Creating charts to present interactions

1. Creating charts to present interactions Jane E. Miller, PhD

2. 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. Tabular presentationof 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. 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. Example: Table of main effect and interaction coefficients Based on multivariate model with controls for work experience, tenure, monthly hours, educational attainment, residence, and occupation characteristics. * p < 0.05

6. Review: Table of overall effect of interaction Calculated from the βs as explained in earlier podcasts. For married men, the net effect involves both main effect terms and the interaction term: βman+ βmarried + βman_married= 3,205 + (–1,595) + 4,771 = 6,381

7. 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. 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. 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. Placement of y-axis • To present coefficientsfrom 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. Interaction chart from logit model x-axis crosses at y = 0

12. 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.

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. 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. 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. 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. 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. Contact information Jane E. Miller, PhD jmiller@ifh.rutgers.edu Online materials available at http://press.uchicago.edu/books/miller/multivariate/index.html