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Analyzing Belief in Climate Change: Interaction Effects and Multi-Level Modeling Workshop

This workshop explores advanced modeling techniques in political science, focusing on the willingness to pay for alternative energy taxes and belief in climate change. Participants will utilize dummy variables to investigate interaction effects between knowledge of climate change and political identification, particularly among Republicans. We will analyze residuals and elaborate on models using recent data. Emphasis will be placed on specifying base categories and understanding non-linear relationships, culminating in the construction of fully interacted models.

yoshio-zamora
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Analyzing Belief in Climate Change: Interaction Effects and Multi-Level Modeling Workshop

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  1. PSC 5940: Interactions as Multi-Level Models Session 3 Fall, 2009

  2. 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?)

  3. 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

  4. 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

  5. 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

  6. 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 • Experimental treatment groups • Race and ethnicity • Region of residence • Type of education • Religious affiliation • “Seasonality” • Adds to modeling flexibility

  7. 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.

  8. 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

  9. Illustration of Slope Interaction Not Republicans Republicans

  10. BREAK

  11. 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

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