1. University of North Carolina at Chapel Hill
Using Stata Graphics as a Method of Understanding and Presenting Interaction Effects
Joanne M. Garrett, PhD
University of North Carolina at Chapel Hill
July 11, 2005

2. Problems with Understanding Interaction
Interaction difficult concept to explain
not a single answer (point estimate)
linear combination of betas
Often ignored because of difficulty
Graph of interaction may be more intuitive for:
students learning the concept
presentations at professional meetings

3. Low Birth Weight Study*
Variable
Description
Coding
low
Low birth weigh
1 = ≤ 2500 gms
0 = >2500 gms
bwt
Birth weight
grams
smk
Smoked during pregnancy
1 = smoked
0 = did not smoke
race
Mother’s race
1 = black
0 = white
age
Mother’s age
years
* “Loosely” adapted from data from Applied Logistic Regression, David W. Hosmer, Jr. and Stanley Lemeshow

4. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
Logistic regression model: Add smk by race interaction
Create interaction term and run logistic regression:
. gen smkxrace = smk * race
. logistic low smk race smkxrace

5. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
low | OR z P>|z| [95% CI]
smk |
race |
smkxrace |
Significant interaction: Relationship differs between smoking and low birth wt depending on mother’s race
Question: How to interpret the interaction OR?

6. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
Convert OR’s to beta coefficients and solve by categories of race: . logit
low | Coef z P>|z| [95% CI]
smk |
race |
smkxrace |
_cons|
White: OR = e [β1 + β3(race)] = e [1.751 – 1.141(0)] = 5.76
Black: OR = e [β1 + β3(race)] = e [1.751 – 1.141(1)] = 1.84

7. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
White: . lincom smk + 0*smkxrace
low | OR z P>|z| [95% CI]
(1) |
Black: . lincom smk + 1*smkxrace
(1) |

8. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
Interpretation:
Among whites, women who smoke have 5.8 times the odds of having a low birth wt baby
Among blacks, there is no relationship between smoking and having a low birth wt baby (OR=1.8, but not statistically significant)

9. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
Misinterpretations:
Black mothers have less “risk” for low birth wt babies compared to white mothers
It’s okay for black mothers to smoke
Alternative:
Solve the equation for values of smk and race
Graph the individual probabilities (“predxcat”)
. predxcat low, xvar(race smk) graph bar

10. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)
| race smk numobs prob lower upper |
| |
| 0:White 0:No |
| 0:White 1:Yes |
| 1:NonWh 0:No |
| 1:NonWh 1:Yes |
Likelihood ratio test of interaction for race * smk:
LR Chi2(1) =
Prob > Chi2 =

11. Example 1: Low birth weight and interaction between smoking and race (1=black, 0=white)

12. Example 2: Low birth weight and interaction between smoking and age (years)
Logistic regression model: Add smk by age interaction
Create interaction term and run logistic regression:
. gen smkxage = smk * age
. logistic low smk age smkxage

13. Example 2: Low birth weight and interaction between smoking and age (years)
low | OR z P>|z| [95% CI]
smk |
age |
smkxage |
Significant interaction: Relationship differs between smoking and low birth wt depending on mother’s age
Question: How to interpret the interaction OR for a continuous interaction variable?

14. Example 2: Low birth weight and interaction between smoking and age (years)
Convert OR’s to beta coefficients and solve for selected values of age: . logit
low | Coef. z P>|z| [95% CI]
smk |
age |
smkxage |
_cons|
Age=15: OR = e [β1 + β3(age)] = e [– (15)] = 1.14
Age=35: OR = e [β1 + β3(age)] = e [– (35)] = 4.93

15. Example 2: Low birth weight and interaction between smoking and age (years)
Age=15: . lincom smk + 15*smkxage
low | OR z P>|z| [95% CI]
(1) |
Age=35: . lincom smk + 35*smkxage
low | OR z P>|z| [95% CI]
(1) |

16. Example 2: Low birth weight and interaction between smoking and age (years)
Interpretation:
Among 15 year olds, women who smoke have 1.1 times the odds of having a low birth wt baby
Among 35 year olds, women who smoke have 4.9 times the odds of having a low birth wt baby

17. Example 2: Low birth weight and interaction between smoking and age (years)
Misinterpretations:
15 year olds are not at risk for low birth wt babies
It’s okay for 15 year olds to smoke
Alternative:
Solve the equation and graph the probabilities for different levels of smoke and age (“predxcon”)
. predxcon low, xvar(age) from(15) to(35) inc(2)
class(smk) graph

18. Example 2: Low birth weight and interaction between smoking and age (years)
-> smk = 0
| age pred_y lower upper |
| |
| |
| |
| |
| (etc) |
-> smk = 1
| |
| |
Likelihood ratio test for interaction of age * smk:
LR Chi2(1) =
Prob > Chi2 =

19. Example 2: Low birth weight and interaction between smoking and age (years)

20. Example 3: Birth weight (grams) and interaction between smoking and race
Linear regression model:
Create interaction term and run linear regression:
. gen smkxrace = smk * race
. regress low smk race smkxrace
Or: . predxcat bwt, xvar(race smk) graph bar

21. Example 3: Birth weight (grams) and interaction between smoking and race

22. Example 4: Birth weight (grams) and interaction between smoking and age
Linear regression model:
Create interaction term and run linear regression:
. gen smkxage = smk * age
. regress low smk age smkxage
Or: . predxcon bwt, xvar(age) from(15) to(35) inc(2)
class(smk) graph

23. Example 4: Birth weight (grams) and interaction between smoking and age

24. Example 5: Birth weight (grams) and interaction between smoking and age, age2, age3
Linear regression model: add quadratic & cubic terms
Create interaction terms and run linear regression:
. gen age2 = age^2
. gen age3 = age^3
. gen smkxage = smk * age
. gen smkxage2 = smk * age2
. gen smkxage3 = smk * age3
. regress low smk age age2 age3 smkxage
smkxage2 smkxage3
Or: . predxcon bwt, xvar(age) from(15) to(35) inc(2)
class(smk) graph poly(3)

25. Example 5: Birth weight (grams) and interaction between smoking and age, age2, age3

26. Conclusions
Interaction can be a difficult concept for people unfamiliar with the methodology
Examining a graph of an interaction is an easier way to get an intuitive feel for the effect
A useful technique for explaining interaction to students hearing it for the first time, before introducing mathematical models
A simple way to present study results at meetings, even to a statistically savvy audience

28. Calculating and Graphing Predicted Values: (when “X” is categorical)
. predxcat yvar, xvar(xvar1 xvar2)
yvar – dependent variable
continuous – defaults to linear regression
binary (0,1) – defaults to logistic regression
xvar(xvar) – nominal variable for categories of estimated
means or proportions
xvar(xvar1 xvar2) – categories of all combinations of xvar1
and xvar2; tests interaction
adjust(cov_list) – adjusts for any covariates

29. Calculating and Graphing Predicted Values: (when “X” is categorical)
graph – display graph (otherwise shows list of predicted
values only)
bar – bar graph (instead of symbols – default)
model – for display purposes only; displays regression model
Some other options: level(#)
cluster(cluster_id)
savepred(ds_name)

30. Calculating and Graphing Predicted Values: (when “X” is continuous)
. predxcon yvar, xvar(xvar) from(#) to(#) inc(#) graph
yvar – dependent variable
continuous – defaults to linear regression
binary (0,1) – defaults to logistic regression
xvar(xvar) – continuous independent variable; probabilities
calculated for each value of X
from(#) – bottom value for xvar
to(#) – top value for xvar
inc(#) – increment desired between bottom and top values
adjust(cov_list) – adjusts for any covariates

31. Calculating and Graphing Predicted Values: (when “X” is continuous)
graph – display graph (otherwise shows list of predicted
values only)
class(class_var) – adds an xvar by class_var interaction term
poly(2 or 3) – polynomial terms added: 2=squared =squared and cubic
model – for display purposes only; displays regression model
Some other options: level(#)
cluster(cluster_id)
nolist
savepred(ds_name)