R 为对数增长曲线添加置信带

我正在处理显示对数增长曲线的数据。我能够很好地使用nlme软件包拟合非线性混合效应回归。然而，我不确定如何在估计线周围添加置信带。有人能帮忙吗？ 请在下面查找数据和代码：

Data:
Harvest Plot Irrigation Graft Rep AwtRun 1 11b 1 b 1 0 2 11b 1 b 1 1.6 3 11b 1 b 1 7.67 4 11b 1 b 1 11.96 5 11b 1 b 1 18.82 6 11b 1 b 1 31.43 11b 1 b 1 41.84 8 11b 1 b 1 45.08 9 11b 1 b 1 48.09 10 11b 1 b 1 48.8 11 11b 1 b 1 51.73 12 11b 1 b 1 54.13 13 11b 1 b 1 60.56 14 11b 1 b 1 63.44 15 11b 1 b 1 65.44 16 11b 1 b 1 67.33 1 11c 1 c 1 0 2 11c 1 c 1 0.86 3 11c 1 c 1 1.6 4 11c 1 c 1 5.41 5 11c 1 c 1 10.17 6 11c 1 c 1 20.4 7 11c 1 c 1 23.32 8 11c 1 c 1 23.99 9 11c 1 c 1 25.23 10 11c 1 c 1 25.89 11 11c 1 c 1 27.71 12 11c 1 c 1 29.64 13 11c 1 c 1 30.81 14 11c 1 c 1 33.09 15 11c 1 c 1 35.66 16 11c 1 c 1 36.59 1 11s 1 s 1 0.82 2 11s 1 s 1 0.82 3 11s 1 s 1 1.19 4 11s 1 s 1 4.39 5 11s 1 s 1 11.77 6 11s 1 s 1 15.81 7 11s 1 s 1 21.9 8 11s 1 s 1 28.16 9 11s 1 s 1 33.63 10 11s 1 s 1 45.22 11 11s 1 s 1 49.45 12 11s 1 s 1 51.71 13 11s 1 s 1 54.82 14 11s 1 s 1 57.44 15 11s 1 s 1 57.61 16 11s 1 s 1 58.38 1 12b 2 b 1 0 2 12b 2 b 1 0.9 3 12b 2 b 1 2.19 4 12b 2 b 1 7.1 5 12b 2 b 1 10.98 6 12b 2 b 1 26.48 7 12b 2 b 1 32.08 8 12b 2 b 1 37.58 9 12b 2 b 1 40.45 10 12b 2 b 1 48.27 11 12b 2 b 1 53.03 12 12b 2 b 1 55.05 13 12b 2 b 1 55.05 14 12b 2 b 1 55.75 15 12b 2 b 1 56.57 16 12b 2 b 1 57.57 1 12c 2 c 1 0 2 12c 2 c 1 0 3 12c 2 c 1 5.05 4 12c 2 c 1 10.08 5 12c 2 c 1 13.65 6 12c 2 c 1 25.03 7 12c 2 c 1 26.9 8 12c 2 c 1 27.47 9 12c 2 c 1 28.66 10 12c 2 c 1 31.98 11 12c 2 c 1 34.79 12 12c 2 c 1 35.2 13 12c 2 c 1 36.65 14 12c 2 c 1 38.41 15 12c 2 c 1 38.68 16 12c 2 c 1 38.94 1 12s 2 s 1 0 2 12s 2 s 1 0 3 12s 2 s 1 0.39 4 12s 2 s 1 4.59 5 12s 2 s 1 8.02 6 12s 2 s 1 17.45 7 12s 2 s 1 25.83 8 12s 2 s 1 33.04 9 12s 2 s 1 35.87 10 12s 2 s 1 52.42 11 12s 2 s 1 57.91 12 12s 2 s 1 57.91 13 12s 2 s 1 57.91 14 12s 2 s 1 57.91 15 12s 2 s 1 57.91 16 12s 2 s 1 58.38 1 21b 1 b 2 0 2 21b 1 b 2 0 3 21b 1 b 2 1.36 4 21b 1 b 2 6.2 5 21b 1 b 2 10.08 6 21b 1 b 2 17.53 7 21b 1 b 2 21.36 8 21b 1 b 2 24.92 9 21b 1 b 2 31.62 10 21b 1 b 2 47.42 11 21b 1 b 2 50.85 12 21b 1 b 2 50.85 13 21b 1 b 2 53.27 14 21b 1 b 2 53.66 15 21b 1 b 2 53.93 16 21b 1 b 2 56.48 1 21c 1 c 2 0 2 21c 1 c 2 0 3 21c 1 c 2 0.74 4 21c 1 c 2 6.44 5 21c 1 c 2 13.8 6 21c 1 c 2 20.12 7 21c 1 c 2 20.75 8 21c 1 c 2 23.58 9 21c 1 c 2 23.58 10 21c 1 c 2 28.69 11 21c 1 c 2 30.4 12 21c 1 c 2 31.74 13 21c 1 c 2 33.86 14 21c 1 c 2 34.06 15 21c 1 c 2 35.15 16 21c 1 c 2 36 1 21s 1 s 2 0 2 21s 1 s 2 0 3 21s 1 s 2 1.67 4 21s 1 s 2 3.41 5 21s 1 s 2 8.36 6 21s 1 s 2 16.97 7 21s 1 s 2 23.85 8 21s 1 s 2 28.16 9 21s 1 s 2 30.54 10 21s 1 s 2 37.33 11 21s 1 s 2 40.11 12 21s 1 s 2 40.41 13 21s 1 s 2 42.03 14 21s 1 s 2 42.03 15 21s 1 s 2 42.03 16 21s 1 s 2 42.03 1 22b 2 b 2 0 2 22b 2 b 2 2.06 3 22b 2 b 2 3.99 4 22b 2 b 2 6.7 5 22b 2 b 2 9.67 6 22b 2 b 2 14.8 7 22b 2 b 2 20.64 8 22b 2 b 2 28.33 9 22b 2 b 2 34.15 10 22b 2 b 2 44.86 11 22b 2 b 2 53.06 12 22b 2 b 2 54.44 13 22b 2 b 2 57.14 14 22b 2 b 2 60.16 15 22b 2 b 2 61.32 16 22b 2 b 2 61.32 1 22c 2 c 2 0 2 22c 2 c 2 0 3 22c 2 c 2 1.55 4 22c 2 c 2 4.93 5 22c 2 c 2 13.63 6 22c 2 c 2 21.98 7 22c 2 c 2 26.7 8 22c 2 c 2 27.23 9 22c 2 c 2 30.56 10 22c 2 c 2 40.73 11 22c 2 c 2 42.01 12 22c 2 c 2 45.52 13 22c 2 c 2 51.7 14 22c 2 c 2 53.59 15 22c 2 c 2 53.59 16 22c 2 c 2 53.59 1 22s 2 s 2 0 2 22s 2 s 2 0 3 22s 2 s 2 1.15 4 22s 2 s 2 9.27 5 22s 2 s 2 13.5 6 22s 2 s 2 23.78 7 22s 2 s 2 24.38 8 22s 2 s 2 27.7 9 22s 2 s 2 33.63 10 22s 2 s 2 41.23 11 22s 2 s 2 44.84 12 22s 2 s 2 48.26 13 22s 2 s 2 51.96 14 22s 2 s 2 54.83 15 22s 2 s 2 54.83 16 22s 2 s 2 54.83 1 31b 1 b 3 0 2 31b 1 b 3 0 3 31b 1 b 3 0 4 31b 1 b 3 0 5 31b 1 b 3 1.32 6 31b 

代码基于Rob Hall@

起始值为自启动逻辑（SSlogis）的非线性混合效应模型 图书馆（nlme） #基本模型：y=（Asym+u）/（1+exp（（收获xmid）/scale），u~N（0，s2u）；（无贪污）

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初始化引导或增量方法。。。（我知道这并不能给你一个完整的答案，但它可能有助于开始寻找解决方案）似乎首先你需要决定如何计算置信区间，然后才能将它们添加到绘图中。这与其说是一个编程问题，不如说是一个统计问题。你们应该在关于统计模型的问题所在的地方问这样的问题。

#nonlinear mixed effects model with self start logistic (SSlogis) for starting values
library(nlme)
#base Model: y = (Asym+u)/(1+exp((Harvest-xmid)/scale)), u ~ N(0,s2u); (no graft)
initVals <- getInitial(sqrtawtrun ~ SSlogis(Harvest, Asym, xmid, scal), data = Data)
#base model without graft, based on starting points found earlier 
baseModel<- nlme(sqrtawtrun ~ SSlogis(Harvest, Asym, xmid, scal),
                 data = Data,
                 fixed = list(Asym ~ 1, xmid ~ 1, scal ~ 1),
                 random = Asym ~ 1|Plot,
                 start = initVals
)
#creating dummy variables for graft; releveling so 's' is the reference category to match SAS code
graft.dummy=model.matrix(~relevel(Data[["Graft"]],"s"))[,2:3]
#updating to include graft in model -- same as above but allowing for diff asym, xmid, and scal vars for each graft
#starting values based on fitted base model values (for those in the base model) & zero for all new parameters
nestedModel <- update(baseModel,fixed=list(Asym ~graft.dummy, xmid ~graft.dummy, scal~graft.dummy), 
                      start = c(fixef(baseModel)[1], 0, 0, fixef(baseModel)[2], 0, 0, fixef(baseModel)[3], 0, 0))

#growth curve plots -- line for each plot, colored on graft
#currently only predicted population level mean at each observed point, plotted as smooth line
ggplot(data=Data,aes(x=Harvest,y=sqrtawtrun,
                    color=Graft,na.rm=T)) +
  geom_point(cex=0.6)  +
  geom_line(aes(x=Harvest,y=nestedModel$fitted[,1],color=Graft),size=2)