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1. FACTOR ANALYSIS
1. Dimension Reduction: 80 characteristics of retail shops and their
services what consumers wanted to be changed. The owner wants to
reduce them into fewer dimensions. The consultant collected data from
consumers and then did factor analysis.
2. Variable Reduction: On the basis of grouping variables, 20 variables
3 factors may emerge.
3. Test Items into Factors: Twenty items proposed to measure ethical
leadership in our study reduced into two factors- empowerment,
motive and character.
The general purpose of FA is to find out a way of condensing
/summarizing the information contained in a number of original
variables into a smaller set of new, composite dimensions or factors
with a minimum loss of information –that is, to search for and define
the fundamental constructs or dimensions assumed to underlie the
original variables.
1. Identify the structure of relationship among variables or respondents.
R FA analyses a set of variables to identify the dimensions that are
latent. Q FA analyses a large no individuals into distinct groups.
2. Identify the representative variables.
3. Create a new set of variables much smaller in number for subsequent
analysis.
Stage 2: Designing a FA
Correlation Among Variables (R)/ Respondents (Q). Correlation
matrix. Q FA (similarity of individuals on variance structure) and Cluster
analysis (distance
among respondents scores).
Variable Selection and Measurement Issues
Metric measurement of variables and some variables may be nonmetric or
dummy. If all variables are dummy, then Boolean FA. Reasonable
number of variables per factor, generally five or more.
Sample Size
Needs to be > 100 or larger. 5 or 10 times observations X number of
variables to be analysed. If there are 30 items in a scale, there needs to be
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2. 150 or 300 respondents to apply FA. Cases per Variable= 5 or 10
minimum. More cases will minimize the over fitting to the data.
Stage 3: Assumptions in FA
Correlation in substantial number of cases is >.30, or partial correlation
low. DV, IV mixed in FA is inadequate. Male and female mixed.
Separate analysis for each group FA.
Stage 4: Deriving Factors and Assessing Overall Fit
Method of extracting factors (common factor analysis vs. component
analysis/principal component analysis) and number of factors selected to
represent the underlying structure in the data. Common factor analysis
extract factors specifying what the variables share in common.
Component analysis/principal component analysis specifies the minimum
number of factors.
Total Variance= Common + specific + error
Criteria for the Number of Factors to be Extracted
1. Latent root criterion 2. A priori criterion; Percentage of variance
extracted =60%, Scree test criterion, latent root :1
Stage 5: Interpreting Factors
Factor loadings are correlation of each variable and the factor. Factor
rotation: for interpretation. The reference axis of the factors are turned
about the origin until some other position has been reached. Orthogonal
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Criterion for Significance of Loadings
350= .30, 250=. 35, 200=.40,
150=. 45, 100=.55, 85=.60, etc.
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