Marketing Research (SPSS)
7. Factor Analysis and Reliability
Dr. Boonghee Yoo
RMI Distinguished Professor in Business and
Professor of Marketing & International Business
Dependence vs. interdependence methods
Dependence Methods
A category of multivariate statistical techniques; dependence methods explain or predict a dependent variable(s) on the basis of two or more independent variables (e.g., regression, general linear model, ANOVA, t-test)
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Independence Methods
A category of multivariate statistical techniques; interdependence methods give meaning to a set of variables or seek to group things together (e.g., correlation, cluster analysis, multidimensional scaling, factor analysis)
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Factor analysis is a data-reduction technique that serves to combine questions or variables (= manifest variables) to create factors (= latent variables)
Factor is a latent variable or construct that is not directly observable but needs to be inferred from the manifest variables
Purpose
To identify underlying constructs in the data
To reduce the number of variables to a more manageable set (e.g., 20 questions can be reduced to 3 factors)
To use factors rather than the individual questions.
What is factor analysis?
Steps of factor analysis
multi-item scales
Obtain a “clear” factor pattern
Factor analysis
Naming &
Reliability
Composite variables
Statistics
X1
X2
X3
X4
X5
F2
F1
Survey questions
(Manifest variables)
Factors
(Latent variables)
Common (= exploratory) factor analysis
X1
X2
X3
X4
X5
F2
F1
One manifest variable is loaded on one factor only.
Confirmatory factor analysis
How many factors to retain?
Plus, A priori criterion:
The analyst decides
the number of factors
(1) Eigenvalue 1
Eigenvalue represents the amount of variance in the original variables associated with a factor
(2) Scree Plot
Plot of the eigenvalues against the number of factors in order of extraction
(3) Percentage of Variance
The number of factors extracted is determined so that the cumulative percentage of variance extracted by the factors reaches a satisfactory level (60% or higher)
Sum of the square of the factor loadings of each variable on a factor represents the eigenvalue
Only factors with eigenvalues greater than 1.0 are retained
iscover the.
Find where the line changes the slope (called an elbow)
Factor analysis terms
Factor Scores
Values of each factor underlying the variables; To replace the manifest variables
Factor Loadings
Correlations between the factors and the original variables; 0.30 is significant, 0.40 more significant, and 0.50 very significant
Communality
The amount of the variable variance that is explained by the factors; Must be larger than 0.50
Factor Rotation
Factor analysis can generate several solutions for any data set. Each solution is termed a particular factor rotation and is generated by a particular factor rotation scheme.
A scale of department store image
Correlations of department store image items
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Variance explained by each factor
A scree plot
A scree test shows the eigenvalues plotted against the number of factors; Find where the line changes the slope, where the “elbow” is.
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Unrotated Factor Loading Matrix
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Scatter diagram using correlations
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Scatter diagram after orthogonal rotation of axes (VARIMAX)
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Factor Loading Matrix after Orthogonal Rotation
A clear factor pattern
F1 = Store attractiveness
F2 = Store convenience
Factor Analysis by SPSS (mobile shopping)
Run separately
Manipulation check questions
y1, y2, y3
All other Likert-scale questions
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DO NOT select Principal components.
When the principal axis factoring fails to produce factors, use other red-marked ones.
Extraction method: Principal axis factoring
Communalities
The amount of the variable variance that is explained by the selected factors.
Must be > 0.05.
PERCENTAGE OF VARIANCE
CRITERION
The first 4 factors account for over
60% of the total variance.
AFTER ROTATION
After the factors are
rotated, eigenvalues
change somewhat.
EIGENVALUE 1
CRITERION
The first 6 factors
exceed eigenvalue 1
each.
Eigenvalues and Total variances explained
Do you see the elbow at Factor 6?
Scree plot
Factor loadings are correlations of items with factors.
Weak loading < 0.60
Cross-loading: An item loaded on more than one factor with the difference between the loadings < 0.2 (e.g., 0.49 vs 0.43).
A matrix of factor loadings
Achieve a clear factor matrix
Delete the “worst” item with cross-loading or weak loading.
Rerun the factor analysis.
Repeat 1. and 2. until there is no cross-loading or weak loading any more.
Then, name each factor based on highest factor loading items with the factor.
Final factor matrix
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No weak loading
No cross-loading
Reliability
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Reliability output
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Cronbach’s alpha does not become better when any item is eliminated.
So, keep all of them.
Create a measure and reliability table.
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Factor loadings > 0.60
Reliability > 0.70
Create composite variables
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COMPUTE PI=mean(Q26_12,Q26_13,Q26_14,Q26_15).
EXECUTE.
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A composite variable = mean of the items of a factor
Give a label to the composite variable in the variable view
Things to consider in factor analysis
How many factors should be finally retained?
Do the member items of each factor carry the same concept together?
Are the factors consistent with a priori theories?
What to do with cross-loaded items?
Have you obtained a clean factor matrix?
What is an appropriate name for each factor?
What is the reliability of each factor?
Have you created a proper summary table?
How to use the composite variables?
General linear model
Regression analysis
Factor analysis guideline for your data
Likert-scale survey questions are qualified.
Don’t include any single-item scale question.
Run factor analysis separately for
Manipulation check questions
y1, y2, y3
All other Likert-scale questions
Report the VARIMAX-rotated factor pattern extracted by principal axis factoring.
Achieve a clear factor pattern.
Exclude cross-loaded and weakly-loaded items one at a time.
Name the factors.
Compute the reliability of each factor.
Create composite variables for the factors.
Note that the composite variables, not the individual items, will be used in analysis.
Make a table called “Measures and reliability” and report factor names, reliability, items, and factor loadings.
Table. Measures and Reliability
Items Factor loading
Satisfaction with the mobile shopping site/app (Reliability = 0.945)
Disgusted with:Contented with 0.825
Unhappy with this site (or app):Happy with this site (or app) 0.825
Did a poor job for me:Did a good job for me 0.824
Very dissatisfied with this site (or app):Very satisfied with this site (or app) 0.824
This site (or app) displeased me:This site (or app) pleased me 0.818
Poor choice in buying from this site (or app):Wise choice in buying from this site (or app) 0.783
Extremely unlikable:Extremely likable 0.686
Very udesirable:Very desirable 0.657
Very unattractive:Very attractive 0.621
Purchase intention from the mobile shopping site/app (Reliability = 0.959)
P14. I expect to purchase through this site (or app) in the near future. 0.903
P13. It is likely that I will purchase through this site (or app) in the near future. 0.883
P12. I intend to purchase through this site (or app) in the near future. 0.869
PI1. I will definitely buy products from this site (or app) in the near future. 0.808
Mobile shopping site/app equity (Reliability = 0.883)
If there is another site (or app) as good as this site (or app), I prefer to buy on this site (or app). 0.810
Even if another site (or app) has same features as this site (or app), I would prefer to buy on this site (or app). 0.786
If another site (or app) is not different from this site (or app) in any way, it seems smarter to purchase on this site (or app). 0.730
It makes sense to buy on this site (or app) instead of any other site (or app), even if they are the same. 0.701
Perceived quality of the mobile shopping site/app (Reliability = 0.878)
The likely quality of this site (or app) is extremely high. 0.795
This site (or app) must be of very good quality. 0.733
This site (or app) is of high quality. 0.723