Using%20Stata%20Graphics%20as%20a%20Method%20of%20Understanding%20and%20Presenting%20Interaction%20Effects

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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

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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

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Low Birth Weight Study
Variable Description Coding
low Low birth weigh 1 2500 gms 0 gt2500 gms
bwt Birth weight grams
smk Smoked during pregnancy 1 smoked 0 did not smoke
race Mothers race 1 black 0 white
age Mothers age years
Loosely adapted from data from Applied
Logistic Regression, David W. Hosmer, Jr. and
Stanley Lemeshow
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Example 1 Low birth weight and interaction
between smoking and race (1black, 0white)
Logistic regression model Add smk by race
interaction Create interaction term and run
logistic regression . gen smkxrace smk
race . logistic low smk race smkxrace
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Example 1 Low birth weight and interaction
between smoking and race (1black, 0white)

• --------------------------------------------------
  
• low OR z Pgtz 95 CI
• -------------------------------------------------
  
• smk 5.76 4.14 0.000 2.51 13.19
• race 5.43 4.13 0.000 2.43 12.15
• smkxrace .320 -2.08 0.038 .109 .936
• --------------------------------------------------
  
• Significant interaction Relationship differs
  between smoking and low birth wt depending on
  mothers race
• Question How to interpret the interaction OR?

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

• Convert ORs to beta coefficients and solve by
  categories of race . logit
• --------------------------------------------------
  
• low Coef. z Pgtz 95 CI
• -------------------------------------------------
  
• smk 1.751 4.14 0.000 0.921
  2.580
• race 1.693 4.13 0.000 0.889
  2.497
• smkxrace -1.141 -2.08 0.038 -2.216
  -0.066
• _cons -2.303
• --------------------------------------------------
  
• White OR e ß1 ß3(race) e 1.751
  1.141(0) 5.76
• Black OR e ß1 ß3(race) e 1.751
  1.141(1) 1.84

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Example 1 Low birth weight and interaction
between smoking and race (1black, 0white)
White . lincom smk 0smkxrace
----------------------------------------------
low OR z Pgtz 95 CI
---------------------------------------------
(1) 5.76 4.14 0.000 2.51 13.2
---------------------------------------------- Bl
ack . lincom smk 1smkxrace
----------------------------------------------
low OR z Pgtz 95 CI
---------------------------------------------
(1) 1.84 1.75 0.081 .928 3.65
----------------------------------------------
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Example 1 Low birth weight and interaction
between smoking and race (1black, 0white)

• 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 (OR1.8,
  but not statistically significant)

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

• Misinterpretations
• Black mothers have less risk for low birth wt
  babies compared to white mothers
• Its 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

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Example 1 Low birth weight and interaction
between smoking and race (1black, 0white)
-------------------------------------------------
race smk numobs prob lower
upper -----------------------------------------
-------- 0White 0No 88 0.091
0.046 0.171 0White 1Yes 104 0.365
0.279 0.462 1NonWh 0No 142
0.352 0.278 0.434 1NonWh 1Yes 44
0.500 0.356 0.644 -----------------------
-------------------------- Likelihood ratio
test of interaction for race smk LR
Chi2(1) 4.56 Prob gt Chi2
0.0328
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Example 1 Low birth weight and interaction
between smoking and race (1black, 0white)
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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
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Example 2 Low birth weight and interaction
between smoking and age (years)

• -------------------------------------------------
• low OR z Pgtz 95 CI
• ------------------------------------------------
  
• smk 0.382 -0.90 0.367 .047 3.110
• age 0.920 -2.61 0.009 .865 0.980
• smkxage 1.076 1.97 0.049 1.001 1.157
• -------------------------------------------------
• Significant interaction Relationship differs
  between smoking and low birth wt depending on
  mothers age
• Question How to interpret the interaction OR for
  a continuous interaction variable?

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

• Convert ORs to beta coefficients and solve for
  selected values of age . logit
• -------------------------------------------------
  
• low Coef. z Pgtz 95 CI
• ------------------------------------------------
  
• smk -.963 -0.90 0.367 -3.058
  1.131
• age -.083 -2.61 0.009 -0.145
  -0.021
• smkxage .073 1.97 0.049 0.001
  0.146
• _cons .805
• -------------------------------------------------
  
• Age15 OR e ß1 ß3(age) e 0.963
  0.073(15) 1.14
• Age35 OR e ß1 ß3(age) e 0.963
  0.073(35) 4.93

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Example 2 Low birth weight and interaction
between smoking and age (years)
Age15 . lincom smk 15smkxage
-----------------------------------------------
low OR z Pgtz 95 CI
----------------------------------------------
(1) 1.14 0.32 0.751 .503 2.59
----------------------------------------------- A
ge35 . lincom smk 35smkxage
-----------------------------------------------
low OR z Pgtz 95 CI
----------------------------------------------
(1) 4.93 2.59 0.010 1.47 16.5
-----------------------------------------------
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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

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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
• Its 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

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Example 2 Low birth weight and interaction
between smoking and age (years)
-gt smk 0 ---------------------------------
age pred_y lower upper
--------------------------------- 15
.392 .272 .527 17 .353
.259 .461 19 .317 .243
.400 (etc) ... ... ...
--------------------------------- -gt smk 1
--------------------------------- age
pred_y lower upper --------------------
------------- 15 .424 .285
.577 17 .419 .303 .546
(etc) ... ... ...
--------------------------------- Likelihood
ratio test for interaction of age smk LR
Chi2(1) 3.88 Prob gt Chi2 0.05
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Example 2 Low birth weight and interaction
between smoking and age (years)
p0.05
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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
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Example 3 Birth weight (grams) and interaction
between smoking and race
p0.006
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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
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Example 4 Birth weight (grams) and interaction
between smoking and age
p0.001
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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 age2 . gen age3
age3 . 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)
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Example 5 Birth weight (grams) and interaction
between smoking and age, age2, age3
p0.045
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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

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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
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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)
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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

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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 2squared

3squared and cubic model
for display purposes only displays regression
model Some other options level()
cluster(cluster_id)
nolist

savepred(ds_name)