Я пытаюсь подогнать и построить (используя ggplot2) двойное уравнение экспоненциального затухания первого порядка "y = [a1 exp (-k1t)] + [a2 exp (-k2t) ] "к моим экспериментальным данным (радиоактивный распад) с помощью функции nls, но я не могу этого сделать, поскольку отображаются следующие предупреждающие сообщения:
Предупреждающие сообщения: 1: In (function (formula, data = parent.frame (), start, control = nls.control (),: Для некоторых параметров не указаны начальные значения. Инициализация «a1», «k1», «a2», «k2» на «1.». Рассмотрите возможность указания start или использования модели selfStart 2: Ошибка вычисления в stat_smooth(): матрице сингулярного градиента при начальных оценках параметров.
Эта ошибка, вероятно, связана с неправильным начальным предположением для a1, k1, a2 и k2. Поэтому я заметил, что R может «угадать» мои стартовые параметры с помощью функции самозапуска (SSasymp). Однако я не могу реализовать эту функцию для уравнения двойного экспоненциального затухания первого порядка, которое является обязательным для моих экспериментальных данных (оба отсека a1 и a2 и необходимы). Я смог подобрать простое уравнение экспоненциального затухания, используя SSasymp, эта строка прокомментирована в коде, но, к сожалению, не соответствует моим потребностям. Мне также нужно зачитать параметры соответствия, которые будут представлены на статистические тесты. Это код, который я использую:
Fig1a <- ggplot(CREMglucose, aes(x = Day, y = Mean, color = factor(Fert, levels = c("Control", "Ammonium nitrate", "Ammonium sulfate", "Diammonium phosphate", "Potassium nitrate", "Struvite", "Urea")))) +
geom_point(aes(size = factor(Fert, levels = c("Control", "Ammonium nitrate", "Ammonium sulfate", "Diammonium phosphate", "Potassium nitrate", "Struvite", "Urea")), shape = factor(Fert, levels = c("Control", "Ammonium nitrate", "Ammonium sulfate", "Diammonium phosphate", "Potassium nitrate", "Struvite", "Urea"))), alpha = 0.7, show.legend = FALSE) +
geom_errorbar(aes(ymin = Mean - se, ymax = Mean + se), size = 0.2, show.legend = FALSE) +
#geom_smooth(method = "nls", formula = y ~ SSasymp(x, Asym, R0, lrc), se = FALSE, lwd = 0.4, show.legend = FALSE) +
geom_smooth(method = "nls", formula = y ~ (a1 * exp(-k1 * x)) + (a2 * exp(-k2 * x)), start = list(a1 = 1, k1 = 0.01, a2 = 1, k2 = 0.01), se = FALSE, lwd = 0.4, show.legend = FALSE) +
xlab(expression('Time after compound addition (d)')) +
ylab(expression({}^{14}*'C remaining (% of the total added)')) +
coord_cartesian(xlim = c(0, 21), ylim = c(0, 100)) +
scale_x_continuous(breaks = c(0, 4, 8, 12, 16, 20)) +
scale_y_continuous(breaks = c(0, 20, 40, 60, 80, 100)) +
scale_shape_manual(values = c(6, 0, 15, 1, 16, 2, 17)) +
scale_size_manual(values = c(2.2, 2.2, 2.3, 2.2, 2.3, 2.2, 2.3)) +
annotate("text", x = 17.5, y = 100, label = "(a) Glucosamine", size = 3.5, fontface = "bold") +
theme(axis.text.y = element_text(size = 10, color = "black"),
axis.text.x = element_blank(),
axis.title.y = element_text(size = 10),
axis.title.x = element_blank(),
legend.text = element_blank(),
legend.title = element_blank(),
panel.background = element_blank(),
panel.grid.major = element_line(color = "gray96", size = 0.50),
panel.grid.minor = element_line(color = "gray96", size = 0.30),
axis.line = element_line(color = "black", size = 0.5),
panel.border = element_rect(color = "black", fill = NA, size = 0.5))
Fig1a
В дополнение к моим данным:
Fert Day CREMglucose
Control 0.00 100
Control 0.00 100
Control 0.00 100
Control 0.00 100
Control 0.08 94
Control 0.08 95
Control 0.08 94
Control 0.08 93
Control 0.17 89
Control 0.17 91
Control 0.17 89
Control 0.17 89
Control 0.33 85
Control 0.33 86
Control 0.33 86
Control 0.33 85
Control 1.00 81
Control 1.00 81
Control 1.00 83
Control 1.00 81
Control 2.00 79
Control 2.00 78
Control 2.00 81
Control 2.00 79
Control 3.00 77
Control 3.00 77
Control 3.00 80
Control 3.00 78
Control 5.00 75
Control 5.00 75
Control 5.00 78
Control 5.00 77
Control 8.00 74
Control 8.00 74
Control 8.00 77
Control 8.00 75
Control 11.00 73
Control 11.00 72
Control 11.00 76
Control 11.00 74
Control 15.00 72
Control 15.00 71
Control 15.00 74
Control 15.00 73
Control 20.00 70
Control 20.00 70
Control 20.00 73
Control 20.00 72
Ammonium nitrate 0.00 100
Ammonium nitrate 0.00 100
Ammonium nitrate 0.00 100
Ammonium nitrate 0.00 100
Ammonium nitrate 0.08 96
Ammonium nitrate 0.08 97
Ammonium nitrate 0.08 96
Ammonium nitrate 0.08 95
Ammonium nitrate 0.17 93
Ammonium nitrate 0.17 94
Ammonium nitrate 0.17 92
Ammonium nitrate 0.17 91
Ammonium nitrate 0.33 86
Ammonium nitrate 0.33 88
Ammonium nitrate 0.33 86
Ammonium nitrate 0.33 85
Ammonium nitrate 1.00 78
Ammonium nitrate 1.00 78
Ammonium nitrate 1.00 80
Ammonium nitrate 1.00 79
Ammonium nitrate 2.00 74
Ammonium nitrate 2.00 74
Ammonium nitrate 2.00 76
Ammonium nitrate 2.00 75
Ammonium nitrate 3.00 71
Ammonium nitrate 3.00 71
Ammonium nitrate 3.00 74
Ammonium nitrate 3.00 73
Ammonium nitrate 5.00 68
Ammonium nitrate 5.00 68
Ammonium nitrate 5.00 71
Ammonium nitrate 5.00 70
Ammonium nitrate 8.00 66
Ammonium nitrate 8.00 65
Ammonium nitrate 8.00 69
Ammonium nitrate 8.00 68
Ammonium nitrate 11.00 64
Ammonium nitrate 11.00 64
Ammonium nitrate 11.00 67
Ammonium nitrate 11.00 66
Ammonium nitrate 15.00 63
Ammonium nitrate 15.00 62
Ammonium nitrate 15.00 65
Ammonium nitrate 15.00 64
Ammonium nitrate 20.00 61
Ammonium nitrate 20.00 59
Ammonium nitrate 20.00 63
Ammonium nitrate 20.00 62
Ammonium sulfate 0.00 100
Ammonium sulfate 0.00 100
Ammonium sulfate 0.00 100
Ammonium sulfate 0.00 100
Ammonium sulfate 0.08 95
Ammonium sulfate 0.08 97
Ammonium sulfate 0.08 95
Ammonium sulfate 0.08 93
Ammonium sulfate 0.17 91
Ammonium sulfate 0.17 94
Ammonium sulfate 0.17 91
Ammonium sulfate 0.17 88
Ammonium sulfate 0.33 85
Ammonium sulfate 0.33 88
Ammonium sulfate 0.33 85
Ammonium sulfate 0.33 84
Ammonium sulfate 1.00 79
Ammonium sulfate 1.00 79
Ammonium sulfate 1.00 81
Ammonium sulfate 1.00 79
Ammonium sulfate 2.00 77
Ammonium sulfate 2.00 76
Ammonium sulfate 2.00 78
Ammonium sulfate 2.00 77
Ammonium sulfate 3.00 75
Ammonium sulfate 3.00 74
Ammonium sulfate 3.00 76
Ammonium sulfate 3.00 75
Ammonium sulfate 5.00 73
Ammonium sulfate 5.00 71
Ammonium sulfate 5.00 74
Ammonium sulfate 5.00 72
Ammonium sulfate 8.00 71
Ammonium sulfate 8.00 68
Ammonium sulfate 8.00 72
Ammonium sulfate 8.00 69
Ammonium sulfate 11.00 69
Ammonium sulfate 11.00 66
Ammonium sulfate 11.00 70
Ammonium sulfate 11.00 68
Ammonium sulfate 15.00 68
Ammonium sulfate 15.00 65
Ammonium sulfate 15.00 69
Ammonium sulfate 15.00 67
Ammonium sulfate 20.00 66
Ammonium sulfate 20.00 63
Ammonium sulfate 20.00 67
Ammonium sulfate 20.00 65
Diammonium phosphate 0.00 100
Diammonium phosphate 0.00 100
Diammonium phosphate 0.00 100
Diammonium phosphate 0.00 100
Diammonium phosphate 0.08 95
Diammonium phosphate 0.08 95
Diammonium phosphate 0.08 95
Diammonium phosphate 0.08 94
Diammonium phosphate 0.17 90
Diammonium phosphate 0.17 90
Diammonium phosphate 0.17 90
Diammonium phosphate 0.17 89
Diammonium phosphate 0.33 83
Diammonium phosphate 0.33 82
Diammonium phosphate 0.33 83
Diammonium phosphate 0.33 82
Diammonium phosphate 1.00 76
Diammonium phosphate 1.00 75
Diammonium phosphate 1.00 77
Diammonium phosphate 1.00 76
Diammonium phosphate 2.00 73
Diammonium phosphate 2.00 71
Diammonium phosphate 2.00 74
Diammonium phosphate 2.00 73
Diammonium phosphate 3.00 71
Diammonium phosphate 3.00 69
Diammonium phosphate 3.00 72
Diammonium phosphate 3.00 71
Diammonium phosphate 5.00 68
Diammonium phosphate 5.00 65
Diammonium phosphate 5.00 69
Diammonium phosphate 5.00 68
Diammonium phosphate 8.00 65
Diammonium phosphate 8.00 63
Diammonium phosphate 8.00 66
Diammonium phosphate 8.00 65
Diammonium phosphate 11.00 64
Diammonium phosphate 11.00 61
Diammonium phosphate 11.00 64
Diammonium phosphate 11.00 63
Diammonium phosphate 15.00 62
Diammonium phosphate 15.00 59
Diammonium phosphate 15.00 62
Diammonium phosphate 15.00 62
Diammonium phosphate 20.00 60
Diammonium phosphate 20.00 57
Diammonium phosphate 20.00 60
Diammonium phosphate 20.00 59
Potassium nitrate 0.00 100
Potassium nitrate 0.00 100
Potassium nitrate 0.00 100
Potassium nitrate 0.00 100
Potassium nitrate 0.08 97
Potassium nitrate 0.08 98
Potassium nitrate 0.08 96
Potassium nitrate 0.08 96
Potassium nitrate 0.17 93
Potassium nitrate 0.17 95
Potassium nitrate 0.17 93
Potassium nitrate 0.17 92
Potassium nitrate 0.33 87
Potassium nitrate 0.33 90
Potassium nitrate 0.33 88
Potassium nitrate 0.33 87
Potassium nitrate 1.00 79
Potassium nitrate 1.00 80
Potassium nitrate 1.00 82
Potassium nitrate 1.00 81
Potassium nitrate 2.00 75
Potassium nitrate 2.00 75
Potassium nitrate 2.00 78
Potassium nitrate 2.00 78
Potassium nitrate 3.00 73
Potassium nitrate 3.00 72
Potassium nitrate 3.00 76
Potassium nitrate 3.00 76
Potassium nitrate 5.00 70
Potassium nitrate 5.00 70
Potassium nitrate 5.00 73
Potassium nitrate 5.00 73
Potassium nitrate 8.00 67
Potassium nitrate 8.00 67
Potassium nitrate 8.00 71
Potassium nitrate 8.00 71
Potassium nitrate 11.00 65
Potassium nitrate 11.00 65
Potassium nitrate 11.00 69
Potassium nitrate 11.00 69
Potassium nitrate 15.00 63
Potassium nitrate 15.00 63
Potassium nitrate 15.00 67
Potassium nitrate 15.00 67
Potassium nitrate 20.00 61
Potassium nitrate 20.00 60
Potassium nitrate 20.00 64
Potassium nitrate 20.00 65
Struvite 0.00 100
Struvite 0.00 100
Struvite 0.00 100
Struvite 0.00 100
Struvite 0.08 95
Struvite 0.08 96
Struvite 0.08 94
Struvite 0.08 95
Struvite 0.17 90
Struvite 0.17 92
Struvite 0.17 89
Struvite 0.17 90
Struvite 0.33 85
Struvite 0.33 86
Struvite 0.33 86
Struvite 0.33 87
Struvite 1.00 81
Struvite 1.00 82
Struvite 1.00 83
Struvite 1.00 83
Struvite 2.00 78
Struvite 2.00 79
Struvite 2.00 81
Struvite 2.00 81
Struvite 3.00 77
Struvite 3.00 77
Struvite 3.00 80
Struvite 3.00 80
Struvite 5.00 75
Struvite 5.00 75
Struvite 5.00 78
Struvite 5.00 78
Struvite 8.00 73
Struvite 8.00 73
Struvite 8.00 76
Struvite 8.00 77
Struvite 11.00 72
Struvite 11.00 72
Struvite 11.00 75
Struvite 11.00 76
Struvite 15.00 71
Struvite 15.00 70
Struvite 15.00 74
Struvite 15.00 75
Struvite 20.00 69
Struvite 20.00 69
Struvite 20.00 72
Struvite 20.00 73
Urea 0.00 100
Urea 0.00 100
Urea 0.00 100
Urea 0.00 100
Urea 0.08 98
Urea 0.08 98
Urea 0.08 99
Urea 0.08 98
Urea 0.17 96
Urea 0.17 95
Urea 0.17 97
Urea 0.17 96
Urea 0.33 90
Urea 0.33 89
Urea 0.33 93
Urea 0.33 90
Urea 1.00 76
Urea 1.00 74
Urea 1.00 80
Urea 1.00 79
Urea 2.00 67
Urea 2.00 66
Urea 2.00 69
Urea 2.00 70
Urea 3.00 62
Urea 3.00 61
Urea 3.00 62
Urea 3.00 64
Urea 5.00 54
Urea 5.00 53
Urea 5.00 53
Urea 5.00 55
Urea 8.00 47
Urea 8.00 45
Urea 8.00 44
Urea 8.00 47
Urea 11.00 42
Urea 11.00 40
Urea 11.00 39
Urea 11.00 41
Urea 15.00 37
Urea 15.00 35
Urea 15.00 35
Urea 15.00 37
Urea 20.00 33
Urea 20.00 31
Urea 20.00 30
Urea 20.00 32
Кто-нибудь знает, как подобрать и построить это уравнение в R?