The following R output shows output from fitting a cumulative logit model to data from the US 2008 General Social Survey. For subject i let yi = belief in existence of heaven (1 = yes, 2 = unsure, 3 = no), xi1 = gender (1 = female, 0 = male) and xi2 = race (1 = black, 0 = white). State the model fitted here, and interpret the race and gender effects. Test goodness-of-fit and construct confidence intervals for the effects.

> cbind(race, gender, y1, y2, y3)
race gender y1 y2 y3 [1,] 1 1 88 16 2 [2,] 1 0 54 7 5 [3,] 0 1 397 141 24 [4,] 0 0 235 189 39 > summary(vglm(cbind(y1,y2,y3)~gender+race,family=cumulative(parallel=T)))
Estimate Std. Error z value (Intercept):1 0.0763 0.0896 0.8515 (Intercept):2 2.3224 0.1352 17.1749 gender 0.7696 0.1225 6.2808 race 1.0165 0.2106 4.8266 Residual deviance: 9.2542 on 4 degrees of freedom Log-likelihood: -23.3814 on 4 degrees of freedom -------------------------------------------------------------------------