Transcript Evaluation of the Observation Method

Chapter 3
Factor Analysis
Instructor : Dr. Shin-Yuan Hung
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What is Factor Analysis?
 Factor Analysis is a generic name given to a class
of multivariate statistical methods whose primary
purpose is to define the underlying structure in a
data matrix.
 Broadly speaking, it addresses the problem of
analyzing the structure of the interrelationships
(correlation) among a large number of variables by
defining a set of common underlying dimensions,
known as factors.
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What is Factor Analysis?
 With factor analysis, the researcher can first
identify the separate dimensions of the structure
and then determine the extent to which each
variable is explained by each dimension.
 Once these dimensions and the explanation of each
variable are determined, the two primary uses for
factor analysis- summarization and data reductioncan be achieved.
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Factor Analysis Decision Process
Stage 1: Objectives of factor analysis;
Stage 2: Designing a factor analysis;
Stage 3: Assumptions in factor analysis;
Stage 4: Deriving factors and assessing overall fit;
Stage 5: Interpreting factors;
Stage 6: Validation of factor analysis;
Stage 7: Additional uses of factor analysis results.
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Stage 1: Objectives of Factor Analysis
 Identifying structure through data summarization
 Identify the structure of relationships among
variables by examining the correlations between
the variables.
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Stage 1: Objectives of Factor Analysis
 Data reduction
1. Identify representative variables from a much
larger set of variables for use in subsequent
multivariate analyses;
2. Create an entirely new set of variables, much
smaller in number, to partially or completely
replace the original set of variables for inclusion in
subsequent techniques.
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Stage 1: Objectives of Factor Analysis
 Using factor analysis with other multivariate
techniques


Members of the same factor would be expected to have
similar profiles of differences across groups.
Large numbers of variables or high intercorrelations
among variables can be substantially reduced by
substitution of the new variables.
 Variable selection

garbage in, garbage out
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Stage 2: Designing a Factor Analysis
 Sample size

As a general rule, the minimum is to have at least five
times as many observations as there are variables to be
analyzed, and the more acceptable size would have a
ten-to-one ratio.
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Stage 3: Assumption in Factor Analysis
 The critical assumptions underlying factor analysis are
more conceptual than statistical (only normality is
necessary).
 Ways to test the data matrix has sufficient correlations
to justify the application of factor analysis: correlation
matrix (substantial number of correlations greater than
0.3), Bartlett test of sphericity (reject H0:|Rp|=1), and
measure of sampling adequacy (acceptable case:
MSA>0.5, best case: MSA>0.8).
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Stage 4: Deriving Factors and Assessing Overall Fit
 Common factor analysis versus component analysis
 Common factor analysis
1. need to account for maximum portion of the covariance;
2. has little knowledge about the amount of specific and error
variance.
 Principle component analysis
1. need to account for maximum portion of the variance;
2. prior knowledge suggests that specific and error variance
represent a relatively small proportion of the total variance.
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Stage 4: Deriving Factors and Assessing Overall Fit
 Criteria for the number of factors to extract

Latent root criterion (eigenvalue greater than 1)
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A prior criterion (based on knowledge already known)
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Percentage of variance criterion (specified cumulative
percentage of total variance)

Scree test criterion (plotting the latent roots against the
number of factors)
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Stage 5: Interpreting the Factors
 Rotation of factors
 QUARTIMAX (orthogonal rotation method): to
simplify the rows of a factor matrix
 VARIMAX (orthogonal rotation method): to
simplify the columns of a factor matrix
 EQUIMAX (orthogonal rotation method)
 Oblique rotation methods
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Stage 5: Interpreting the Factors
 Criteria for the significance of factor loadings
 Guideline for identifying significant factor loadings
based on sample size
 Interpreting a factor matrix
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2.
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Examining the factor matrix of loadings;
Identifying the highest loading for each variable;
Assess communalities of the variables;
Label the factors.
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Stage 6: Validation of Factor Analysis
 Assessing the degree of generalizability of the
results to the population and the potential
influence of individual cases or respondents on
the overall results.
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Stage 7: Additional Use of Factor Analysis Results
 Selecting surrogate variables for subsequent analysis

the variable with the highest factor loading on each factor to
act as a surrogate variable that is representative of that factor
 Creating summated scales
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all of the variables loading highly on a factor are combined
 Computing factor scores

factor score is computed based on the factor loadings of all
variables on the factor
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The End
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