我构建了一个负二项式模型，用于检查另一个“juv_cneb_den”（偏移量=“Area_towed”）上的1个计数变量=“carid_den”的关系，以及一个位置因子=“区域”。
我的完整模型上的摘要命令表明该因子的所有级别在统计上都不显着（> 0.05）。然而，在放弃这个因素后，我得到了一个稍高的 AIC 值，我认为这意味着这个因素以某种方式使模型变得更好。如果因素不重要，为什么 AIC 值会下降？较低的 AIC 值不是表明模型更好吗？有直观的解释吗？
我的数据：
> head(df)
Zone TOTAL juv_cneb_count Area_towed
1 Whipray 2 0 383.9854
2 West 38 0 382.2256
3 Crocodile 25 0 408.3697
4 Rankin 2 0 422.1000
5 Rankin 3 0 165.5196
6 West 6 1 266.7000
> summary(nb_full)
Call:
glm.nb(formula = juv_cneb_count ~ TOTAL + Zone + offset(log(Area_towed)),
data = dat, init.theta = 0.2371440904, link = log)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.3378 -0.7787 -0.6540 0.0000 4.0603
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.930e+01 1.575e+06 0.000 1.0000
TOTAL 1.946e-03 9.294e-04 2.094 0.0363 *
ZoneRankin 3.220e+01 1.575e+06 0.000 1.0000
ZoneWest 3.282e+01 1.575e+06 0.000 1.0000
ZoneWhipray 3.119e+01 1.575e+06 0.000 1.0000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for Negative Binomial(0.2371) family taken to be 1)
Null deviance: 278.96 on 449 degrees of freedom
Residual deviance: 241.60 on 445 degrees of freedom
AIC: 751.89
Number of Fisher Scoring iterations: 1
Theta: 0.2371
Std. Err.: 0.0407
2 x log-likelihood: -739.8900
> summary(base)
Call:
glm.nb(formula = juv_cneb_count ~ TOTAL + offset(log(Area_towed)),
data = dat, init.theta = 0.1965321662, link = log)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.4967 -0.6980 -0.6810 -0.5667 4.1964
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.776742 0.135157 -50.140 < 2e-16 ***
TOTAL 0.003362 0.000984 3.416 0.000634 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for Negative Binomial(0.1965) family taken to be 1)
Null deviance: 252.73 on 449 degrees of freedom
Residual deviance: 246.63 on 448 degrees of freedom
AIC: 775.16
Number of Fisher Scoring iterations: 1
Theta: 0.1965
Std. Err.: 0.0329
2 x log-likelihood: -769.1590