a smaller set of dimensions
(factors) with a minimum loss of information
Purpose
of factor analysis
·
To reduce a large number of variables to a
smaller number of factors for modelling purposes
·
To select a subset of variables from a larger
set , based on which original variables have the highest correlations with the
principal component factors.
·
To establish that multiple tests measure the
same factor, thereby giving justification for administering fewer tests.
Types of factor analysis
Exploratory
factor analysis seeks to uncover the underlying structure of a relatively large
set of variables. The researcher's assumption is that any indicator may be
associated with any factor. This is the most common form of factor analysis
Confirmatory
factor analysis seeks to determine if the number of factors and the loadings of
measured (indicator) variables on them conform to what is expected on the basis
of pre-established theory
Once the purpose of factor
analysis is specified, the researcher must then define the set of variables to
be examined. The researcher implicitly specifies the potential dimensions that
can be identified through the character and nature of the variables submitted
to factor analysis.
Designing
a Factor Analysis
The design of a factor analysis involves three
basic decisions:
·
Choice of the input data (a correlation
matrix) to meet the specified objectives of grouping variables or respondents;
·
The design of the study in terms of number of
variables, measurement properties of variables, and the types of allowable
variables; and
·
The sample size necessary, both in absolute
terms and as a function of the number of variables in the analysis.
Criteria
for the Number of Factors to Extract
Latent
Root Criterion The most commonly used technique is the latent root criterion.
This technique is simple to apply to either components analysis or common
factor analysis. The rationale for the latent root criterion is that any
individual factor should account for the variance of at least a single variable
if it is to be retained for interpretation. Each variable contributes a value
of 1 to the total eigen value. Thus, only the factors having latent roots or
eigen values greater than 1 are considered significant; all factors with latent
roots less than 1 are considered insignificant and are disregarded.
A Priori
Criterion This can be useful when the researcher already knows how many
factors to extract before undertaking the factor analysis. The researcher
simply instructs the computer to stop the analysis when the desired number of
factors has been extracted..
Percentage of Variance Criterion The
percentage of variance criterion is an approach based on achieving a specified
cumulative percentage of total variance extracted by successive factors.
By
Ruchika.M.S
14044
HR - Team F
14044
HR - Team F
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