1. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Writing prose to present results of interactions Jane E. Miller, PhD

2. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Overview Review of “generalization, example, exception” approach. Complementary use of table, chart and prose. Present the overall pattern of the interaction. – Calculated behind the scenes. “Poor, better, best” illustration.

3. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. The GEE approach to presenting interactions Conduct the calculations behind the scenes. – Present the results of the calculations. Generalize the overall pattern, rather than reporting each coefficient or value. Communicate direction and magnitude of pattern. – Often easiest to see using a chart instead of a table. See earlier podcast on charts to present interactions.

4. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Introducing the interaction pattern Orient readers to the purpose of testing for interactions, referring to the specific topics you are studying Name the dependent variable Name the two independent variables involved in the interaction. Use phrasing that alerts your readers to the fact that the association among those variables escapes a simple generalization. For wording suggestions, see podcast on summarizing a pattern among many numbers.

5. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Generalization, example, exception Generalization: – Describe an overall pattern, rather than going through every cell in the table or point on the chart. Example: – Give 1 or 2 representative numeric contrasts to illustrate generalization. Exception(s): – If parts of the pattern deviate from your generalization, describe that departure. – Give a numeric example to illustrate the exception.

6. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Example coefficients on main effects and interaction terms Table 1. Estimated coefficients for a model of monthly earnings (NT$) in Taiwan, 1992 VariableCoefficient Man3,205* Married–1,595* Interaction: Man and married4,771* Compared to unmarried women. Based on multivariate model with controls for work experience, tenure, monthly hours worked, educational attainment, residence, and occupation characteristics. * p <.05

7. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Poor writing about interactions “The main effect of ‘man’ was 3,205 and the main effect of ‘married’ was – 1,595, while the interaction term ‘man and married’ was 4,771 (all p <.05; table 1).” Fails to mention dependent variable (earnings). Does not explain that the main effect and interaction terms must be considered together to calculate net effect of interaction.

8. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Another poor way to write about interactions “Gender and marital status interacted in their effects on earnings.” Conveys that there is an interaction. Names the concepts under study. Does not explain the direction or size of the relationship.

9. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Better, step 1: Table showing overall pattern of interaction Table 2. Predicted difference in monthly earnings (NT$) by gender and marital status, Taiwan, 1992 MarriedUnmarried Women–1,5950 Men 6,3813,205 Unmarried women = reference category. For married men, the net effect involves both main effect terms and the interaction term: β man + β married + β man _ married = 3,205 + ( – 1,595) + 4,771 = 6,381.

10. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Better, step 2: Prose description “ The net effect of being a married man on earnings was NT$6,381 compared to unmarried women (p <.01; table 2).” Reports result of calculation involving two main effects terms and interaction term pertaining to married men. Specifies the reference category (unmarried women). Does not – Interpret meaning of the calculation. – Compare other gender and marital status combinations to reveal the overall pattern.

11. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Best, step 1: Chart showing overall interaction pattern Figure 1. Predicted difference in monthly earnings (NT$) by gender and marital status, Taiwan, 1992 Compared to unmarried women. Based on multivariate model with controls for work experience, tenure, monthly hours, educational attainment, residence, and occupation characteristics.

12. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Best, step 2: Prose GEE of the interaction pattern “As shown in figure 1, men earn more than women regardless of marital status. But, the effect of marriage on earnings works in opposite directions for men than for women: although marriage confers a substantial earnings advantage for men (NT$3,176 extra per month for married compared to unmarried men), it is associated with a sizeable deficit for women (NT$1,595 less per month for married compared to unmarried women).” Figure 1. Predicted difference in monthly earnings (NT$) by gender and marital status, Taiwan, 1992

13. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Annotated prose GEE of interaction “As shown in figure 1, men earn more than women regardless of marital status.” – Generalizes one part of the pattern, covering all four gender/marital status groups. “But, the effect of marriage on earnings works in opposite directions for men than for women.” – Identifies the exception. “Although marriage confers a substantial earnings advantage for men (NT$3,176 extra per month for married compared to unmarried men), it is associated with a sizeable deficit for women (NT$1,595 less per month for married compared to unmarried women).” – Documents the exception including direction and size, citing evidence from the behind the scenes calculation of the net effect from the OLS βs.

14. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Summary: Advantages of the GEE approach for interactions Uses tables and charts to report detailed numbers for the full pattern. Uses prose to summarize the patterns, relating The values to one another; The observed pattern to the hypothesis about how the two independent variables together determine the value of the dependent variable. Avoids reporting every number involved in the interaction in the narrative description.

15. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested resources Miller, J.E. 2013. The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. – Chapter 2, section on “generalization, example, exception” – Chapter 14, section on “generalization, example, exceptions revisited” – Chapter 16, on interactions – Appendix A, on step-by-step approach to identifying and writing a GEE

16. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Supplemental online resources Podcasts on – Calculating interaction pattern from regression coefficients – Choosing tools to present numbers – Summarizing a pattern with many numbers “GEE” – Creating charts to present interactions

17. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested practice exercises Study guide to The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. – Questions #3, 4, and 5 in the problem set for Chapter 16 – Suggested course extensions for Chapter 16 “Reviewing” exercises #3, 4, and 5. “Applying statistics and writing” exercises #3 and 4. “Revising” exercises #1, 2, and 3.

18. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Contact information Jane E. Miller, PhD jmiller@ifh.rutgers.edu Online materials available at http://press.uchicago.edu/books/miller/multivariate/index.html