MULTIPLE CORRESPONDENCE ANALYSIS A BRIEF INTRODUCTION

1. MULTIPLE CORRESPONDENCE ANALYSIS A BRIEF INTRODUCTION September, 2006 John Kochevar, Ph.D. WWW/.Kochevarresearch.com

2. INTRODUCTION • 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.

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

4. A SIMPLIFIED APPROACH • 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. * Approximately….

5. 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).

6. FACTORS ASSOCIATED WITH WORK STRESS Demographics Income Education Age Personality Work Motivations Perfectionism Career Goals Stress is Stimulating Reasons for Working Home Factors Work Factors Environment Home Problems Social support Children Control Marital Status Occupation Culture Nationality Work Stress Incidence Severity Duration

7. WORK STRESS AND STRONG PREDICTORS UNIVERSAL Age 4 18-25 5 26-30 6 31-35 7 36-40 8 41-45 9 46-50 10 51-55 11 56+ Education 12 Less than high school 13 High School 14 Voc/Trade 15 Jr college/some educ 16 College 17 Graduate school 18 Work to support myself Perfectionist - Describes 19 Very well 20 Somewhat 21 Describes 22 Somewhat does not 23 Does not Stimulated by stress/ pressure 24 Yes 25 Pressure, not stress 26 Seldom 27 Moved 28 Changed jobs Occupation 29 Managers 30 Professionals 31 Craftsmen 32 Technicians and Admin. 33 Bureaucratized Service 34 Commercialized Service 35 Routinized workers 36 Laborers 37 Marginal Workers (Students) 38 No privacy 39 Too many interruptions 40 Too much work to do a good job Can control pace - describes 41 Very well 42 Somewhat 43 Describes 44 Somewhat doesn’t 45 Does not Hours per week 46 1-20 47 21-34 48 35-39 49 40 50 41-45 51 46-59 52 60+ Colleagues under stress 53 Majority 54 A few 55 Don’t know Female Work Friends 56 None 57 1-2 58 3-5 59 6+ Stress 1 Low 2 Moderate 3 High

8. WORK STRESS AND STRONG PREDICTORS NATION INFLUENCE Age 4 18-25 5 26-30 6 31-35 7 36-40 8 41-45 9 46-50 10 51-55 11 56+ Education 12 Less than high school 13 High School 14 Voc/Trade 15 Jr college/some educ 16 College 17 Graduate school 18 Work to support myself Perfectionist - Describes 19 Very well 20 Somewhat 21 Describes 22 Somewhat does not 23 Does not Stimulated by stress/ pressure 24 Yes 25 Pressure, not stress 26 Seldom 27 Moved 28 Changed jobs Occupation 29 Managers 30 Professionals 31 Craftsmen 32 Technicians and Admin. 33 Bureaucratized Service 34 Commercialized Service 35 Routinized workers 36 Laborers 37 Marginal Workers (Students) 38 No privacy 39 Too many interruptions 40 Too much work to do a good job Can control pace - describes 41 Very well 42 Somewhat 43 Describes 44 Somewhat doesn’t 45 Does not Hours per week 46 1-20 47 21-34 48 35-39 49 40 50 41-45 51 46-59 52 60+ Colleagues under stress 53 Majority 54 A few 55 Don’t know Female Work Friends 56 None 57 1-2 58 3-5 59 6+ Stress 1 Low 2 Moderate 3 High Country 60 US 61 Japan 62 Australia 63 Germany 64 Brazil

9. WORKING WOMEN AND WORK STRESS NOTES ON INTERPRETATION • 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.

10. 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….