What does the variable β₁mean in the 2nd logistic regression (Table 13.63)? How does it differ from the meaning of β₁in the 1st logistic regression (Table 13.62)? 

Two logistic models were run with Stata Version 11 using these data. For the 1st model (Table 13.62) we fit

Logit (P_i) = Î± + Î²₁x₁ + β₂x₂, 

Where x₁ = age at menarche (1 represents ‰¥ 12, 0 represents < 12),

X₂ = race (1 = African American, 0 Caucasian).

For the 2^nd model (Table 13.63) we fit

Logit (Pi) = Î± + Î²₁x₁ + β₂x₂ + β₃x₁x₂. 

Table 13.62 Logistic regression of ovarian cancer on age at menarche and race

 

Table 13.63 Logistic regression of ovarian cancer on age at menarche, race, and age at menarche × race

 

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logit case ageatmenarche race [fweight=freq] Logistic regression Number of obs 1907 LR chi2 (2) 15.76 Prob > chi2 0.0004 Pseudo R2 Log likelihood = -1303.3411 0.0060 P>|z| [95% Conf. Interval] Coef. Std. Err. case ageatmenar-e | -.2860765 0.010 -.5043864 .1113846 -2.57 -.0677666 -.4082626 .1304354 -3.13 0.002 -.6639112 -.152614 race .0735805 .1010801 0.73 0.467 -.1245329 .271694 cons gen agemenarche_race=ageatmenarche * race I| || || logit case ageatmenarche race agemenarche_race [fweight=freq] Logistic regression Number of obs 1907 LR chi2 (3) 18.66 Prob > chi2 0.0003 Log 1ikelihood = -1301.8882 Pseudo R2 0.0071 Coef. Std. Err. P>|z| [95% Conf. Interval] case .--- ageatmenar-e | -.3731935 1228254 -3.04 0.002 -.6139268 -.1324601 race -.7803386 .2578292 -3.03 0.002 -1.285675 -.2750027 agemenarche * race .5053452 .29869 1.69 0.091 -.0800764 1.090767 cons .1422512 .1090609 1.30 0.192 -.0715043 .3560067