data(gala, package = "faraway")
head(gala)
## Species Endemics Area Elevation Nearest Scruz Adjacent
## Baltra 58 23 25.09 346 0.6 0.6 1.84
## Bartolome 31 21 1.24 109 0.6 26.3 572.33
## Caldwell 3 3 0.21 114 2.8 58.7 0.78
## Champion 25 9 0.10 46 1.9 47.4 0.18
## Coamano 2 1 0.05 77 1.9 1.9 903.82
## Daphne.Major 18 11 0.34 119 8.0 8.0 1.84
ポアソン回帰
res <- glm(Species ~ ., gala, family = poisson)
summary(res)
##
## Call:
## glm(formula = Species ~ ., family = poisson, data = gala)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.99 -2.93 -0.43 1.32 7.47
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.83e+00 5.96e-02 47.47 < 2e-16 ***
## Endemics 3.39e-02 1.74e-03 19.46 < 2e-16 ***
## Area -1.07e-04 3.74e-05 -2.85 0.0043 **
## Elevation 2.64e-04 1.93e-04 1.36 0.1726
## Nearest 1.05e-02 1.61e-03 6.50 7.9e-11 ***
## Scruz -6.83e-04 5.80e-04 -1.18 0.2388
## Adjacent 4.54e-05 4.80e-05 0.95 0.3444
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 3510.73 on 29 degrees of freedom
## Residual deviance: 313.36 on 23 degrees of freedom
## AIC: 488.2
##
## Number of Fisher Scoring iterations: 5
##
超過分散の指標(逸脱度/自由度>1かどうか)
res$deviance/res$df.residual
## [1] 13.62
擬似ポアソン回帰
res.q <- glm(Species ~ ., gala, family = quasipoisson)
summary(res.q)
##
## Call:
## glm(formula = Species ~ ., family = quasipoisson, data = gala)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.99 -2.93 -0.43 1.32 7.47
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.83e+00 2.15e-01 13.17 3.4e-12 ***
## Endemics 3.39e-02 6.28e-03 5.40 1.8e-05 ***
## Area -1.07e-04 1.35e-04 -0.79 0.437
## Elevation 2.64e-04 6.97e-04 0.38 0.709
## Nearest 1.05e-02 5.81e-03 1.80 0.084 .
## Scruz -6.83e-04 2.09e-03 -0.33 0.747
## Adjacent 4.54e-05 1.73e-04 0.26 0.795
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 13)
##
## Null deviance: 3510.73 on 29 degrees of freedom
## Residual deviance: 313.36 on 23 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 5
##
負の二項回帰
library(MASS)
res.nb <- glm.nb(Species ~ ., gala, link = log)
summary(res.nb)
##
## Call:
## glm.nb(formula = Species ~ ., data = gala, link = log, init.theta = 3.006375104)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.119 -0.874 -0.188 0.410 1.720
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.51e+00 2.02e-01 12.43 < 2e-16 ***
## Endemics 4.78e-02 9.93e-03 4.81 1.5e-06 ***
## Area -2.47e-04 2.32e-04 -1.06 0.29
## Elevation 3.36e-05 9.85e-04 0.03 0.97
## Nearest 6.12e-03 1.03e-02 0.60 0.55
## Scruz -5.16e-04 2.23e-03 -0.23 0.82
## Adjacent 8.71e-05 2.46e-04 0.35 0.72
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(3.006) family taken to be 1)
##
## Null deviance: 152.304 on 29 degrees of freedom
## Residual deviance: 33.396 on 23 degrees of freedom
## AIC: 289.9
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 3.006
## Std. Err.: 0.904
##
## 2 x log-likelihood: -273.894