检查残差并可视化零充气泊松系数
[英]examining residuals and visualizing zero-inflated poission r
问题描述
I am running a zero-inflated model for CPUE data. 
我正在为CPUE数据运行零膨胀模型。 This data has evidence of zero-inflation which I have confirmed with a Vuong test (in code below). 这些数据具有零通货膨胀的证据，我已经通过Vuong测试确认了这一点（在下面的代码中）。 The full model (zint) is better than the null according to AIC. 根据AIC，完整模型（zint）优于null模型。 I now want to: 我现在要：
- Examine the residuals of the full model to determine model fit (having trouble due to lack of info from colleagues, internet, and R books) 检查完整模型的残差以确定模型拟合（由于缺乏同事，互联网和R书的信息而出现问题）
- If model fit appears to be okay, visualize the output of the model (how to formulate equations of real-parameter values when using an offset variable) 如果模型拟合看起来可以，请可视化模型的输出（使用偏移变量时如何公式化实参数值的方程式）
I have asked help from a few statisticians in the department (they have never done this before and send me to the same google search sites), outside to the stats department itself (everyone is too busy), and stackoverflow feeds. 我已经从部门的一些统计人员那里寻求帮助（他们以前从未这样做过，并把我发送到相同的Google搜索网站），在统计部门本身之外（每个人都很忙）以及stackoverflow提要。
I would appreciate code or guidance to books (available free online) with code that deal with visualizing ZIPs and model fit when using an offset variable. 我希望使用代码或书籍指南（可免费在线获得），其中包含使用偏移量时可视化ZIP和模型拟合的代码。
yc=read.csv("CPUE_ycs_trawl_withcobb_BLS.csv",header=TRUE)
yc=yc[which(yc$countinyear<150),]
yc$fyear=as.factor(yc$year_cap)
yc$flocation=as.factor(yc$location)
hist(yc$countinyear,20)
yc$logoffset=log(yc$numtrawlyr)
###Run Zero-inflated poisson with offset for CPUE####
null <- formula(yc$countinyear ~ 1| 1)
znull <- zeroinfl(null, offset=logoffset,dist = "poisson",link = "logit",
data = yc)
int <- formula(yc$countinyear ~ assnage * spawncob| assnage * spawncob)
zint <- zeroinfl(int, offset=logoffset,dist = "poisson",link = "logit", data
= yc)
AIC(znull,zint)
g1=glm(countinyear ~ assnage * spawncob,
offset=logoffset,data=yc,family=poisson)
summary(g1)
####Vuong test to see if ZIP is even needed##
vuong(g1,zint)
##########DATASET###########
countinyear is column #1 countinyear是第1栏
##########DATASET###########
count assnage spawncob logoffset
56 0 0.32110173 2.833213
44 1 0.33712 2.833213
60 2 0.34053264 2.833213
0 4 0.19381496 2.833213
1 3 0.30819333 2.833213
33 0 0.32110173 2.833213
40 1 0.33712 2.833213
25 2 0.34053264 2.833213
0 3 0.30819333 2.833213
2 4 0.19381496 2.833213
6 0 0.32110173 2.833213
13 1 0.33712 2.833213
7 2 0.34053264 2.833213
0 3 0.30819333 2.833213
0 4 0.19381496 NA
5 0 0.32110173 2.833213
31 1 0.33712 2.833213
73 2 0.34053264 2.833213
0 3 0.30819333 2.833213
1 4 0.19381496 2.833213
0 0 0.32110173 2.833213
7 1 0.33712 2.833213
75 2 0.34053264 2.833213
3 3 0.30819333 2.833213
0 4 0.19381496 2.833213
19 0 0.32110173 2.833213
13 1 0.33712 2.833213
18 2 0.34053264 2.833213
0 3 0.30819333 2.833213
2 4 0.19381496 2.833213
11 0 0.32110173 2.833213
14 1 0.33712 2.833213
32 2 0.34053264 2.833213
1 3 0.30819333 2.833213
1 4 0.19381496 2.833213
12 0 0.32110173 2.833213
3 1 0.33712 2.833213
9 2 0.34053264 2.833213
2 3 0.30819333 2.833213
0 4 0.19381496 2.833213
5 0 0.32110173 2.833213
15 1 0.33712 2.833213
22 2 0.34053264 2.833213
5 3 0.30819333 2.833213
1 4 0.19381496 2.833213
1 0 0.32110173 2.833213
16 1 0.33712 2.833213
33 2 0.34053264 2.833213
4 3 0.30819333 2.833213
2 4 0.19381496 2.833213
6 0 0.32110173 2.833213
17 1 0.33712 2.833213
26 2 0.34053264 2.833213
1 3 0.30819333 2.833213
0 4 0.19381496 2.833213
16 0 0.32110173 2.833213
16 1 0.33712 2.833213
11 2 0.34053264 2.833213
1 3 0.30819333 2.833213
1 4 0.19381496 2.833213
2 0 0.32110173 2.833213
8 1 0.33712 2.833213
18 2 0.34053264 2.833213
0 3 0.30819333 2.833213
0 4 0.19381496 2.833213
2 0 0.32110173 2.833213
27 1 0.33712 2.833213
49 2 0.34053264 2.833213
1 3 0.30819333 2.833213
0 4 0.19381496 2.833213
1 0 0.32110173 2.833213
6 1 0.33712 2.833213
36 2 0.34053264 2.833213
17 3 0.30819333 2.833213
0 4 0.19381496 2.833213
10 0 0.32110173 2.833213
21 1 0.33712 2.833213
78 2 0.34053264 2.833213
32 3 0.30819333 2.833213
0 4 0.19381496 2.833213
0 0 0.32110173 2.833213
8 1 0.33712 2.833213
14 2 0.34053264 2.833213
7 3 0.30819333 2.833213
0 4 0.19381496 2.833213
0 1 0.13648433 2.833213
6 1 0.23952033 2.833213
12 2 0.32110173 2.833213
0 3 0.33712 2.833213
0 4 0.34053264 2.833213
30 0 0.13648433 2.833213
30 1 0.23952033 2.833213
25 2 0.32110173 2.833213
30 3 0.33712 2.833213
30 4 0.34053264 2.833213
68 0 0.13648433 2.833213
68 1 0.23952033 2.833213
55 2 0.32110173 2.833213
68 3 0.33712 2.833213
68 4 0.34053264 2.833213
0 0 0.13648433 2.833213
12 1 0.23952033 2.833213
26 2 0.32110173 2.833213
2 3 0.33712 2.833213
1 4 0.34053264 2.833213
0 0 0.13648433 2.833213
17 1 0.23952033 2.833213
36 2 0.32110173 2.833213
1 3 0.33712 2.833213
4 4 0.34053264 2.833213
1 0 0.13648433 2.833213
1 1 0.23952033 2.833213
4 2 0.32110173 2.833213
4 3 0.33712 2.833213
0 4 0.34053264 2.833213
3 0 0.13648433 2.833213
3 1 0.23952033 2.833213
3 2 0.32110173 2.833213
3 3 0.33712 2.833213
3 4 0.34053264 2.833213
0 0 0.13648433 2.833213
29 1 0.23952033 2.833213
33 2 0.32110173 2.833213
0 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
10 1 0.23952033 2.833213
7 2 0.32110173 2.833213
1 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
6 1 0.23952033 2.833213
18 2 0.32110173 2.833213
1 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
18 1 0.23952033 2.833213
37 2 0.32110173 2.833213
1 3 0.33712 2.833213
1 4 0.34053264 2.833213
0 0 0.13648433 2.833213
13 1 0.23952033 2.833213
26 2 0.32110173 2.833213
8 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
0 1 0.23952033 2.833213
1 2 0.32110173 2.833213
0 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
1 1 0.23952033 2.833213
5 2 0.32110173 2.833213
0 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
29 1 0.23952033 2.833213
15 2 0.32110173 2.833213
2 3 0.33712 2.833213
0 4 0.34053264 2.833213
0 0 0.13648433 2.833213
19 1 0.23952033 2.833213
25 2 0.32110173 2.833213
3 3 0.33712 2.833213
1 4 0.34053264 2.833213
0 0 0.13648433 2.833213
24 1 0.23952033 2.833213
40 2 0.32110173 2.833213
6 3 0.33712 2.833213
1 4 0.34053264 2.833213
0 0 0.03678637 2.772589
28 1 0.07414634 2.772589
28 2 0.13648433 2.772589
3 3 0.23952033 2.772589
2 4 0.32110173 2.772589
0 0 0.03678637 2.772589
3 1 0.07414634 2.772589
2 2 0.13648433 2.772589
0 3 0.23952033 2.772589
0 4 0.32110173 2.772589
4 0 0.03678637 2.772589
14 1 0.07414634 2.772589
6 2 0.13648433 2.772589
0 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
6 1 0.07414634 2.772589
3 2 0.13648433 2.772589
2 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
8 1 0.07414634 2.772589
2 2 0.13648433 2.772589
4 3 0.23952033 2.772589
1 4 0.32110173 2.772589
1 0 0.03678637 2.772589
12 1 0.07414634 2.772589
23 2 0.13648433 2.772589
0 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
24 1 0.07414634 2.772589
56 2 0.13648433 2.772589
7 3 0.23952033 2.772589
4 4 0.32110173 2.772589
0 0 0.03678637 2.772589
22 1 0.07414634 2.772589
45 2 0.13648433 2.772589
3 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
2 1 0.07414634 2.772589
18 2 0.13648433 2.772589
1 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
5 1 0.07414634 2.772589
18 2 0.13648433 2.772589
5 3 0.23952033 2.772589
1 4 0.32110173 2.772589
0 0 0.03678637 2.772589
9 1 0.07414634 2.772589
25 2 0.13648433 2.772589
6 3 0.23952033 2.772589
1 4 0.32110173 2.772589
0 0 0.03678637 2.772589
1 1 0.07414634 2.772589
3 2 0.13648433 2.772589
1 3 0.23952033 2.772589
1 4 0.32110173 2.772589
0 0 0.03678637 2.772589
3 1 0.07414634 2.772589
16 2 0.13648433 2.772589
0 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
7 1 0.07414634 2.772589
21 2 0.13648433 2.772589
8 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
5 1 0.07414634 2.772589
22 2 0.13648433 2.772589
6 3 0.23952033 2.772589
0 4 0.32110173 2.772589
0 0 0.03678637 2.772589
11 1 0.07414634 2.772589
22 2 0.13648433 2.772589
6 3 0.23952033 2.772589
0 4 0.32110173 2.772589
1 0 0.11532605 2.564949
7 1 0.05628636 2.564949
11 2 0.03678637 2.564949
0 3 0.07414634 2.564949
0 4 0.13648433 2.564949
0 0 0.11532605 2.564949
4 1 0.05628636 2.564949
4 2 0.03678637 2.564949
0 3 0.07414634 2.564949
0 4 0.13648433 2.564949
0 0 0.11532605 2.564949
0 1 0.05628636 2.564949
5 2 0.03678637 2.564949
0 3 0.07414634 2.564949
1 4 0.13648433 2.564949
0 0 0.11532605 2.564949
3 1 0.05628636 2.564949
4 2 0.03678637 2.564949
0 3 0.07414634 2.564949
0 4 0.13648433 2.564949
0 0 0.11532605 2.564949
3 1 0.05628636 2.564949
0 2 0.03678637 2.564949
1 3 0.07414634 2.564949
0 4 0.13648433 2.564949
0 0 0.11532605 2.564949
1 1 0.05628636 2.564949
0 2 0.03678637 2.564949
0 3 0.07414634 2.564949
0 4 0.13648433 2.564949
0 0 0.11532605 2.564949
6 1 0.05628636 2.564949
9 2 0.03678637 2.564949
3 3 0.07414634 2.564949
0 4 0.13648433 2.564949
0 0 0.11532605 2.564949
3 1 0.05628636 2.564949
4 2 0.03678637 2.564949
3 3 0.07414634 2.564949
1 4 0.13648433 2.564949
0 0 0.11532605 2.564949
1 1 0.05628636 2.564949
3 2 0.03678637 2.564949
4 3 0.07414634 2.564949
0 4 0.13648433 2.564949
1 0 0.11532605 2.564949
3 1 0.05628636 2.564949
10 2 0.03678637 2.564949
2 3 0.07414634 2.564949
1 4 0.13648433 2.564949
0 0 0.11532605 2.564949
0 1 0.05628636 2.564949
3 2 0.03678637 2.564949
3 3 0.07414634 2.564949
1 4 0.13648433 2.564949
0 0 0.11532605 2.564949
24 1 0.05628636 2.564949
43 2 0.03678637 2.564949
11 3 0.07414634 2.564949
3 4 0.13648433 2.564949
0 0 0.11532605 2.564949
3 1 0.05628636 2.564949
19 2 0.03678637 2.564949
14 3 0.07414634 2.564949
2 4 0.13648433 2.564949
0 0 0.09016875 NA
25 1 0.14227471 2.833213
2 2 0.11532605 2.833213
0 3 0.05628636 2.833213
0 4 0.03678637 2.833213
0 0 0.09016875 2.833213
14 1 0.14227471 2.833213
0 2 0.11532605 2.833213
0 3 0.05628636 2.833213
0 4 0.03678637 2.833213
0 0 0.09016875 2.833213
12 1 0.14227471 2.833213
4 2 0.11532605 2.833213
0 3 0.05628636 2.833213
0 4 0.03678637 2.833213
1 0 0.09016875 2.833213
42 1 0.14227471 2.833213
20 2 0.11532605 2.833213
1 3 0.05628636 2.833213
2 4 0.03678637 2.833213
0 0 0.09016875 2.833213
48 1 0.14227471 2.833213
40 2 0.11532605 2.833213
1 3 0.05628636 2.833213
0 4 0.03678637 2.833213
10 0 0.09016875 2.833213
23 2 0.11532605 2.833213
0 3 0.05628636 2.833213
2 4 0.03678637 2.833213
2 0 0.09016875 2.833213
89 1 0.14227471 2.833213
5 2 0.11532605 2.833213
1 3 0.05628636 2.833213
6 4 0.03678637 2.833213
0 0 0.09016875 2.833213
27 1 0.14227471 2.833213
9 2 0.11532605 2.833213
3 3 0.05628636 2.833213
2 4 0.03678637 2.833213
1 0 0.09016875 2.833213
6 1 0.14227471 2.833213
0 2 0.11532605 2.833213
1 3 0.05628636 2.833213
0 4 0.03678637 2.833213
0 0 0.09016875 2.833213
65 1 0.14227471 2.833213
35 2 0.11532605 2.833213
1 3 0.05628636 2.833213
2 4 0.03678637 2.833213
0 0 0.09016875 2.833213
29 1 0.14227471 2.833213
26 2 0.11532605 2.833213
3 3 0.05628636 2.833213
1 4 0.03678637 2.833213
4 0 0.09016875 2.833213
105 1 0.14227471 2.833213
5 2 0.11532605 2.833213
0 3 0.05628636 2.833213
1 4 0.03678637 2.833213
4 0 0.09016875 2.833213
107 1 0.14227471 2.833213
5 2 0.11532605 2.833213
0 3 0.05628636 2.833213
0 4 0.03678637 2.833213
0 0 0.09016875 2.833213
17 1 0.14227471 2.833213
1 2 0.11532605 2.833213
0 3 0.05628636 2.833213
0 4 0.03678637 2.833213
3 0 0.09016875 2.833213
106 1 0.14227471 2.833213
1 2 0.11532605 2.833213
1 3 0.05628636 2.833213
0 4 0.03678637 2.833213
0 0 0.09016875 2.833213
21 1 0.14227471 2.833213
14 2 0.11532605 2.833213
5 3 0.05628636 2.833213
1 4 0.03678637 2.833213
0 0 0.09016875 2.833213
35 1 0.14227471 2.833213
12 2 0.11532605 2.833213
8 3 0.05628636 2.833213
2 4 0.03678637 2.833213
4 0 0.13510174 1.791759
1 1 0.10188844 1.791759
4 2 0.09016875 1.791759
0 3 0.14227471 1.791759
0 4 0.11532605 1.791759
3 0 0.13510174 1.791759
16 1 0.10188844 1.791759
11 2 0.09016875 1.791759
0 3 0.14227471 1.791759
0 4 0.11532605 1.791759
4 0 0.13510174 1.791759
20 1 0.10188844 1.791759
7 2 0.09016875 1.791759
0 3 0.14227471 1.791759
0 4 0.11532605 1.791759
0 0 0.13510174 1.791759
3 1 0.10188844 1.791759
1 2 0.09016875 1.791759
1 3 0.14227471 1.791759
1 4 0.11532605 1.791759
0 0 0.13510174 1.791759
2 1 0.10188844 1.791759
8 2 0.09016875 1.791759
2 3 0.14227471 1.791759
1 4 0.11532605 1.791759
0 0 0.13510174 1.791759
1 1 0.10188844 1.791759
40 2 0.09016875 1.791759
8 3 0.14227471 1.791759
0 4 0.11532605 1.791759
0 0 0.33638851 2.70805
0 1 0.20354567 2.70805
18 2 0.13510174 2.70805
2 3 0.10188844 2.70805
0 4 0.09016875 2.70805
0 0 0.33638851 2.70805
0 1 0.20354567 2.70805
1 2 0.13510174 2.70805
0 3 0.10188844 2.70805
0 4 0.09016875 2.70805
0 0 0.33638851 2.70805
1 1 0.20354567 2.70805
1 2 0.13510174 2.70805
0 3 0.10188844 2.70805
0 4 0.09016875 2.70805
0 0 0.33638851 2.70805
13 1 0.20354567 2.70805
23 2 0.13510174 2.70805
1 3 0.10188844 2.70805
13 4 0.09016875 2.70805
0 0 0.33638851 2.70805
1 1 0.20354567 2.70805
8 2 0.13510174 2.70805
3 3 0.10188844 2.70805
4 4 0.09016875 2.70805
0 0 0.33638851 2.70805
2 1 0.20354567 2.70805
9 2 0.13510174 2.70805
2 3 0.10188844 2.70805
0 4 0.09016875 2.70805
26 0 0.33638851 2.70805
2 1 0.20354567 2.70805
2 2 0.13510174 2.70805
0 3 0.10188844 2.70805
0 4 0.09016875 2.70805
57 0 0.33638851 2.70805
4 1 0.20354567 2.70805
6 2 0.13510174 2.70805
0 3 0.10188844 2.70805
1 4 0.09016875 2.70805
26 0 0.33638851 2.70805
3 1 0.20354567 2.70805
10 2 0.13510174 2.70805
2 3 0.10188844 2.70805
3 4 0.09016875 2.70805
9 0 0.33638851 2.70805
1 1 0.20354567 2.70805
3 2 0.13510174 2.70805
2 3 0.10188844 2.70805
0 4 0.09016875 2.70805
0 0 0.33638851 2.70805
0 1 0.20354567 2.70805
6 2 0.13510174 2.70805
1 3 0.10188844 2.70805
0 4 0.09016875 2.70805
0 0 0.33638851 2.70805
4 1 0.20354567 2.70805
16 2 0.13510174 2.70805
12 3 0.10188844 2.70805
3 4 0.09016875 2.70805
0 0 0.33638851 2.70805
7 1 0.20354567 2.70805
19 2 0.13510174 2.70805
8 3 0.10188844 2.70805
2 4 0.09016875 2.70805
14 0 0.33638851 2.70805
8 1 0.20354567 2.70805
33 2 0.13510174 2.70805
25 3 0.10188844 2.70805
4 4 0.09016875 2.70805
5 1 0.20354567 2.70805
15 2 0.13510174 2.70805
20 3 0.10188844 2.70805
10 4 0.09016875 2.70805
8 0 0.17597738 2.833213
28 1 0.25832942 2.833213
6 2 0.33638851 2.833213
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1 个解决方案
解决方案1
1 已采纳 2017-04-24 09:24:01
For visualizing the goodness of fit of probabilistic regression models, "standard" residuals (eg, Poisson or deviance) are often not so informative because they mostly capture the modeling of the mean but not of the entire distribution. 为了可视化概率回归模型的拟合优度，“标准”残差（例如，泊松或偏差）通常没有那么多信息，因为它们主要捕获均值而不是整个分布的模型。 One alternative that is somtimes used are (randomized) quantile residuals. 有时使用的一种替代方法是（随机）分位数残差。 Without randomization they are defined as qnorm(pdist(y)) where pdist() is the fitted distribution function (here a ZIP model), y are the observations, and qnorm() is the quantile function of the standard normal distribution. 如果没有随机化，则将它们定义为qnorm(pdist(y)) ，其中pdist()是拟合的分布函数（此处是ZIP模型）， y是观测值， qnorm()是标准正态分布的分位数函数。 If the model fits, the distribution of the residuals should be standard normal and can be checked in a QQ plot. 如果模型适合，则残差的分布应为标准正态分布，并可以在QQ图中进行检查。 In case of discrete distributions (as here), randomization is needed to break up the discrete nature of the data. 在离散分布的情况下（如此处），需要随机化以破坏数据的离散性质。 See Dunn & Smyth (1996, Journal of Computational and Graphical Statistics , 5 , 236-244) for more details. 见邓恩和史密斯（1996年， 杂志计算和图形统计 ，5，236-244），了解更多详情。 In R you can use the countreg package from R-Forge (hopefully soon also on CRAN) for these. 在R中，您可以使用R-Forge的countreg软件包（希望很快也会在CRAN上使用）。
Another alternative which checks the marginal distribution of the data is the so-called rootogram. 检查数据的边际分布的另一种方法是所谓的根图。 It visually compares the observed and fitted frequencies for the counts, 0, 1, ... It is often better at displaying the problems of excess zeros and/or overdispersion than QQ plots of randomized quantile residuals. 它直观地比较了观察到的和拟合的频率，分别为0、1，...。与显示随机分位数残差的QQ图相比，显示零和/或过度分散的问题通常更好。 See our paper Kleiber & Zeileis (2016, The American Statistician , 70 (3), 296–303, doi:10.1080/00031305.2016.1173590 ) for more details. 有关更多详细信息，请参见我们的论文Kleiber＆Zeileis（2016， The American Statistician ， 70 （3），296–303， doi：10.1080 / 00031305.2016.1173590 ）。
Applying these to your regression model quickly shows that a zero-inflated Poisson is not accounting for the overdispersion in the response. 将这些快速应用于回归模型表明，零膨胀的泊松不能说明响应中的过度分散。 (With counts up to and beyond 100 a Poisson-based distribution almost never fits well.) Furthermore, a zero inflation model does not fit very well because for assnage = 1 and = 2 there are very few zeros and no zero inflation is needed. （当计数达到或超过100时，基于Poisson的分布几乎不适合。）此外，零通货膨胀模型不太适合，因为当assnage = 1和= 2时，零很少，因此不需要零通货膨胀。 This leads to corresponding coefficients in the zero inflation part that go towards -Inf with very large standard errors (like in quasi-separation in binary regression). 这导致零膨胀部分中的相应系数朝着-Inf方向-Inf并具有非常大的标准误差（例如在二元回归中的准分离中）。 Therefore, a two-part hurdle model fits somewhat better and is likely easier to interpret. 因此，由两部分组成的跨栏模型比较合适，并且可能更易于解释。 Finally, due to the two assnage groups being different I would code assnage as a factor (it is not clear to me whether you did that already). 最后，由于两个assnage组不同，因此我将assnage编码为一个因素（尚不清楚您是否已经这样做）。
Thus, for analyzing your data I use yc as provided in your post and ensure: 因此，为了分析您的数据，我使用您帖子中提供的yc并确保：
yc$assnage <- factor(yc$assnage)
For a first explorative look at the influence of assnage I plot whether or not the count is positive (left: zero hurdle) and the positive count on a log-scale (right: count). 为了assnage的影响，我绘制了count是否为正（左：零障碍）和正count在对数刻度上（右：计数）。
plot(factor(count > 0, levels = c(FALSE, TRUE), labels = c("=0", ">0")) ~ assnage,
data = yc, ylab = "count", main = "Zero hurdle")
plot(count ~ assnage, data = yc, subset = count > 0,
log = "y", main = "Count (positive)")
Then, I fit the ZIP, ZINB, and hurdle NB models using the countreg package from R-Forge. 然后，我使用R-Forge的countreg软件包安装了ZIP，ZINB和跨栏NB模型。 This also contains updated versions of the zeroinfl() and hurdle() functions. 它还包含zeroinfl()和hurdle()函数的更新版本。
install.packages("countreg", repos = "http://R-Forge.R-project.org")
library("countreg")
zip <- zeroinfl(count ~ assnage * spawncob, offset = logoffset,
data = yc, dist = "poisson")
zinb <- zeroinfl(count ~ assnage * spawncob, offset = logoffset,
data = yc, dist = "negbin")
hnb <- hurdle(count ~ assnage * spawncob, offset = logoffset, data = yc,
dist = "negbin")
The ZIP is clearly inappropriate and the hurdle NB is slightly better than the ZINB. ZIP显然不合适，而NB栏比ZINB稍好。
BIC(zip, zinb, hnb)
## df BIC
## zip 20 7700.085
## zinb 21 3574.720
## hnb 21 3556.693
If you check summary(zinb) you will also see that some coefficients in the zero-inflation part are around 10 (for a dummy variable) with standard errors one or two orders of magnitude larger. 如果您查看summary(zinb)您还将看到零通胀部分的一些系数大约为10（对于虚拟变量），标准误差summary(zinb)到两个数量级。 This essentially means that the zero-inflation probability in the corresponding groups goes to zero because the negative binomial distribution already has more than enough probability weight for the zero responses ( assnage groups 1 and 2). 从本质上讲，这意味着相应组中的零膨胀概率变为零，因为负二项式分布对于零响应（ assnage组1和2）已经具有足够的概率权重。
To visualize that the ZIP model does not fit while the HNB appropriately captures the response, we can now use the rootograms. 为了可视化HNB正确捕获响应时ZIP模型不适合，我们现在可以使用根图。
rootogram(zip, main = "ZIP", ylim = c(-5, 15), max = 50)
rootogram(hnb, main = "HNB", ylim = c(-5, 15), max = 50)
The wave-like pattern for the ZIP clearly shows the overdispersion in the data that is not appropriately captured by the model. ZIP的波形模式清楚地显示了模型无法正确捕获的数据中的过度分散。 In contrast, the hurdle fits reasonably well. 相比之下，该障碍相当合适。
As a final check we can also look at the QQ plot of the quantile residuals in the hurdle model. 最后，我们还可以查看跨栏模型中分位数残差的QQ图。 These look fairly normal and show no suspicious departures from the model. 这些看起来很正常，并且没有显示出与模型可疑的偏离。
qqrplot(hnb, main = "HNB")
As the residuals are randomized, you can re-run the code a couple of times to get an impression of the variation. 由于残差是随机的，因此您可以重新运行代码几次，以得到变化的印象。 qqrplot() has also some arguments that let's you explore this variation in a single plot. qqrplot()还具有一些参数，可让您在单个图中探索这种变化。
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