检验残差和可视化零膨胀波分裂r
检验残差和可视化零膨胀波分裂r
提问于 2017-03-28 17:17:19
我运行的CPUE数据的零充气模型。这个数据有零通胀的证据，我已经用Vuong检验证实了这一点(代码如下)。AIC的全模型(zint)优于null。我现在想：
- 检查整个模型的剩余部分，以确定模型是否适合(由于缺乏来自同事、互联网和R类书籍的信息)
- 如果模型合适，则可视化模型的输出(如何在使用偏移量变量时建立实际参数值的方程)。
我向部门的一些统计人员寻求帮助(他们以前从未这样做过，并将我发送到相同的google搜索站点)，在统计部门之外(每个人都太忙)和堆叠溢出源。
我希望代码或指导书籍(免费在线)的代码，处理可视化压缩和模型适合时，使用偏移变量。
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###########年份是第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
0 3 0.20354567 2.833213
0 4 0.13510174 2.833213
4 0 0.17597738 2.833213
15 1 0.25832942 2.833213
27 2 0.33638851 2.833213
0 3 0.20354567 2.833213
0 4 0.13510174 2.833213
5 0 0.17597738 2.833213
13 1 0.25832942 2.833213
6 2 0.33638851 2.833213
0 3 0.20354567 2.833213
1 4 0.13510174 2.833213
0 0 0.17597738 2.833213
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2 3 0.33638851 2.302585
3 4 0.20354567 2.302585回答 1
Stack Overflow用户
回答已采纳
发布于 2017-04-24 09:24:01
为了可视化概率回归模型的拟合优度，“标准”残差(如泊松或偏差)往往信息不多，因为它们主要是捕捉平均分布的模型，而不是整个分布的模型。有时使用的一种选择是(随机)分位数残差。没有随机化，它们被定义为qnorm(pdist(y))，其中pdist()是拟合的分布函数(这里是ZIP模型)，y是观测值，qnorm()是标准正态分布的分位数函数。如果模型符合，残差的分布应该是标准正态分布，并且可以在Q-Q图中检查。在离散分布(如这里)的情况下，需要随机化来分解数据的离散性质。详见邓恩与斯迈思(1996年，计算与图形统计杂志，5，236-244)。在R中，您可以使用来自package的countreg包(希望不久也能在CRAN上)用于这些。
另一种检查数据边缘分布的方法是所谓的根图。它直观地比较了计数的观测频率和拟合频率，0，1，.它通常比随机分位数残差的Q-Q图更好地显示过零和/或过分散问题。详见我们的论文Kleiber & Zeileis (2016年，美国统计学家，70(3)，296-303，指定用途:10.1080/00031305.2016.1173590)。
把这些应用到你的回归模型中，很快就会发现，零膨胀的泊松并不能解释反应中的过度分散。(以泊松为基础的分布数量达到和超过100，几乎不太适合。)此外，零通货膨胀模型不太适合，因为对于assnage =1和=2时，只有很少的零，并且不需要零通货膨胀。这导致向-Inf方向的零膨胀部分对应的系数具有很大的标准误差(如二元回归中的准分离)。因此，两部分的跨栏模型比较适合，而且可能更容易解释。最后，由于两个assnage组是不同的，所以我会将assnage编码为一个因素(我不清楚您是否已经这么做了)。
因此，为了分析您的数据，我使用了您在文章中提供的yc，并确保：
yc$assnage <- factor(yc$assnage)为了第一次探索assnage的影响，我绘制了count是否为正(左:零栏)和对数尺度上的正count (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)")
然后，我使用来自package的countreg包来拟合ZIP、ZINB和跨栏NB模型.这还包含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")ZIP显然是不合适的，而跨栏NB略好于ZINB。
BIC(zip, zinb, hnb)
## df BIC
## zip 20 7700.085
## zinb 21 3574.720
## hnb 21 3556.693如果你检查summary(zinb)，你也会发现零通货膨胀部分中的一些系数在10左右(对于一个虚拟变量)，标准误差大一个或两个数量级。这在本质上意味着对应组中的零通货膨胀概率为零，因为负二项分布对零响应的概率权重已经足够大(assnage群1和2)。
为了可视化ZIP模型不适合，而HNB适当地捕获响应，我们现在可以使用根目录。
rootogram(zip, main = "ZIP", ylim = c(-5, 15), max = 50)
rootogram(hnb, main = "HNB", ylim = c(-5, 15), max = 50)
ZIP的类波模式清楚地显示了模型未适当捕获的数据中的过分散。相比之下，这一障碍相当合适。
作为最后的检验，我们还可以查看跨栏模型中分位数残差的Q-Q图。这些看起来相当正常，并没有显示出可疑的偏离模型。
qqrplot(hnb, main = "HNB")
由于残值是随机的，您可以重新运行代码几次，以获得变化的印象。qqrplot()也有一些参数，让我们在一个图中探索这种变化。
页面原文内容由Stack Overflow提供。腾讯云小微IT领域专用引擎提供翻译支持
原文链接：
https://stackoverflow.com/questions/43075911
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