Sociology 601 Class 24: November 19, 2009 (partial)

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

Review: Types of 3-variable Causal Models

• Spurious• x2 causes both x1 and y• e.g., age causes both marital status and earnings

• Intervening• x1 causes x2 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 x1 and y depends on the value of another variable, x2

• e.g., the relationship between marital status and earnings is different for men and women.

2

Review: Regression models using Stata

see:

http://www.bsos.umd.edu/socy/vanneman/socy601/conrinc.do

3

Review: Regression models with EarningsMarital status, Age, and Hours worked.

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Model 0 Model 1 Model 2 Model 2

Married 10,383.4*** 8,243.1*** 7,328.5*** 7,465.1***

Age 702.1*** 631.6*** 640.2***

Hours worked 281.3*** 278.3***

Constant 35,065.3*** 8,836.3* -232.1n.s. -493.8n.s.

N 725 725 664 725

R-square 0.042 0.091 0.102 0.133

Regression with Dummy Variables

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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

Regression with Dummy Variables: example

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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 78.11never married | 407 21.89 100.00--------------+----------------------------------- Total | 1,859 100.00

Dummy Variables: stata programming

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* 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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. 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) b1 = 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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Omitted category = never married (mar5) b2 = 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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Omitted category = never married (mar5) b3 = 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 b3 < b2, but b3 is statistically significant even though b2 is not.

• High standard error of b2 (because few widowed men 25-54).

Inferences: F-tests Comparing models

11

Comparing Regression Models, Agresti & Finlay, p 409:

Where:Rc

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, andN = number of cases.

€

F =Rc2− Rr2( ) / k − g( )

(1− Rc2) / [N − (k +1)]

df 1= k − g; df 2 = N − (k +1)

Next: Regression with Interaction Effects

12

Examples with earnings:• age x gender• marital status x gender

Sociology 601 Class 24: November 19, 2009 (partial)

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