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

Creating charts to present
interactions
Jane E. Miller, PhD
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Example: Table of main effect and
interaction coefficients
Table 1. Estimated coefficients for a model of
monthly earnings (NT$) in Taiwan, 1992
Variable
Coefficient
Man
Married
Interaction: Man and married
3,205*
–1,595*
4,771*
Based on multivariate model with controls for work experience, tenure,
monthly hours, educational attainment, residence, and occupation
characteristics. * p < 0.05
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Review: Table of
overall effect of interaction
Table 2. Predicted difference in monthly
earnings (NT$) by gender and marital
status, Taiwan, 1992
Married
Unmarried
Women
Men
–1,595
Reference category
6,381
3,205
Calculated from the βs as explained in earlier podcasts.
For married men, the net effect involves both main
effect terms and the interaction term: βman + βmarried
+ βman_married = 3,205 + (–1,595) + 4,771 = 6,381
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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).
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Placement of y-axis
• To present coefficients from an OLS model, yaxis 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Interaction chart from logit model
Odds ratios of disenrollment from NJ KidCare by
plan level, race of family, and percentage of
physicians in the county who are black (1990)
5.0
x-axis crosses
at y = 0
Odds ratio
4.0
White (any % black MDs)
Hispanic (any % black MDs)
Black (0% black MDs)
Black (7% black MDs)
3.0
2.0
1.0
Plan B
Plans C&D
0.0
NJ KidCare plan
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Predicted birth weight by income/poverty ratio (IPR) and
mother's age
3,700
IPR:
3,650
0.5
1.5
2.5
3.5
4.5
Birth weight (grams)
3,600
3,550
3,500
3,450
3,400
3,350
3,300
3,250
3,200
15
20
25
30
35
Mother's age (years)
40
45
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Contact information
Jane E. Miller, PhD
[email protected]
Online materials available at
http://press.uchicago.edu/books/miller/multivariate/index.html
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.