This document discusses factor analysis, a statistical technique used to reduce a large number of variables into a smaller set of underlying factors that can explain their interrelationships. It distinguishes between exploratory factor analysis (EFA), which is used when the researcher has no prior theory about the structure of the data, and confirmatory factor analysis (CFA), which validates a proposed model based on preconceived theories. The document also outlines assumptions, extraction methods, rotation techniques, and evaluation criteria for conducting effective factor analysis.

1. Factor
Analysis
K.THIYAGU,
Assistant Professor,
Department of Education,
Central University of Kerala, Kasaragod
1

2. Factor analysis is a technique that is
used to reduce a large number of
variables into fewer numbers of
factors.
The basic assumption of factor analysis
is that for a collection of observed
variables there are a set
of underlying variables
called factors (smaller than the
observed variables), that can explain
the interrelationships among those
variables.
For example, people may respond similarly to
questions about income, education, and occupation,
which are all associated with the latent variable
socioeconomic status. ThiyaguSuriya 2

3. Objectives
of
Factor
Analysis
Reduce the
number of
variables
Examine the
structure or
relationship
between
variables
Detection and
assessment of
uni-
dimensionality
of a theoretical
construct
Evaluates the
construct
validity of a
scale, test, or
instrument
Addresses
multi-
collinearity
(two or more
variables that
are correlated)
Used to
develop
theoretical
constructs
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4. • Exploratory factor analysis is if you don’t have any idea about
what structure your data is or how many dimensions are in a
set of variables.
• Assumes that any indicator or variable may be associated with
any factor.
• It is not based on any prior theory.
Exploratory factor
analysis
(EFA)
• Confirmatory Factor Analysis is used for verification as long as you have a
specific idea about what structure your data is or how many dimensions
are in a set of variables.
• CFA assumes that each factor is associated with a specified subset of
measured variables.
• Used to determine the factor and factor loading of measured variables,
and to confirm what is expected on the basic or pre-established theory..
Confirmatory factor
analysis
(CFA)
Types of Factor Analysis
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5. Types of Factor Analysis
Exploratory Factor Analysis (EFA)
EFA is heuristic.
In EFA, the investigator has no
expectations of the number or nature
of the variables and as the title
suggests, is exploratory in nature.
That is, it allows the researcher to
explore the main dimensions to
generate a theory, or model from a
relatively large set of latent constructs
often represented by a set of items.
Confirmatory Factor Analysis
(CFA)
Confirmatory Factor Analysis is used
by the researcher to test a proposed
theory (CFA is a form of structural
equation modelling), or model and in
contrast to EFA, has assumptions and
expectations based on priori theory
regarding the number of factors, and
which factor theories or models best
fit.
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6. Assumptions of FA
No outlier: Assume that there are no outliers in data.Assumption # 1
Adequate sample size: The case must be greater than the factor.Assumption # 2
No perfect multicollinearity: Factor analysis is an interdependency technique. There
should not be perfect multicollinearity between the variables.Assumption # 3
• Homoscedasticity: Since factor analysis is a linear function of measured variables, it
does not require homoscedasticity between the variables.Assumption # 4
• Linearity: Factor analysis is also based on linearity assumption. Non-linear variables
can also be used. After transfer, however, it changes into linear variableAssumption # 5
• Interval Data: Interval data are assumed. (although ordinal variables are very frequently
used).Assumption # 6
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7. Linear Vs NonLinear (Curvilinear)
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8. Vs
Heteroscedasticity Homoscedasticity
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9. Outlier
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10. FA Steps
Factor Extractions
Factor Rotation
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11. Types of Factor Extractions
• PCA starts extracting the maximum variance and puts them into the
first factor. After that, it removes that variance explained by the first
factors and then starts extracting maximum variance for the second
factor. This process goes to the last factor.
Principal Component
Analysis
• The second most preferred method by researchers, it extracts the
common variance and puts them into factors. This method does not
include the unique variance of all variables. This method is used in
SEM.
Common Factor Analysis
• This method is based on correlation matrix. OLS Regression method is
used to predict the factor in image factoring.Image factoring
• This method also works on correlation metric but it uses maximum
likelihood method to factor.Maximum likelihood method
• Alfa factoring outweighs least squares. Weight square is another
regression based method which is used for factoring.
Other methods of factor
analysis
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12. ThiyaguSuriya 12

13. Rotation Methods
After deciding on the number of factors to extract and with analysis model to
use, the next step is to interpret the factor loadings. Factor rotations help us
interpret factor loadings. There are two general types of rotations, orthogonal
and oblique.
Rotation Methods
orthogonal rotation assume factors are independent or
uncorrelated with each other
oblique rotation factors are not independent and are
correlated
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14. Varimax
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15. Direct Quartimin
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16. ThiyaguSuriya 16

17. SPSS Path Factor Analysis
FactorDimension
ReductionAnalyse
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18. Descriptive
Univariate
Descriptive
Coefficients
Determinant
KMO and
Bartlett's test of
sphericity &
Reproduced
Extraction
Fixed number of
Factors
Rotation
Varimax
Options
Suppress absolute
value
SPSS Path Factor Analysis
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19. ThiyaguSuriya 19

20. ThiyaguSuriya 20

21. Factor Analysis in SPSS
• First, a correlation matrix is generated for all the
variables. A correlation matrix is a rectangular array
of the correlation coefficients of the variables with
each other.
• Second, factors are extracted from the correlation
matrix based on the correlation coefficients of the
variables.
• Third, the factors are rotated in order to maximize
the relationship between the variables and some of
the factors
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22. The KMO measures the sampling
adequacy (which determines if the
responses given with the sample are
adequate or not) which should be close
than 0.5 for satisfactory factor analysis
to proceed.
Kaiser (1974) recommend
Value of KMO Interpretation
0.5 Barely accepted
(Minimum)
0.7 -0.8 Acceptable
Above 0.9 SuperbFiedel (2005) says that in general over
300 Respondents for sampling analysis
is probably adequate. There is
universal agreement that factor
analysis is inappropriate when sample
size is below 50.
Kaiser Meyer Olkin (KMO)
(Sample Adequacy Test)
This measure varies between 0 and 1, and
values closer to 1 are better.
A value of .6 is a suggested minimum.
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23. Bartlett’s Test of Sphericity
(Measures the strength of relationship among the variables)
Ho: Correlation Matrix is an identity matrix.
(An identity matrix is matrix in which all of the diagonal elements are 1 and all of diagonal
elements (terms explained above) are close to 0.
We need to reject the null hypothesis.
(means that correlation matrix is not an identity matrix)
This tests the null hypothesis that the correlation
matrix is an identity matrix. An identity matrix is matrix
in which all of the diagonal elements are 1 and all off
diagonal elements are 0. You want to reject this null
hypothesis.
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24. Communalities
• Communalities which shows how
much of the variance (i.e. the
communality value which should be
more than 0.5 to be considered for
further analysis.
• Else these variables are to be
removed from further steps factor
analysis) in the variables has been
accounted for by the extracted
factors. For instance over
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25. Scree Plot
The scree plot is a graph of the eigenvalues
against all the factors. The graph is useful for
determining how many factors to retain. The point
of interest is where the curve starts to flatten. It
can be seen that the curve begins to flatten
between factors 3 and 4. Note also that factor 4
onwards have an eigenvalue of less than 1, so only
three factors have been retained.
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26. Thank You
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