REGRESSION ON SUBSETS OF OBSERVATIONS: USING DUMMY VARIABLES AND INTERACTIONS

Transcription

1 PLS 802 Spring 2018 Professor Jacoby REGRESSION ON SUBSETS OF OBSERVATIONS: USING DUMMY VARIABLES AND INTERACTIONS Assume that you believe the regression analysis of the influences on issue attitudes should be carried out separately for men and women. One way to accomplish this would be to estimate the equation twice, obtaining separate sets of OLS coefficients and related statistics for men and women. But, another strategy would be to use a dummy variable and multiplicative terms (or interactions ) to enable the intercept and the effects of all independent variables to differ by gender. The potential advantage of this latter approach is that it facilitates assessment of the statistical significance of the differences between males and females. The remainder of this handout shows the log of a Stata session that uses these two strategies (i.e., separate regression equations and a model with interactions) to examine differences in the determinants of issue attitudes by gender. - name: <unnamed> log: l:\pls 802, spring 2018\dummy vars\subsets\subsets.smcl log type: smcl.. set more off. #delimit ; delimiter now ; Use the issues dataset. use issues; (Written by R. ) Estimate regression using all observations in dataset. regress att party ideol racism welfare > poor afamer fedgov egal moral; Source SS df MS Number of obs = F( 9, 1470) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = party ideol racism welfare

2 Page 2 poor afamer fedgov egal moral _cons Convert the gender variable to a zero-one dummy variable. generate female = gender - 1; Use the "by" prefix to carry out the regression analysis of issue attitudes separately for men (female = 0) and for women (female = 1).. by female, sort: > regress att party ideol racism welfare > poor afamer fedgov egal moral; - -> female = 0 Source SS df MS Number of obs = F( 9, 734) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = party ideol racism welfare poor afamer fedgov egal moral _cons

3 Page 3 - -> female = 1 Source SS df MS Number of obs = F( 9, 726) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = party ideol racism welfare poor afamer fedgov egal moral _cons Create multiplicative terms between "female" and all nine independent variables. generate fparty = female * party;. generate fideol = female * ideol;. generate fracism = female * racism;. generate fwelf = female * welfare;. generate fpoor = female * poor;. generate fafamer = female * afamer;. generate ffed = female * fedgov;. generate fegal = female * egal;. generate fmoral = female * moral; Estimate equation with the nine original variables, the dummy variable, and all nine multiplicative terms

4 Page 4. regress att party ideol racism welfare > poor afamer fedgov egal moral > female fparty fideol fracism > fwelf fpoor fafamer ffed > fegal fmoral; Source SS df MS Number of obs = F( 19, 1460) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = party ideol racism welfare poor afamer fedgov egal moral female fparty fideol fracism fwelf fpoor fafamer ffed fegal fmoral _cons Obtain critical value of F and carry out F test for the new subset of coefficients. display invftail(10, 1460, 0.05); test female fparty fideol fracism > fwelf fpoor fafamer ffed > fegal fmoral;

5 Page 5 ( 1) female = 0 ( 2) fparty = 0 ( 3) fideol = 0 ( 4) fracism = 0 ( 5) fwelf = 0 ( 6) fpoor = 0 ( 7) fafamer = 0 ( 8) ffed = 0 ( 9) fegal = 0 (10) fmoral = 0 F( 10, 1460) = 3.33 Prob > F = Examine conditional effects by using coefficients and linear combinations.. lincom _cons + female; ( 1) female + _cons = 0 (1) lincom party + fparty; ( 1) party + fparty = 0 (1) lincom ideol + fideol; ( 1) ideol + fideol = 0 (1)

6 Page 6. lincom racism + fracism; ( 1) racism + fracism = 0 (1) lincom welfare + fwelf; ( 1) welfare + fwelf = 0 (1) lincom poor + fpoor; ( 1) poor + fpoor = 0 (1) lincom afamer + fafamer; ( 1) afamer + fafamer = 0 (1) lincom fedgov + ffed; ( 1) fedgov + ffed = 0 (1)

7 Page 7. lincom egal + fegal; ( 1) egal + fegal = 0 (1) lincom moral + fmoral; ( 1) moral + fmoral = 0 (1) log close; name: <unnamed> log: l:\pls 802, spring 2018\dummy vars\subsets\subsets.smcl log type: smcl -