For the horseshoe crab data, the negative binomial modeling shown in the R output first treats color as nominal-scale and then in a quantitative manner, with the category numbers as scores. Interpret the result of the likelihoodratio test comparing the two models. For the simpler model, interpret the color effect and interpret results of the likelihood-ratio test of the null hypothesis of no color effect.

-------------------------------------------------------------------

> fit.nb.color <- glm.nb(y ~ factor(color)) # Using Crabs.dat file

> summary(fit.nb.color)

Estimate Std. Error z value Pr(>|z|)

(Intercept) 1.4069 0.3526 3.990 6.61e-05 factor(color)2 -0.2146 0.3750 -0.572 0.567 factor(color)3 -0.6061 0.4036 -1.502 0.133 factor(color)4 -0.6913 0.4508 -1.533 0.125

---

> fit.nb.color2 <- glm.nb(y ~ color) # using color scores (1,2,3,4)

> summary(fit.nb.color2)

Estimate Std. Error z value Pr(>|z|)

(Intercept) 1.7045 0.3095 5.507 3.66e-08 color -0.2689 0.1225 -2.194 0.0282

---

> anova(fit.nb.color2, fit.nb.color)

Likelihood ratio tests of Negative Binomial Models Response: y Model theta Res.df 2 x log-lik. Test df LR stat. Pr(Chi)

1 0.7986 171 -762.6794 2 0.8019 169 -762.2960 1 vs. 2 2 0.3834 0.8256

---

> 1 - pchisq(767.409-762.679, df=172-171) # LR test vs. null model

[1] 0.0296

-------------------------------------------------------------------