如何解决奇异梯度矩阵误差？
How to solve singular gradient matrix error?
我正在创建一个非线性回归模型来拟合以下数据
情节
我一直收到错误消息：
singular gradient matrix at initial parameter estimates
谁能解释一下我的模型有什么问题？我要写的等式是 y = (p1*logbasep2 (x))/(x^p3)，其中 p1、p2 和 p3 是常数。
p1 <- 1
p2 <- 1
p3 <- 2
model1 = nls(ydata ~ ((p1*log(xdata, p3))/(xdata)^p2), start = list(p1 = p1, p2 = p2, p3 = p3))
下面是 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)
事实证明，您的问题实际上更多是数学问题而不是统计问题。问题在于 log(x,b1) 和 log(x,b2) 仅相差一个常数因子 (log(x,b1) = log(x,b2)*log(b2,b1))。这意味着您的 p1 和 p3 参数是多余的。所以如果你省略 p3 一切都有效（这只是更改公式的许多合理方法中的一种选择......）
最好将 nls 与 data 参数结合使用，因为这样可以更轻松地执行预测新值等操作：
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（该线系统地错过了下端和上端的数据）...
我正在创建一个非线性回归模型来拟合以下数据
情节
我一直收到错误消息：
singular gradient matrix at initial parameter estimates
谁能解释一下我的模型有什么问题？我要写的等式是 y = (p1*logbasep2 (x))/(x^p3)，其中 p1、p2 和 p3 是常数。
p1 <- 1
p2 <- 1
p3 <- 2
model1 = nls(ydata ~ ((p1*log(xdata, p3))/(xdata)^p2), start = list(p1 = p1, p2 = p2, p3 = p3))
下面是 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)
事实证明，您的问题实际上更多是数学问题而不是统计问题。问题在于 log(x,b1) 和 log(x,b2) 仅相差一个常数因子 (log(x,b1) = log(x,b2)*log(b2,b1))。这意味着您的 p1 和 p3 参数是多余的。所以如果你省略 p3 一切都有效（这只是更改公式的许多合理方法中的一种选择......）
最好将 nls 与 data 参数结合使用，因为这样可以更轻松地执行预测新值等操作：
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（该线系统地错过了下端和上端的数据）...