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Logistic Regression July 28, 2008

Logistic Regression July 28, 2008. Ivan Katchanovski , Ph.D. POL 242Y-Y. Binary Logistic Regression. Appropriate when the dependent variable is a dummy variable Dummy variable: a variable that includes two categories which assume values 1 and 0

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Logistic Regression July 28, 2008

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  1. Logistic RegressionJuly 28, 2008 Ivan Katchanovski, Ph.D. POL 242Y-Y

  2. Binary Logistic Regression • Appropriate when the dependent variable is a dummy variable • Dummy variable: a variable that includes two categories which assume values 1 and 0 • Example: “Conservative party supporter”: Yes=1; No=0 • Binary: two values • One or many independent variables • Assumes non-linear relationship

  3. Regression Coefficients and Odds Ratio • Regression coefficients: • Interpretation is similar to interpretation of unstandardized regression coefficients in linear regression • Effect of a change of one unit of an independent variable on the logged odds of the dependent variable • Logged odds are not very easy to grasp • Odds Ratio: • Effect of a change of one unit of an independent variable on the change in the odds of the dependent variable • Better to grasp • If odds ratio more than 1: positive relationship • If odds ratio less than 1: negative relationship • If odds ratio equal to1: no relationship

  4. Statistical Significance • Statistical significanceof a regression coefficient: • Statistically significant if p(obtained)<p(critical)=.05 or .01 or .001 • Statistically nonsignificant if p(obtained)>p(critical)=.05 • Direction of association should be reported only for statistically significant regression coefficients

  5. Pseudo R Square • RSquare analogs in logistic regression • Power of independent variables in predicting the dependent variable • Cox & Snell R square • Ranges between 0 (no association) and less than 1 (perfect association) • Nagelkerke R square • Adjusts Cox & Snell R square so that its maximum value can equal 1 • Ranges between 0 (no association) and 1 (perfect association)

  6. Example: Multiple Research Hypotheses • First : The level of economic development has a positive effect on the odds that countries are democratic • Second: Former British colonies are more likely to be democratic compared to other countries • Third : Protestant countries are more likely to be democratic compared to other countries • Fourth: Ethnic and linguistic homogeneity has a positive effect on the odds of countries being democratic

  7. Example: Variables • Dataset: World • Dependent Variable: • Democracy (Is country democratic?) • Dummy variable • Independent Variables: • GDP per capita ($1000) • Interval-ratio • Ethno-linguistic heterogeneity • Ordinal treated as interval-ratio • Colony variable • Transformed into dummy variables • Religious culture variable • Transformed into dummy variables

  8. Binary Logistic Regression: SPSS Commands • SPSS Command: Analyze-Regression-Binary Logistic • “Dependent” box: Select the dependent variable • “Covariates” box: Select independent variables • Method: “Enter”

  9. Table: Determinants of democracy *** Statistically significant at the .01 level, ** statistically significant at the .05 level, * statistically significant at the .1 level

  10. Example: Statistical Significance • Number of cases: N=92 • .1 or 10% significance level can be used • Regression coefficient of the GDP variable: • SPSS: p(obtained)=.001 <p(critical)=.01=1% • Statistically significant at the .01 or 1% level • Regression coefficients of the other independent variables: • SPSS: p(obtained)=from .159 to .866 >p(critical)=.1 • Statistically insignificant

  11. Example: Regression Coefficients and Odds Ratio • Regression Coefficient of GDP per capita variable=.336 • Increase of $1000 in the level of GDP per capita increases the logged odds of country being democratic by .336 • Odds ratio of GDP per capita: • Increase of $1000 in the level of GDP per capita increases the odds of country being democratic by about 1.4 times

  12. Example: Interpretation • Nagelkerke R square=.645 • The logistic regression model has a strong predictive power • The first research hypothesis is supported by logistic regression analysis • The level of economic development has a positive and statistically significant effect on the odds of countries being democracies • All other research hypotheses are not supported by logistic regression analysis

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