MULTIPLE CORRESPONDENCE ANALYSIS

A BRIEF INTRODUCTION

September, 2006

John Kochevar, Ph.D. WWW/.Kochevarresearch.com

Multiple Correspondence Analysis (MCA) is a analytic tool for showing the relationships between large sets of variables. As in principal components analysis, it organizes the variables onto dimensions on the basis of variance explained. The distance between variables is a function of the strength of their relationships.

Value

• Detects complex interactions.

• Shows patterns (syndromes, clusters) of relationships.

• Displays the “Big Picture.”

KRA has the expertise and software to make it happen.

INTRODUCTION

MCA – THEORY & METHOD

Widely Used in Europe and Japan • MCA was developed in Japan and France. There are different traditions of labeling and interpretation.

• MCA is a.k.a. Correspondence Analysis, dual scaling, additive scaling, optimal scaling, homogeneity analysis, Quantification III.

• “A special kind of canonical correlation analysis.”

• “A method for the analysis of large contingency tables.”

• “A method for displaying the associations between cases and categorical levels of analysis.”

Note: A full description can be found at WWW.Statsoft.com, or, Clausen, S. Applied Correspondence Analysis. Sage University Paper 121, 1998.

Software

• The SPSS program HOMALS (under “optimal scaling”) performs MCA.

• SPSS output is not readable for large numbers of categories/variables. Re- enter coordinates in KRA Excel/graph program, drop graph into Power Point.

Interpretation

• The distance between graphed categories in CA is based on a chi-square metric.

• Categories which are closer together have higher chi-squares if analyzed in a conventional cross-tabular format. *

• A multiple correspondence graph allows the analyst to spot the strongest relationships in a set n-way crosstabs - at a glance.

Applications

• Data mining.

• Uncover complex interactions before doing regression analysis.

• Summarize and pinpoint the strongest relationships in easy to read graphs.

A SIMPLIFIED APPROACH

* Approximately….

CROSS-NATIONAL SURVEY EXAMPLE

WOMEN AND WORK STRESS

• An American woman’s magazine asked us to do a cross-national comparative study of job stress among working women.

• Sample: Working women magazine readers in five nations: United States, Japan, Germany, Brazil and Australia.

• Questionnaires were in magazines, self-completed and returned by mail (N=22,500). We randomly sampled returns.

• Final sample N=4,500. Data quality varied.

• There were approximately 100 questions/variables. We analyzed them in blocks organized according to the following model.

• For each block we determined which variables were most strongly associated with job stress. The strongest predictors in each block were selected for final analysis.

• The two example graphs show 1) Top predictors associated with job stress; 2) Top predictors controlling for culture (nationality).

Demographics

FACTORS ASSOCIATED WITH WORK STRESS

Personality

EducationIncome

Work Stress

Incidence DurationSeverity

Age

PerfectionismStress is Stimulating

Work Motivations

Career GoalsReasons for Working

Home Factors Work Factors

Culture

Nationality

Home Problems

Children

Marital Status

Environment

ControlSocial support

Occupation

WORK STRESS AND STRONG PREDICTORS

UNIVERSAL

1 Low 2 Moderate 3 High

Stress

Age 4 18-25 5 26-30 6 31-35 7 36-40 8 41-45 9 46-5010 51-5511 56+

Education12 Less than high school13 High School14 Voc/Trade15 Jr college/some educ16 College17 Graduate school

18 Work to support myself

Perfectionist - Describes19 Very well20 Somewhat21 Describes22 Somewhat does not23 Does not

Stimulated by stress/ pressure24 Yes25 Pressure, not stress26 Seldom

27 Moved28 Changed jobs

Occupation29 Managers30 Professionals31 Craftsmen32 Technicians and Admin.33 Bureaucratized Service34 Commercialized Service35 Routinized workers36 Laborers37 Marginal Workers (Students)

38 No privacy39 Too many interruptions40 Too much work to do a good job

Can control pace - describes41 Very well42 Somewhat43 Describes44 Somewhat doesn’t 45 Does not

Hours per week46 1-2047 21-3448 35-3949 4050 41-4551 46-5952 60+

Colleagues under stress53 Majority54 A few55 Don’t know

Female Work Friends56 None57 1-258 3-559 6+

59

58

57

56

55

5453

52

51

50

49

48

47

46

45

44 43

42

4140

39 38

37

36

35

34

3332

31

30

29

282726

25

24

23

22

2120

19

18

17

16

15

14

1312

11109

8

7

6

5

4

3

2

1

64

63

62

61

60

59

5857 56

55

54

53

5251

50

4948

47

46

45

4443

42 41

4039 38

37

36

35

3433

32

31

3029

2827

26

25

24

23

22

2120

19

18

17

1615

14

13

12

1110

98

7

6

54

3

2

1

WORK STRESS AND STRONG PREDICTORSNATION INFLUENCE

1 Low 2 Moderate 3 High

Stress

Country60 US 61 Japan 62 Australia 63 Germany 64 Brazil

Age 4 18-25 5 26-30 6 31-35 7 36-40 8 41-45 9 46-5010 51-5511 56+

Education12 Less than high school13 High School14 Voc/Trade15 Jr college/some educ16 College17 Graduate school

18 Work to support myself

Perfectionist - Describes19 Very well20 Somewhat21 Describes22 Somewhat does not23 Does not

Stimulated by stress/ pressure24 Yes25 Pressure, not stress26 Seldom

27 Moved28 Changed jobs

Occupation29 Managers30 Professionals31 Craftsmen32 Technicians and Admin.33 Bureaucratized Service34 Commercialized Service35 Routinized workers36 Laborers37 Marginal Workers (Students)

38 No privacy39 Too many interruptions40 Too much work to do a good job

Can control pace - describes41 Very well42 Somewhat43 Describes44 Somewhat doesn’t 45 Does not

Hours per week46 1-2047 21-3448 35-3949 4050 41-4551 46-5952 60+

Colleagues under stress53 Majority54 A few55 Don’t know

Female Work Friends56 None57 1-258 3-559 6+

• Data Display. We show only two charts from a much larger analysis. In addition, we have not displayed some data points.

• Occupation. We coded results to a standard used by job safety researchers - except in Japan. At the time of the survey there was a controversy concerning stress-related worker deaths (karaoshi) in Japan. Japanese workers were classified only as “part-time” or “full-time” under the orders of a unit manager (not a researcher) who was afraid the results might reflect badly on certain businesses. Unfortunately, almost all female Japanese workers are customarily classified as part-time workers, and all tables with occupation as a variable are distorted by the unique relationship between Japan and occupation.

• Job stress. The Universal table supports the findings of earlier

studies that show that immediate factors in the worker’s environment - “Control of Pace”, “Too much work” - are the most important cause of worker stress. This relationship held while controlling for a variety of other relationships and was even stronger in the presence of other work conditions, e.g. “Colleagues under stress.”

• Nationality. German women tended to experience more stress in response to bad work conditions. Some of this can be explained by the higher proportion of factory workers in the German sample, but not all.

WORKING WOMEN AND WORK STRESS

NOTES ON INTERPRETATION

MCA FOR DATA MININGADVANTAGES

• Exploratory. Comprehensive.

• Logic is obvious.

• Few assumptions – E.g. Linearity of relationships, homogeneity of variance, etc.

• Interactions become apparent.

• Efficient.

• Easy to read displays.

Ask to see our cross-national study of fear of hypoglycemia….