> age <- c(25,35,45,55,25,35,45,55) > mr <- c(0,0,0,0,1,1,1,1) > ed.0 <- c(77,205,131,73,25,32,14,2) > ed.1 <- c(35,101,77,53,35,55,44,27) > > # Note that y is made up of (number of Ss, # of Fs) > y <- cbind(ed.1,ed.0) > > print(cbind(age,mr,y)) age mr ed.1 ed.0 [1,] 25 0 35 77 [2,] 35 0 101 205 [3,] 45 0 77 131 [4,] 55 0 53 73 [5,] 25 1 35 25 [6,] 35 1 55 32 [7,] 45 1 44 14 [8,] 55 1 27 2 > > mod0 <- glm(y~1, family=binomial("logit")) > summary(mod0) Call: glm(formula = y ~ 1, family = binomial("logit")) Deviance Residuals: Min 1Q Median 3Q Max -3.685 -2.037 1.027 4.059 5.736 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.26937 0.06427 -4.191 2.78e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 101.62 on 7 degrees of freedom Residual deviance: 101.62 on 7 degrees of freedom AIC: 141.82 Number of Fisher Scoring iterations: 4 > > mod1 <- glm(y~age, family=binomial("logit")) > summary(mod1) Call: glm(formula = y ~ age, family = binomial("logit")) Deviance Residuals: Min 1Q Median 3Q Max -3.0953 -1.9333 0.9069 4.2101 5.0860 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.915497 0.274247 -3.338 0.000843 *** age 0.016486 0.006785 2.430 0.015114 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 101.618 on 7 degrees of freedom Residual deviance: 95.684 on 6 degrees of freedom AIC: 137.89 Number of Fisher Scoring iterations: 4 > > anova(mod0,mod1,test="Chisq") Analysis of Deviance Table Model 1: y ~ 1 Model 2: y ~ age Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 7 101.618 2 6 95.684 1 5.9332 0.01486 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > mod2 <- glm(y~age+mr, family=binomial("logit")) > summary(mod2) Call: glm(formula = y ~ age + mr, family = binomial("logit")) Deviance Residuals: 1 2 3 4 5 6 7 8 0.9127 0.1527 -0.3859 -0.5244 -0.5908 -0.8941 0.5033 2.2625 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.602726 0.299229 -5.356 8.5e-08 *** age 0.025036 0.007186 3.484 0.000494 *** mr 1.468761 0.163629 8.976 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 101.6176 on 7 degrees of freedom Residual deviance: 7.8012 on 5 degrees of freedom AIC: 52.002 Number of Fisher Scoring iterations: 4 > > anova(mod1,mod2,test="Chisq") Analysis of Deviance Table Model 1: y ~ age Model 2: y ~ age + mr Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 6 95.684 2 5 7.801 1 87.883 < 2.2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > mod3 <- glm(y~age+mr+age:mr, family=binomial("logit")) > summary(mod3) Call: glm(formula = y ~ age + mr + age:mr, family = binomial("logit")) Deviance Residuals: 1 2 3 4 5 6 7 8 0.28400 -0.21156 -0.09437 0.18448 0.70005 -0.76602 -0.41088 1.17720 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.257466 0.334854 -3.755 0.000173 *** age 0.016436 0.008141 2.019 0.043509 * mr 0.013092 0.676970 0.019 0.984570 age:mr 0.039497 0.018047 2.189 0.028628 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 101.6176 on 7 degrees of freedom Residual deviance: 2.7998 on 4 degrees of freedom AIC: 49.001 Number of Fisher Scoring iterations: 4 > > anova(mod2,mod3,test="Chisq") Analysis of Deviance Table Model 1: y ~ age + mr Model 2: y ~ age + mr + age:mr Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 5 7.8012 2 4 2.7998 1 5.0014 0.02533 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1