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Sociology 601 Class 24: November 19, 2009 (partial) Review –regression results for spurious & intervening effects –care with sample sizes for comparing models Dummy variables F-tests comparing models Example from ASR 1

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Review: Types of 3-variable Causal Models Spurious x 2 causes both x 1 and y e.g., age causes both marital status and earnings Intervening x 1 causes x 2 which causes y e.g., marital status causes more hours worked which raises annual earnings No statistical difference between these models. Statistical interaction effects: The relationship between x 1 and y depends on the value of another variable, x 2 e.g., the relationship between marital status and earnings is different for men and women. 2

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Review: Regression models using Stata see: http://www.bsos.umd.edu/socy/vanneman/socy601/conrinc.do 3

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Review: Regression models with Earnings Marital status, Age, and Hours worked. 4 Model 0Model 1Model 2 Married10,383.4***8,243.1***7,328.5***7,465.1*** Age702.1***631.6***640.2*** Hours worked281.3***278.3*** Constant35,065.3***8,836.3*-232.1n.s.-493.8n.s. N725 664725 R-square0.0420.0910.1020.133

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Regression with Dummy Variables 5 Agresti and Finlay 12.3 (skim 12.1-12.2 on analysis of variance) Example: marital status, 5 categories married widowed divorced separated never married

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Regression with Dummy Variables: example 6 Example: marital status, 5 categories married widowed divorced separated never married. tab marital marital | status | Freq. Percent Cum. --------------+----------------------------------- married | 969 52.12 52.12 widowed | 48 2.58 54.71 divorced | 337 18.13 72.83 separated | 98 5.27 78.11 never married | 407 21.89 100.00 --------------+----------------------------------- Total | 1,859 100.00

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Dummy Variables: stata programming 7 * create 5 dummy variables from marital status: gen byte married=0 if marital<. replace married=1 if marital==1 gen byte widow=0 if marital<. replace widow=1 if marital==2 gen byte divorced=0 if marital<. replace divorced=1 if marital==3 gen byte separated=0 if marital<. replace separated=1 if marital==4 gen byte nevermar=0 if marital<. replace nevermar=1 if marital==5 * check marital dummies (maritalcheck should =1 for all nonmissing cases) egen byte maritalcheck=rowtotal(married widow divorced separated nevermar) tab marital maritalcheck, missing * shortcut method: tab marital, gen(mar) describe mar* * check new mar dummies (marcheck should =1 for all nonmissing cases) egen byte marcheck=rowtotal(mar1-mar5) tab marital marcheck, missin

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Regression with Dummy Variables: example 8. regress conrinc mar1-mar4 if sex==1 Source | SS df MS Number of obs = 725 -------------+------------------------------ F( 4, 720) = 9.78 Model | 2.4002e+10 4 6.0006e+09 Prob > F = 0.0000 Residual | 4.4177e+11 720 613572279 R-squared = 0.0515 -------------+------------------------------ Adj R-squared = 0.0463 Total | 4.6577e+11 724 643334846 Root MSE = 24770 ------------------------------------------------------------------------------ conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mar1 | 14111.68 2316.232 6.09 0.000 9564.302 18659.05 mar2 | 11331.78 7143.717 1.59 0.113 -2693.223 25356.79 mar3 | 6709.996 2970.39 2.26 0.024 878.3349 12541.66 mar4 | 8404.298 5074.261 1.66 0.098 -1557.817 18366.41 _cons | 31336.99 1958.271 16.00 0.000 27492.38 35181.59 ------------------------------------------------------------------------------ Omitted category = never married (mar5) b 1 = 14111; Currently married men earn on average $14,111 more than never married men. t= 6.09; p<001; so, statistically significant (more than single men).

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Regression with Dummy Variables: example 9. regress conrinc mar1-mar4 if sex==1 Source | SS df MS Number of obs = 725 -------------+------------------------------ F( 4, 720) = 9.78 Model | 2.4002e+10 4 6.0006e+09 Prob > F = 0.0000 Residual | 4.4177e+11 720 613572279 R-squared = 0.0515 -------------+------------------------------ Adj R-squared = 0.0463 Total | 4.6577e+11 724 643334846 Root MSE = 24770 ------------------------------------------------------------------------------ conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mar1 | 14111.68 2316.232 6.09 0.000 9564.302 18659.05 mar2 | 11331.78 7143.717 1.59 0.113 -2693.223 25356.79 mar3 | 6709.996 2970.39 2.26 0.024 878.3349 12541.66 mar4 | 8404.298 5074.261 1.66 0.098 -1557.817 18366.41 _cons | 31336.99 1958.271 16.00 0.000 27492.38 35181.59 ------------------------------------------------------------------------------ Omitted category = never married (mar5) b 2 = 11331; Currently widowed men earn on average $11,331 more than never married men. t= 1.59; p=.11; so, not statistically significant. So, no earnings difference between widowed men and never married men.

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Regression with Dummy Variables: example 10. regress conrinc mar1-mar4 if sex==1 Source | SS df MS Number of obs = 725 -------------+------------------------------ F( 4, 720) = 9.78 Model | 2.4002e+10 4 6.0006e+09 Prob > F = 0.0000 Residual | 4.4177e+11 720 613572279 R-squared = 0.0515 -------------+------------------------------ Adj R-squared = 0.0463 Total | 4.6577e+11 724 643334846 Root MSE = 24770 ------------------------------------------------------------------------------ conrinc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mar1 | 14111.68 2316.232 6.09 0.000 9564.302 18659.05 mar2 | 11331.78 7143.717 1.59 0.113 -2693.223 25356.79 mar3 | 6709.996 2970.39 2.26 0.024 878.3349 12541.66 mar4 | 8404.298 5074.261 1.66 0.098 -1557.817 18366.41 _cons | 31336.99 1958.271 16.00 0.000 27492.38 35181.59 ------------------------------------------------------------------------------ Omitted category = never married (mar5) b 3 = 6709.996; Currently divorced men earn on average $6,710 more than never married men. t= 2.26; p<.05; so, statistically significant (more than single men). Note that b 3 < b 2, but b 3 is statistically significant even though b 2 is not. High standard error of b 2 (because few widowed men 25-54).

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Inferences: F-tests Comparing models 11 Comparing Regression Models, Agresti & Finlay, p 409: Where: R c 2 = R-square for complete model, R r 2 = R-square for reduced model, k = number of explanatory variables in complete model, g = number of explanatory variables in reduced model, and N = number of cases.

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Next: Regression with Interaction Effects 12 Examples with earnings: age x gender marital status x gender

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