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PSC 5940: Interactions as MultiLevel Models
Session 3
Fall, 2009
September 8, 2009
Session 3
Slide 1
Workshop: PRCs
• Load EE data
• Run a simple model:
• Willingness to pay for an alternative energy tax
• Use randomly assigned “price” as IV
• Plot to relationship (use jitter)
• Now add: Income, Ideology
• Change in price variable? (Why?)
September 8, 2009
Session 3
Slide 2
Model Elaboration
• EE09 & NS09 Data: research thinking
• Analysis of residuals
• Additions to the ERDF model:
• Belief in anthropogenic climate change
• Recodes?
• Understanding of GCC science
• Recode “What scientists’ believe…” variables
• Turn in 1 page summaries
September 8, 2009
Session 3
Slide 3
Dummy Intercept Variables
• Dummy variables allow for tests of the differences
in overall value of the Y for different nominal
groups in the data (akin to a difference of means)
• Coding: 0 and 1 values (e.g., men versus women)
Y
X2,0
X2,1
X1
September 8, 2009
Session 3
Slide 4
Modeling Belief in GCC as a function of
knowledge and Republican Party Identification
Call:
lm(formula = gcc_bel ~ R_id + gcc_knowl)
Residuals:
Min
1Q Median
3Q Max
-16.158 -2.582 1.842 3.842 12.460
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.4467 0.5529 -2.617 0.00897 **
R_id
-3.0135 0.3110 -9.688 < 2e-16 ***
gcc_knowl 1.5210 0.1310 11.613 < 2e-16 ***
--Residual standard error: 5.526 on 1507 degrees of freedom
(188 observations deleted due to missingness)
Multiple R-squared: 0.1468,
Adjusted R-squared: 0.1457
F-statistic: 129.7 on 2 and 1507 DF, p-value: < 2.2e-16
Belief in GCC systematically lower for those who identify as
Republicans
September 8, 2009
Session 3
Slide 5
Dummy Variable Applications
• Implies a comparison (the omitted group)
– Be clear about the “comparison category”
• Multinomial Dummies
– When categories exceed 2
• Importance of specifying the base category
• Examples of Category Variables
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Experimental treatment groups
Race and ethnicity
Region of residence
Type of education
Religious affiliation
“Seasonality”
• Adds to modeling flexibility
September 8, 2009
Session 3
Slide 6
Interaction Effects
• Interactions occur when the effect of one X is
dependent on the value of another
• Modeling interactions:
– Use Dummy variables (requires categories)
– Use multiplicative interaction effect
• Multiply an interval scale times a dummy (also known as a “slope
dummy”)
• Example: the effect of GCC knowledge (gcc_knowl)
on belief in climate change (gcc_bel) may be affected
by whether the respondent identifies with the
Republican Party (R_id)
– Re-code the interaction; run it.
September 8, 2009
Session 3
Slide 7
Modeling belief in Climate Change with a
Dummy Slope Variable: Knowledge*
Republican ID (=1)
Call:
lm(formula = gcc_bel ~ R_id + gcc_knowl + gcc_kn_R)
Residuals:
Min
1Q Median
3Q Max
-15.971 -2.610 1.691 4.029 13.826
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.6831 0.6696 -1.020 0.3079
R_id
-5.1433 1.1007 -4.673 3.24e-06 ***
gcc_knowl 1.3308 0.1613 8.252 3.37e-16 ***
gcc_kn_R
0.5563 0.2758 2.017 0.0439 *
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.521 on 1506 degrees of freedom
(188 observations deleted due to missingness)
Multiple R-squared: 0.1491,
Adjusted R-squared: 0.1474
F-statistic: 87.99 on 3 and 1506 DF, p-value: < 2.2e-16
September 8, 2009
Session 3
Slide 8
Illustration of Slope Interaction
Not
Republicans
Republicans
September 8, 2009
Session 3
Slide 9
BREAK
September 8, 2009
Session 3
Slide 10
Workshop
• Build Fully Interacted Models
• Dependent Variable Suggestions:
• Willingness to pay for an alternative energy tax
• Importance of Retaining US nuclear weapons
stockpile
• Risk of Climate Change
• Risk of Nuclear Energy
• Independent Variables: Income, Ideology
• Interact with Party ID
• Interact with religion
• Constructed category (options…)
• 1-page paper due next week
September 8, 2009
Session 3
Slide 11