如何解决奇异梯度矩阵误差？

Question

我正在创建一个非线性回归模型以适合下面的数据

剧情

我一直在收到错误：

  

初始参数估计时的奇异梯度矩阵

任何人都能解释我的模特有什么问题吗？我想写的等式是y = (p1*logbasep2 (x))/(x^p3)，其中p1，p2和p3是常量。

p1 <- 1
p2 <- 1 
p3 <- 2


model1 = nls(ydata ~ ((p1*log(xdata, p3))/(xdata)^p2), start = list(p1 = p1, p2 = p2, p3 = p3))

以下是xdata和ydata

的示例输出

  > dput(ydata)
c(2.675967443, 5.262229596, 2.756358345, 2.582628563, 2.578517983, 
2.572149035, 2.572149035, 2.419269246, 4.342393324, 4.57849526, 
2.414960542, 2.414960542, 2.414960542, 2.414960542, 2.655729394, 
5.205391565, 3.137641723, 2.503911184, 2.499359843, 2.499198257, 
2.498768034, 2.693594595, 5.231803091, 2.998312831, 2.520387095, 
2.518634129, 2.518634129, 2.518634129, 2.711184536, 5.229303652, 
3.003137243, 2.551123783, 2.516552812, 2.504450358, 2.484247615, 
2.581875759, 5.157438135, 3.310365728, 2.620786825, 2.458420168, 
2.436577883, 2.434535502, 2.606225185, 5.265676214, 2.71775484, 
2.61596361, 2.598126717, 2.598126717, 2.598126717, 2.803018082, 
4.934368949, 3.595430381, 3.031594421, 2.227695807, 2.207278748, 
2.200613613, 2.594364366, 5.215228585, 3.07169941, 2.694566482, 
2.511361391, 2.456389883, 2.456389883, 2.862120485, 5.202934582, 
3.056182323, 2.469690653, 2.469690653, 2.469690653, 2.469690653, 
2.437314286, 4.587186915, 4.302037827, 2.711703229, 2.346318322, 
2.308501078, 2.306938344, 2.30614524, 4.657971143, 4.158221237, 
2.943632973, 2.350070603, 2.296930829, 2.287027975, 2.531924554, 
5.071156271, 3.541488012, 2.65287316, 2.420471714, 2.391688, 
2.39039829, 2.477102765, 5.030773262, 3.642446383, 2.620965051, 
2.424021444, 2.402895805, 2.40179529, 2.584714789, 5.03335416, 
3.619673092, 2.583602564, 2.533903128, 2.326437301, 2.318314966, 
2.49144927, 4.897950266, 3.585821617, 3.227165648, 2.53767512, 
2.221395797, 2.038542282, 2.354867369, 4.95865857, 3.766909175, 
2.715186396, 2.382613432, 2.372757351, 2.449007707, 2.20573524, 
4.55514547, 3.91611881, 3.606189025, 2.303604277, 2.20810652, 
2.205100659, 3.300879888, 5.151795375, 2.75624017, 2.449071065, 
2.447337834, 2.447337834, 2.447337834, 2.528936269, 4.955034368, 
3.754254308, 2.751181588, 2.399415789, 2.308263059, 2.302914619, 
2.350317116, 4.873892721, 3.39391574, 2.606991064, 2.443820718, 
2.33106264, 2.33106264, 2.621925026, 5.267786769, 2.622588101, 
2.621925026, 2.621925026, 2.621925026, 2.621925026, 2.425160063, 
5.022138529, 3.663550495, 2.612718078, 2.425326541, 2.42594623, 
2.425160063, 2.625820509, 5.265415337, 2.713068882, 2.638650782, 
2.585780084, 2.586285083, 2.584979323, 2.508232606, 4.902729122, 
3.746937795, 3.015086226, 2.332707845, 2.267248424, 2.227057981, 
2.947719346, 5.098315798, 3.368997979, 2.39886785, 2.402312015, 
2.392233622, 2.39155339, 2.548810552, 4.525931048, 4.3760105, 
2.589251919, 2.429896804, 2.281201495, 2.248897682)
dput(xdata)
c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 
2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 
4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 
6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 
1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 
3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 
5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 
7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 
2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 
4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 
6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 
1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L)

Answer 1

事实证明，你的问题实际上比数学更具数学性。问题是log(x,b1)和log(x,b2)仅有一个常数因子（log(x,b1) = log(x,b2)*log(b2,b1)）。这意味着您的p1和p3参数是多余的。如果你遗漏p3，这一切都有效（这只是改变公式的许多合理方法中的一种选择......）

首选使用带有nls参数的data，因为它可以更轻松地执行预测新值的操作：

dd <- data.frame(x=xdata,y=ydata)
model1 = nls(y ~ ((p1*log(x))/(x)^p2),
             start = list(p1 = 1, p2 = 1),
             data=dd)

现在预测：

xvec <- seq(1,7,length=101)
par(las=1,bty="l")  ## cosmetic
plot(y~x,data=dd)
lines(xvec,predict(model1,newdata=data.frame(x=xvec)))

请注意，此拟合存在一些问题（该行系统地错过了低端和高端的数据）...