Assignment 1
11. Factor Analysis
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CONTENT
Commercial Application
Analysis
Follow-up Procedures
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Commercial Application
Through qualitative research, a bank discovered 10 different characteristics of banks that consumers mentioned as affecting their patronage choice among banks.
Does the bank appear modern?
Are the staff friendly?
Is the bank for rich customers only?
Does the bank appear successful?
Does the bank appear stagnant (not dynamic)?
Are the staff kind?
Does the bank provide good service to average workers?
Does the bank provide good housing advice?
Does the bank provide good tax advice?
Is this bank for me?
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Commercial Application
But it’ll be impossible for the bank to develop action plans for this many characteristics.
It’ll be more effective for the bank to identify general evaluative dimensions (from these specific characteristics) to develop action plans.
Does the bank appear modern?
Are the staff friendly?
Is the bank for rich customers only?
Does the bank appear successful?
Does the bank appear stagnant (not dynamic)?
Are the staff kind?
Does the bank provide good service to average workers?
Does the bank provide good housing advice?
Does the bank provide good tax advice?
Is this bank for me?
A small number of factors
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Commercial Application
To identify these general evaluative dimensions or factors, the bank could conduct a survey asking for consumer evaluations on each of the 10 items.
Factor analysis would be used to identify the factors.
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Factor Analysis
A method of data reduction
10 variables -> a small number of factors
Factor 1 = LF1X1X1 + LF1X2X2 + … + LF1X10X10
Factor 2 = LF2X1X1 + LF2X2X2 + … + LF2X10X10
…
Factor loading
Describe the connection between a variable and a factor
LF1X1: connection between Factor 1 and Variable 1
Vary between 0 (no connection) and 1 (perfect connection)
Loading can be positive or negative. An absolute value >.50 means strong connection
Used with interval-scaled data only
Modern _:_:_:_:_:_:_:_ Old-fashioned
Friendly _:_:_:_:_:_:_:_ Cold
For rich customers _:_:_:_:_:_:_:_ For all customers
…
Stagnant _:_:_:_:_:_:_:_ Dynamic
(1)(2)(3)(4)(5)(6)(7)
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| Variable | Factor 1 | Factor 2 |
| Modern (X1) | .75 | -.35 |
| Friendly (X2) | .79 | -.27 |
| For rich customers (X3) | -.65 | .11 |
| Successful (X4) | .78 | -.17 |
| Stagnant (X5) | -.75 | .06 |
| Kind (X6) | .78 | -.21 |
| Good for workers (X7) | .55 | .64 |
| Good housing advice (X8) | .58 | .55 |
| Good tax advice (X9) | .56 | .52 |
| A bank for me (X10) | .80 | -.09 |
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Factor Rotation
To solve cross-loading
One variable has high loadings (>. 50) on more than one factor
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Factor 1
Factor 2
X7
.50
.50
.55
.56
.58
.52
.55
.64
X8
X9
X1
-.50
-.50
X2
X3
X4
X5
X6
X10
10
Factor 1
Factor 2
X7
.50
.50
X8
X9
-.50
-.50
X1
X2
X3
X4
X5
X6
X10
Factor 1 Rotated
Factor 2 Rotated
.50
-.50
-.50
.50
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| Variable | Factor 1 | Factor 2 |
| Modern (X1) | .83 | .07 |
| Friendly (X2) | .83 | .16 |
| For rich customers (X3) | -.62 | -.23 |
| Successful (X4) | .76 | .24 |
| Stagnant (X5) | -.68 | -31 |
| Kind (X6) | .78 | .21 |
| Good for workers (X7) | .16 | .82 |
| Good housing advice (X8) | .23 | .77 |
| Good tax advice (X9) | .23 | .73 |
| A bank for me (X10) | .74 | .32 |
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Factor Rotation
Varimax
Factor number unchanged
Reassignment of loadings
Maximize loading of each variable on a single factor and minimize loading on all other factors.
Quartimax
Factor reduction
Equamax
Compromise
Oblique & Promax
Factors rotate by different degrees
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Factor Analysis
Sample data
Chapter 11 Factor Analysis
X1: Does the bank appear modern?
X2: Are the staff friendly?
X3: Is the bank for rich customers only?
X4: Does the bank appear successful?
X5: Does the bank appear stagnant (not dynamic)?
X6: Are the staff kind?
X7: Does the bank provide good service to average workers?
X8: Does the bank provide good housing advice?
X9: Does the bank provide good tax advice?
X10: Is this bank for me?
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Data View
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Variable View
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Analyze -> Dimension Reduction -> Factor
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Select Modern (X1) from the variable list and next click on the top arrow to enter it into Variables
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Modern (X1) is now in Variables. Select Friendly (X2) from the variable list and next click on the top arrow to enter it into Variables. Repeat the same procedure for X3 to X10.
e.
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All variables are entered. Click on Rotation.
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Select Varimax under Method. Click on “Continue” to close this window.
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Click on OK to run factor analysis.
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SPSS gives you more outputs than you need. You only need one table: Rotated Component Matrix.
Interpretation: Two factors were identified in the analysis. X1, X2, X3, X4, X5, X6, and X10 belong to Factor 1 because the absolute values of their loadings on Factor 1 are larger than .50. Factor 1 is about the image dimension of a bank. X7, X8, and X9 belong to Factor 2 because the absolute values of their loadings on Factor 2 are larger than .50. Factor 2 is about the service dimension of a bank.
| Rotated Component Matrixa | ||
| Component | ||
| 1 | 2 | |
| Modern X1 | .825 | .073 |
| Friendly X2 | .825 | .155 |
| For rich customers X3 | -.615 | -.226 |
| Successful X4 | .761 | .244 |
| Stagnant X5 | -.678 | -.314 |
| Kind X6 | .780 | .205 |
| Good for workers X7 | .160 | .823 |
| Good housing advice X8 | .226 | .766 |
| Good tax advice X9 | .227 | .727 |
| A bank for me X10 | .738 | .319 |
| Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. | ||
| a. Rotation converged in 3 iterations. |
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| Variable | Factor 1 | Factor 2 |
| Modern (X1) | .83 | .07 |
| Friendly (X2) | .83 | .16 |
| For rich customers (X3) | -.62 | -.23 |
| Successful (X4) | .76 | .24 |
| Stagnant (X5) | -.68 | -31 |
| Kind (X6) | .78 | .21 |
| Good for workers (X7) | .16 | .82 |
| Good housing advice (X8) | .23 | .77 |
| Good tax advice (X9) | .23 | .73 |
| A bank for me (X10) | .74 | .32 |
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Labeling the factor
The statistical computation to generate factors is a scientific procedure
Labeling of each factor is not derived by the factor analysis. It is intuitively developed by the researchers based on their understanding of what the factor represents.
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Fellow-up
How is my bank doing on the two dimensions?
Image score: the average of X1, X2, X3, X4, X5, X6, and X10
But
Reverse coding X3 (for rich customers only)
Reverse coding X5 (stagnant)
Service score: the average of X7, X8, X9
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Reverse Coding
X3 -> X3R
X5 -> X5R
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Transform -> Recoding into Different Variables
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Select For Rich Customers (X3) from the variable list and next click on the arrow to enter it into Input Variables -> Output Variables
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X3 is now in Input Variables -> Output Variables. Type X3R under Name and X3 Recoded under Label. Next, click on “Change.”
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The ? in Input Variables -> Output Variables is now replaced with X3R. Now SPSS knows you want to recode X3 to X3R.
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Select Stagnant (X5) from the variable list and next click on the arrow to enter it into Input Variables -> Output Variables
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X5 is now in Input Variables -> Output Variables. Type X5R under Name and X5 Recoded under Label. Next, click on “Change.”
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The ? in Input Variables -> Output Variables is now replaced with X5R. Now SPSS knows you want to recode X5 to X5R. Next, click on “Old and New Values.”
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Old and New Values
Reverse coding
X1 Modern _:_:_:_:_:_:_:_ Old-fashioned
X3 For rich customers _:_:_:_:_:_:_:_ For all customers
X5 Stagnant _:_:_:_:_:_:_:_ Dynamic
(1)(2)(3)(4)(5)(6)(7)
For X3R and X5R
1 -> 7
2 -> 6
3 -> 5
4 -> 4
5 -> 3
6 -> 2
7 -> 1
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Type “1” in Value under Old Value. Type “7” in Value under New Value. Next, click on “Add.”
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The recoding between “1” and “7” is now in Old -> New. Type “2” in Value under Old Value. Type “6” in Value under New Value. Next, click on “Add.”
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The recoding between “2” and “6” is now in Old -> New. Type “3” in Value under Old Value. Type “5” in Value under New Value. Next, click on “Add.”
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The recoding between “3” and “5” is now in Old -> New. Type “4” in Value under Old Value. Type “4” in Value under New Value. Next, click on “Add.”
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The recoding between “4” and “4” is now in Old -> New. Type “5” in Value under Old Value. Type “3” in Value under New Value. Next, click on “Add.”
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The recoding between “5” and “3” is now in Old -> New. Type “6” in Value under Old Value. Type “2” in Value under New Value. Next, click on “Add.”
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The recoding between “6” and “2” is now in Old -> New. Type “7” in Value under Old Value. Type “1” in Value under New Value. Next, click on “Add.”
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The recoding between “7” and “1” is now in Old -> New. Next, click on “Continue” to close the window.
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Click on “OK” to run recoding.
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Two new variables “X3R” and “X5R” are added to the data.
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Compute Average Scores
Image score: the average of X1, X2, X3R, X4, X5R, X6, and X10
Service score: the average of X7, X8, X9
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Transform -> Compute Variable
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Type Image in Target Variable. Click on All in Function Group. Scroll down the list in Functions and Special Variables to look for Mean. Select Mean from the list in Functions and Special Variables. Next, click on the Up arrow.
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MEAN (?, ?) is now in Numeric Expression. ? refers to X1, X2, X3R, X4, X5R, X6, and X10 to be entered to calculate the image score. Select X1 from the variable list, and click on the Enter arrow.
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X1 now replaces the first “?”. Highlight the second “?”, select X2 from the variable list, and click on the Enter arrow.
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X2 now replaces the second “?”. Enter a comma after X2 from your keyboard, select X3R from the variable list, and click on the Enter arrow.
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Repeat the same procedure with X3R to enter X4, X5R, X6, and X10. Next, click “OK” to compute the Image score.
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A new variable “Image” is added to the data.
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Transform -> Compute Variable
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Type Service in Target Variable. Highlight X1, X2, X3R, X4, X5R, X6, X10 in Numeric Expression ,and delete these variables by clicking on “Delete.”
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Enter “X7, X8, X9” into Numeric Expression. X7/X8/X9 are entered from the variable list, “,” is entered from the keyboard. Next, click on OK to computer “Service.”
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A new variable “Service” is added to the data.
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How is my bank doing on Image and Service
Descriptive
Mean
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Analyze -> Descriptive Statistics -> Descriptives
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Scroll down the variable list to look for Image. Select Image from the list, and click on the Enter button.
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Select Service from the list, and click on the Enter button.
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Click on OK to run descriptives.
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SPSS gives you one table: Descriptive Statistics.
Interpretation: The image score is 2.17, and the service score is 2.86. The performance is above average (4 out of 7), so the bank is perceived quite favorably both in terms of image and service.
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When to use what technique
T-test
Difference between two (demographic) groups in consumption, product attitude, etc
Do males and females differ in their consumption of wine?
Do baby boomers and generation Xers differ in their attitude toward online advertising?
Do Chinese and Japanese differ in their attitude toward German cars?
ANOVA
Difference between three (demographic) groups in consumption, product attitude, etc
Do low-income, mid-income, and high-income groups differ in their consumption of wine?
Do baby boomers, generation Xers, and generation Yers differ in their attitude toward online advertising?
Do Chinese/Japanese/Koreans differ in their attitude toward German cars?
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When to use what technique
Multiple Regression
Relative impact of a set of independent variables (interval and/or ratio variables) on one dependent variable (interval or ratio variable)
Which one, sales promotion or advertising, will have a relatively larger impact on sales?
Which aspect (s) of the product, quality, price, …, will have a relatively larger impact on customer satisfaction.
Help identify certain trend between independent variables and dependent variable
Increasing expenditure on which one, sales promotion or advertising, will be more likely to increase sales?
Improving on which aspect (s) of the product, quality, price,…, will be more likely to increase customer satisfaction?
Discriminant Analysis/Logistic Regression
Relative impact of a set of independent variables (interval and/or ratio variables) on one dependent variable (nominal variable, typically user/non-user)
Which one, age or years of education, will have a relatively larger impact in identifying users from non-users?
Which aspect (s) of the product, quality, price, …, will have a relatively larger impact in idenifying users from non-users?
Help identify certain trend between independent variables and dependent variable
Will consumers of higher age or more years of education be more likely to be users?
Consumers reporting higher evaluations of which aspect (s) the product, quality, price, …, will be more likely to be users?
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When to use what technique
Factor Analysis
Reduce data especially from qualitative research
10 characteristics identified, and they can be reduced to 2 dimensions
Assess business operation on the dimensions
Favorable perceptions