Factor Analysis - Statswork
Factor
Analysis
The
analysis of variance is not a mathematical theorem, but rather a convenient
method of arranging the arithmetic.- Ronald
Fisher
The
inexpensive Factor Analysis is a
prominent statistical tool to identify a lot of underlying dormant factors. For
more than a century it is used in psychology and also in a wide variety of
situations.
Factor
analysis explains correlations among multiple outcomes as a result of one or
more factors. As it attempts to
represent a set of variables by a smaller number, it involves data
reduction. It explores unexplained
factors that represent underlying concepts that cannot be adequately measured
by a single variable. It is most popular
nowadays in survey research where the responses to each question represent an
outcome. It is because multiple
questions are often related and the underlying factor may influence the subject
responses.
The
reduction technique of factor analysis in reducing a large number of variables
into a fewer number of factors enables to extract maximum common variance. The
common score from all variables as an index can be used for further analysis.
Being part of the GLM, it assumes several assumptions including:
·
There exists a linear relationship.
·
There is no multicollinearity.
·
Includes relevant variables into the analysis
·
No true correlation between variables and factors.
From
its start of psychological usage in 1904, it is now widely used in a variety of
industries and fields. Its use in physical sciences to identify factors that
affect the availability and location of underground sources, water quality, and
weather patterns. It is also extensively and successfully used in the marketing
field and market research related to product attributes and perceptions. Along
with other Quantitative Research and Quantitative Analysis tools, it is
used in the construction of perceptual maps and product positioning studies.
Many social scientists are seeking the help of
factor analysis to uncover major social and international patterns when
confronted with
·
Entangled behavior
·
Unknown interdependencies
·
Masses of qualitative and quantitative variables
Factor
analysis capabilities:
Factor analysis helps to find solutions for a
social scientist with capabilities like:
·
To simultaneously manage over hundred variables.
·
Compensate for random error & invalidity.
·
Disentangles complex inter-relationships into their
major & distinct regularities.
Factor
analysis through inexpensive has its costs, including:
·
Its mathematical complications.
·
Entails diverse & numerous considerations in
the application.
·
Strange terms in the technical vocabulary.
·
Huge Analysis Reports covering most
of the pages leaving less space for methodological introduction or explanation
of terms.
·
Students unable to learn it in their formal
learning.
All
these costs make factor analysis results incomprehensible for non-specialists,
social scientists, and policymakers to identify its nature and
significance.
Types of factor analysis:
There
are many methods which extract factor from data set differently, including:
1.
EFA
(Exploratory factor analysis)
EFA
is the most common factor analysis method used in multivariate statistics to
uncover the underlying structure of a relatively large set of variables. EFA assumes that any indicator or variable
may be associated with any factor to identify the underlying relationship
between measured variables. It is not based on any prior theory and uses Multiple Regression and partial
correlation theory to model sets of manifest or observed variables.
2.
CFA
(Common factor analysis)
CFA
is the second most preferred method to extract the common variance and put them
into factors. It determines the factor and factor loading of measured
variables. It also confirms what is expected on the basic or pre-established
theory by assuming that each factor is associated with a specified subset of
measured variables.
CFA commonly uses two approaches
·
The
traditional method:
This
method is based on principle factor analysis than CFA and allows the researcher
to know more about insight factor loading.
·
SEM (structural
equating model) method:
In
Structural Equating Model (SEM) approach,
it is assumed that when the standardized error term is below the absolute value
of two then it is good for the factor. And if it is more than two, it implies
that there is still unexplained variance left to be explained by factor.
3.
PCA
(principal component analysis)
The
PCA starts by extracting maximum variance and puts them into the first factor.
Then it starts with the second factor after removing the first variance and the
analysis goes on until the last factor. Hence this method is most commonly used
by researchers.
PCA VS CFA:
·
PCA analyzes all the variance of data while CFA
does it only for the reliable, common variance of data
·
PCA is unfit for examining the structure of data as
it tends to increase factor loadings in the study with a small number of
variables. But in CFA there is a
hypothetical underlying process or construct involved which is not in PCA.
·
Since CFA provides an accurate result, it is the
most preferred research. PCA is only a choice and could be used as an initial
step in CFA to provide information regarding the maximum number and nature of
factors.
4.
GLM:
GLM
also known as Multivariate Regression model is a
useful framework to compare how several variables affect different continuous
variables. Being a linear statistical
model, it is the foundation for several statistical tests like ANOVA, ANCOVA, and regression analysis. GLM is described as
Data = Model + Error
5.
Image
factoring:
It
uses the OLS (Ordinary Least Square) Regression method to predict the factor,
and this method is based on the correlation matrix.
6.
Maximum
likelihood method:
It
also uses the correlation matrix and has the advantage to analyze statistically
models with different characters on the same basis.
7.
Factor
loading:
Being
the correlation coefficient for the variable, factor loading explains variance
by the variable on that particular factor.
8.
Factor
score:
All
analysis of factor score will assume that the variables will behave as factor scores and will move. Also known as the component score, it is all of rows and columns used as an index of variables
for further analysis.
9.
Eigen
Values:
Also
known as characteristic roots, Eigenvalues portray variance explained by that
particular factor out of the total variance. Eigenvalues show how much
variance is explained by the first factor out of the total variance.
10.Rotation method:
Rotation the method is not affected by Eigenvalues or the percentage of variance extracted
but it affects to make it more reliable to understand the output. Rotation
methods have a lot of available methods, including:
·
No rotation method.
·
Varimax rotation method.
·
Quatrimax rotation method.
·
Direct oblimum rotation method.
·
Promax rotation method.
Assumptions in factor analysis:
·
No
outlier:
Assuming
that there are no outliers in data.
·
Interval
data:
·
Adequate
sample size:
The case used must be greater than the factor.
·
No
perfect multicollinearity:
There
should not be any multicollinearity between variables in factor analysis as it
is an independency technique.
·
Homoscedasticity:
Being
a linear function of measured variables, factor analysis does not require
homoscedasticity between the variables.
·
Linearity:
As
it is based on linearity assumption, factor analysis can use non-linear
variables but on transfer, they change to linear variables.
The
above facts of factor analysis will help in successful dissertation writing and
for further assistance, seek professional help.
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