Sociology 601 Class 26: December 1, 2009 (partial) Review –curvilinear regression results –cubic polynomial Interaction effects –example: earnings on married and gender –example: earnings on marital statuses and gender –example: earnings on age and gender –example: earnings on age and education F-tests comparing models Article example 1

Review: Regression with Curvilinearity 2

Example 1: Regression with Interaction, step 0 Regress earnings on gender and married/not married y i = β 0 + β 1 gender + β 2 married + e i both gender and married are dummy variables easier calculations if all dummy variables are 0/1 no interaction: assumes marriage has same association with (higher) earnings for both men and women. regress conrinc gender mar1 Source | SS df MS Number of obs = F( 2, 1471) = Model | e e+10 Prob > F = Residual | e R-squared = Adj R-squared = Total | e Root MSE = conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] gender | mar1 | _cons | married people (m&f) earn $5466 more than non married women (gender=1) earn $13,867 less than men 3

Example 1: Regression with Interaction, step 1 Separate regressions of earnings on married, by gender:. regress conrinc mar1 if gender==0 /* men */ Source | SS df MS Number of obs = F( 1, 723) = Model | e e+10 Prob > F = Residual | e R-squared = Adj R-squared = Total | e Root MSE = conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] mar1 | _cons | regress conrinc mar1 if gender==1 /* women */ Source | SS df MS Number of obs = F( 1, 747) = 0.26 Model | Prob > F = Residual | e R-squared = Adj R-squared = Total | e Root MSE = conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] mar1 | _cons | looks like marriage is associated with higher earnings more for men (+$10,383, p<001) than for women (+$755, n.s.) 4

Example 1: Regression with Interaction, step 2 to test whether the male and female coefficients are significantly different, we must calculate an interaction model: y i = β 0 + β 1 gender i + β 2 married i + β 3 gender i *married i + e i. gen byte margen=gender*mar1 (1 missing value generated). regress conrinc gender mar1 margen Source | SS df MS Number of obs = F( 3, 1470) = Model | e e+10 Prob > F = Residual | e R-squared = Adj R-squared = Total | e Root MSE = conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] gender | mar1 | margen | _cons | t(b 3 ) = -4.06; p<001; so marriage has different associations with earnings for men and women 5

Example 1: Regression with Interaction, step 2b results for the interaction model: y hat = $35,065 - $8,864*gender + $10,383*married - $9,628 *gender i *married Calculate average earnings for different types: The marriage effect: The marriage effect for men is = = b 2 The marriage effect for women is = 755 = b 2 + b 3 The gender effect: The gender effect for the not married is = = b 1 The gender effect for the married is = = b 1 + b 3 b 3 = the difference in the marriage effect between men & women b 3 = the difference in the gender effect between the married & unmarried 6 constantgendermarriedmargentotal unmarried men = * *0-9628*0* unmarried women * *0-9628*1* married men = * *1-9628*0* married women = * *1-9628*1*126956