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

2. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Overview Advantages of charts for presenting interaction patterns – Complementary use of table and prose Title and labeling Placement of variables Axis design considerations Range of values for independent variables

3. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Tabular presentation of regression results For a statistically oriented audience, create a table to report detailed regression results: – Coefficients and statistical test results for Each main effect and interaction term Other variables in the model – Measurement and specification attributes Reference categories Units Functional form of the model

4. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Chart to present an interaction Easier to see the shape of the overall interaction pattern from a chart than from a table. – Is interaction in terms of direction? E.g., Opposite-signed slope – Is interaction in terms of magnitude? E.g., varying Steepness of slopes Gaps between bars

5. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Example: Table of main effect and interaction coefficients 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* Based on multivariate model with controls for work experience, tenure, monthly hours, educational attainment, residence, and occupation characteristics. * p < 0.05

6. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Review: Table of overall effect of interaction Table 2. Predicted difference in monthly earnings (NT$) by gender and marital status, Taiwan, 1992 MarriedUnmarried Women–1,595Reference category Men 6,3813,205 Calculated from the βs as explained in earlier podcasts. 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

7. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Chart showing net effect of interaction 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.

8. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Organization of independent variables in an interaction chart When possible, put – focal predictor on the x-axis – modifier variable in the legend For categorical variables, order the categories in legend and on x-axis to match substantive points related to your research question. Empirical order Theoretical grouping – See podcast on organizing data in tables and charts.

9. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Chart title Title should convey – Dependent variable and pertinent units. E.g., Difference in original units of the DV – E.g., “Difference in birth weight (grams)” Predicted value of the DV Odds ratios of the category being modeled – E.g., “Odds ratios of low birth weight” – Both independent variables involved in the interaction. E.g., “by educational attainment and race” – Ws (when, where, who).

10. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Placement of y-axis To present coefficients from an OLS model, y- axis should cross x-axis at y = 0. – E.g., earnings by gender and marital status chart To present log-odds (NONexponentiated βs from a logit model), y-axis should also cross x-axis at y = 0. To present odds ratios from a logit model, y-axis should cross x-axis at y = 1.0 – Corresponds to equal odds of the outcome for groups being compared.

11. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Interaction chart from logit model x-axis crosses at y = 0

12. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Range of values of independent variables Choose range of values for continuous independent variables that fit the topic and data. E.g., in model of birth weight. – Mother’s age at child’s birth plotted from 15 to 45 years of age Corresponds with reproductive age range for women. – Income/poverty ratio (IPR) plotted from 0.0 to 5.0 Range that captures most of the observed values in the data set used to estimate the model.

13. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.

14. Summary Create a chart to portray the association of the two independent variables in the interaction with the dependent variable. – Based on calculations from estimated regression βs. Follow general chart guidelines for – Labeling the concepts, units, and categories of each variable. – Organization of categories to match narrative. – Choosing pertinent range of your independent variables to graph.

15. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Summary, continued Place the variables on the chart as follows: – Focal predictor on the x-axis. – Modifier in the legend. – Dependent variable on the y-axis. Consider the type of model when deciding where to the x-axis cross the y-axis. – At y = 0 for OLS models. – At y = 1 for odds ratios.

16. 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 6 on creating effective charts Includes material on organizing data in tables and charts – Chapter 16 on interactions Cohen et al. 2003. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences, 3rd Edition. Florence, KY: Routledge.

17. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested online materials Podcasts on – Organizing data in tables and charts – Creating effective tables and charts – Calculating overall interaction pattern from regression coefficients Spreadsheets for calculating interaction patterns between – 2 categorical independent variables – 1 continuous and 1 categorical independent variable – 2 continuous independent variables

18. 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 and 4 in the problem set for Chapter 16 – Suggested course extensions for Chapter 16 “Reviewing” exercises #2, 3, and 4. “Applying statistics and writing” exercises #1 and 2. “Revising” exercises #2 and 3.

19. 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