检查残差和可视化零膨胀的裂变r

时间:2017-03-28 17:17:19

标签: r poisson

我正在为CPUE数据运行零膨胀模型。这个数据有零膨胀的证据,我已经用Vuong测试证实了这一点(见下面的代码)。根据AIC,完整模型(zint)优于null。我现在想:

  1. 检查完整模型的残差以确定模型适合性(由于缺乏来自同事,互联网和R书的信息而出现问题)
  2. 如果模型拟合似乎没问题,可视化模型的输出(如何在使用偏移变量时形成实参数值的方程式)
  3. 我已经向部门的一些统计人员寻求过帮助(他们以前从未这样做过,并将我发送到相同的谷歌搜索网站),在统计部门本身以外(每个人都太忙),以及stackoverflow feed。 / p>

    我会很感激书籍的代码或指导(可在线免费获得),其代码涉及使用偏移变量时可视化ZIP和模型拟合。

     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是第1列

     ##########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
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1 个答案:

答案 0 :(得分:1)

用于可视化概率回归模型的拟合优度,&#34;标准&#34;残差(例如,泊松或偏差)通常不那么有用,因为它们主要捕获平均值的建模而不是整个分布的建模。有时使用的一种替代方案是(随机化的)分位数残差。没有随机化,它们被定义为qnorm(pdist(y)),其中pdist()是拟合分布函数(这里是ZIP模型),y是观察值,qnorm()是分位数函数。标准正态分布。如果模型拟合,残差的分布应该是标准法线,并且可以在Q-Q图中检查。在离散分布的情况下(如此处),需要随机化来打破数据的离散性质。见Dunn&amp; Smyth(1996年,计算和图形统计杂志 5 ,236-244)了解更多详情。在R中,您可以使用R-Forge的countreg包(希望很快也会在CRAN上)。

检查数据边际分布的另一种方法是所谓的根图。它在视觉上比较了计数,0,1,......的观察和拟合频率。通常比显示随机分位数残差的Q-Q图更好地显示过量零和/或过度离散的问题。请参阅我们的论文Kleiber&amp; Zeileis(2016年,美国统计学家 70 (3),296-303,doi:10.1080/00031305.2016.1173590)了解更多详情。

将这些应用于您的回归模型可以快速显示零膨胀的 Poisson 并不能解释响应中的过度离散。 (计数高达100以上,基于泊松的分布几乎从不适合。)此外,零通胀模型不太适合,因为assnage = 1和= 2那里是非常少的零,不需要零通货膨胀。这导致零膨胀部分中的相应系数朝向具有非常大的标准误差的-Inf(如在二元回归中的准分离中)。因此,两部分障碍模型适合更好,并且可能更容易解释。最后,由于两个assnage组不同,我会将assnage编码为一个因素(我不清楚你是否已经这样做了。)

因此,为了分析您的数据,我使用帖子中提供的yc并确保:

yc$assnage <- factor(yc$assnage)

第一次探索assnage的影响我会在对数刻度上绘制count是否为正(左:零障碍)和正count。对: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)")

exploratory plots

然后,我使用R-Forge的countreg包来适应ZIP,ZINB和障碍NB模型。这还包含zeroinfl()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明显不合适,障碍NB略胜ZINB。

BIC(zip, zinb, hnb)
##      df      BIC
## zip  20 7700.085
## zinb 21 3574.720
## hnb  21 3556.693

如果检查summary(zinb),您还会看到零膨胀部分中的某些系数大约为10(对于虚拟变量),标准误差大一到两个数量级。这实质上意味着相应组中的零通胀概率变为零,因为负二项分布已经具有足够的零响应概率权重(assnage组1和2)。

为了在HNB正确捕获响应时可视化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)

rootograms

ZIP的波浪状图案清楚地显示了模型未正确捕获的数据中的过度离散。相比之下,障碍相当合适。

作为最终检查,我们还可以查看障碍模型中分位数残差的Q-Q图。这些看起来相当正常,并且没有显示模型的可疑偏离。

qqrplot(hnb, main = "HNB")

Q-Q plot

由于残差是随机的,您可以重新运行代码几次以获得变化的印象。 qqrplot()还有一些论据让您可以在单个图中探索这种变化。