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

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Example 1: Regression with Interaction, step 0

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Example 1: Regression with Interaction, step 1Separate regressions of earnings on married, by gender:. regress conrinc mar1 if gender==0 /* men */ Source | SS df MS Number of obs = 725-------------+------------------------------ F( 1, 723) = 31.29 Model | 1.9321e+10 1 1.9321e+10 Prob > F = 0.0000 Residual | 4.4645e+11 723 617501240 R-squared = 0.0415-------------+------------------------------ Adj R-squared = 0.0402 Total | 4.6577e+11 724 643334846 Root MSE = 24850------------------------------------------------------------------------------ conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- mar1 | 10383.4 1856.279 5.59 0.000 6739.057 14027.74 _cons | 35065.27 1380.532 25.40 0.000 32354.94 37775.6------------------------------------------------------------------------------

. regress conrinc mar1 if gender==1 /* women */ Source | SS df MS Number of obs = 749-------------+------------------------------ F( 1, 747) = 0.26 Model | 106732224 1 106732224 Prob > F = 0.6129 Residual | 3.1118e+11 747 416578779 R-squared = 0.0003-------------+------------------------------ Adj R-squared = -0.0010 Total | 3.1129e+11 748 416164546 Root MSE = 20410------------------------------------------------------------------------------ conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- mar1 | 755.3387 1492.253 0.51 0.613 -2174.17 3684.848 _cons | 26201 1038.855 25.22 0.000 24161.57 28240.42------------------------------------------------------------------------------

•looks like marriage is associated with higher earnings more for men (+$10,383, p<001) than for women (+$755, n.s.)

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Example 1: Regression with Interaction, step 2

• to test whether the male and female coefficients are significantly different, we must calculate an interaction model:

• yi = β0 + β1genderi + β2marriedi + β3genderi*marriedi + ei

. gen byte margen=gender*mar1(1 missing value generated)

. regress conrinc gender mar1 margen Source | SS df MS Number of obs = 1474-------------+------------------------------ F( 3, 1470) = 60.89 Model | 9.4145e+10 3 3.1382e+10 Prob > F = 0.0000 Residual | 7.5764e+11 1470 515399826 R-squared = 0.1105-------------+------------------------------ Adj R-squared = 0.1087 Total | 8.5178e+11 1473 578263951 Root MSE = 22702------------------------------------------------------------------------------ conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- gender | -8864.271 1710.548 -5.18 0.000 -12219.65 -5508.897 mar1 | 10383.4 1695.885 6.12 0.000 7056.784 13710.01 margen | -9628.059 2372.993 -4.06 0.000 -14282.87 -4973.246 _cons | 35065.27 1261.245 27.80 0.000 32591.24 37539.3------------------------------------------------------------------------------

•t(b3) = -4.06; p<001; so marriage has different associations with earnings for men and women

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Example 1: Regression with Interaction, step 2b• results for the interaction model:

• yhat = $35,065 - $8,864*gender + $10,383*married - $9,628 *genderi*married

• Calculate average earnings for different types:

• The marriage effect:

• The marriage effect for men is 45448-35065 = 10383 = b2

• The marriage effect for women is 26956-26201 = 755 = b2 + b3

• The gender effect:

• The gender effect for the not married is 26201-35065= -8864 = b1

• The gender effect for the married is 26956-45448 = -18492 = b1+ b3

• b3 = the difference in the marriage effect between men & women

• b3 = the difference in the gender effect between the married & unmarried

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constant gender married margen total

unmarried men = 35065 -8864*0 +10383*0 -9628*0*0 35065

unmarried women 35065 -8864*1 +10383*0 -9628*1*0 26201

married men = 35065 -8864*0 +10383*1 -9628*0*1 45448

married women = 35065 -8864*1 +10383*1 -9628*1*1 26956