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Sociology 601 Class 26: December 1, 2009 (partial)

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

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Sociology 601 Class 26: December 1, 2009 (partial)

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  1. 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

  2. Review: Regression with Curvilinearity

  3. Example 1: Regression with Interaction, step 0 • Regress earnings on gender and married/not married • yi = β0 + β1gender + β2married + ei • 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 = 1474 • -------------+------------------------------ F( 2, 1471) = 82.24 • Model | 8.5661e+10 2 4.2830e+10 Prob > F = 0.0000 • Residual | 7.6612e+11 1471 520817334 R-squared = 0.1006 • -------------+------------------------------ Adj R-squared = 0.0993 • Total | 8.5178e+11 1473 578263951 Root MSE = 22821 • ------------------------------------------------------------------------------ • conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • gender | -13867.11 1191.798 -11.64 0.000 -16204.91 -11529.3 • mar1 | 5465.959 1192.441 4.58 0.000 3126.894 7805.025 • _cons | 37785.12 1073.949 35.18 0.000 35678.49 39891.75 • ------------------------------------------------------------------------------ • married people (m&f) earn $5466 more than non married • women (gender=1) earn $13,867 less than men

  4. 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 = 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.)

  5. 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

  6. 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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