我想建立一个非线性混合效应模型，该模型描述了两个变量"x"和"y"之间的关系，这两个变量通过第三个变量"r"随机变化，使用指数上升到最大值，如以下方程所描述的：y = θ（1-exp（-β * x））。
我已经能够使用nls（）创建x和y的非线性模型，但是我还没有成功地将随机效应合并到nlme（）中。
当我使用nlme（）构建模型时，我得到了一条错误消息："eval（预测值、数据、环境）中出错：未找到对象"theta""。由于nls（）模型使用相同的 Dataframe 运行时没有问题，因此我意外遇到此错误。
要构建数据集：

x = c(33,35,16,8,31,31,31,23,7,7,7,7,11,11,3,3,6,6,32,32,1,17,17,17,25,40,40,6,6,29,29,13,23,23,44,44,43,43,13,4,6,15,17,22,28,8,11,22,32,6,12,20,27,15,29,29,29,29,29,12,12,16,16,12,12,2,49,49,14,14,14,37,2.87,4.86,7.90,11.95,16.90,16.90,18.90,18.89,22.00,24.08,27.14,30.25,31.22,32.26,7,14,19,31,36,7,14,19,31,36,7,16,16,16,16,16,16,32,32,32,32,32,32,11,11,11,13,13,13,13,13,13,13,13,13,13,13,13,9,9)

y = c(39.61,32.66,27.06,21.74,22.18,38.19,35.02,23.13,9.70,14.20,13.40,15.30,18.80,19.00,3.80,4.90,15.00,14.20,24.90,16.56,1.76,29.29,28.49,18.64,27.10,9.47,14.14,10.27,8.44,26.15,25.43,22.00,19.00,13.00,73.19,67.76,32.34,36.86,8.00,1.57,8.33,16.20,14.69,18.95,20.52,4.92,8.28,15.27,18.37,6.60,10.98,12.56,19.04,5.49,21.00,12.90,17.30,11.40,12.20,15.63,15.22,33.80,17.78,19.33,3.86,8.57,30.40,13.39,11.93,4.55,6.18,12.70,2.71,7.23,5.61,22.74,15.71,16.95,18.31,20.78,17.64,20.00,19.52,24.86,30.06,24.92,4.17,11.02,10.08,14.94,25.98,0.00,3.67,3.67,6.69,11.90,5.06,13.21,10.33,0.00,0.00,6.47,8.38,28.57,25.26,28.67,27.92,33.69,29.61,6.11,7.13,6.93,4.81,15.34,4.90,14.94,8.88,10.24,8.80,10.46,10.48,9.19,9.67,9.40,24.98,50.79)

r = c("A","A","A","A","A","A","A","A","B","B","B","B","B","B","B","B","B","B","C","C","D","E","E","E","F","G","G","H","H","H","H","I","I","I","J","J","J","J","K","L","L","L","L","L","L","L","L","L","L","L","L","L","L","M","N","N","N","N","N","O","P","P","P","P","P","Q","R","R","S","S","S","T","U","U","U","U","U","U","U","U","U","U","U","U","U","U","V","V","V","V","V","V","V","V","V","V","W","X","X","X","X","Y","Y","Z","Z","Z","Z","Z","Z","AA","AA","AA","AB","AB","AB","AB","AB","AB","AB","AB","AB","AB","AB","AB","AC","AC")

df = data.frame(x,y,r)

建立无"r"随机效应的非线性模型。

nls_test = nls(y~theta*(1-exp(-beta*x)),
              data = df,
              start = list(beta = 0.2, theta = 38), 
              trace = TRUE)

在我的模型中，唯一的固定效应是x，唯一的随机效应是r。我尝试构建了一个nlme（）模型来反映这一点，该模型基于nlme包文档（https://cran.r-project.org/web/packages/nlme/nlme.pdf），更具体地说，是上面链接的文档第186页上的这些代码行。
我尝试用我的数据创建的nlme（）对象如下所示：

nlme_test = nlme(y ~ theta*(1-exp(-beta*x)),
                 fixed = x~1,
                 random = r~1,
                 data = df,
                 start = c(theta = 38,
                           beta = 0.2))

并导致以下错误。
eval（预测值、数据、环境）出错：未找到对象'theta'
据我所知，这与"theta"未包含在用于构建nlme对象的 Dataframe （"df"）中有关，但我不清楚为什么会发生这种情况，因为我找到的大多数错误示例都与predict（）函数的使用和缺少列或列名之间的不一致有关。
此外，由于nls（）模型（nls_Test）使用相同的start = c（theta = 38，beta = 0.2）并且df中没有"theta"或"beta"数据列，因此工作正常，我有点困惑为什么会收到有关列名错误的错误。
有人有建议或参考资料来帮助我将随机效应纳入我的nlme模型吗？
谢谢!