Nonlinear model convergence - r

Question

I have a time series data set and each time series has datapoint of 30-year from different/same species. I am developing a forecasting model using the first 23 years of data from each time series data point and I am using the rest 7 years as test set to know the predictive ability of model but the nonlinear model (Model 6 and Model 7) don't give succinct result?
Data:
DD <- structure(list(Plot = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L), .Label = c("A",
"B", "C", "D"), class = "factor"), Species = structure(c(2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L), .Label = c("BD", "BG"), class = "factor"), Year = c(37L,
38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L,
51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L,
64L, 65L, 66L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L,
47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L,
60L, 61L, 62L, 63L, 64L, 65L, 66L, 37L, 38L, 39L, 40L, 41L, 42L,
43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L,
56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 37L, 38L,
39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L,
52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L,
65L, 66L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L,
48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L,
61L, 62L, 63L, 64L, 65L, 66L, 37L, 38L, 39L, 40L, 41L, 42L, 43L,
44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L,
57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 37L, 38L, 39L,
40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L,
53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L,
66L), Count = c(81L, 45L, 96L, 44L, 24L, 8L, 28L, 32L, 39L, 29L,
40L, 17L, 4L, 12L, 18L, 11L, 63L, 98L, 78L, 76L, 67L, 36L, 56L,
43L, 81L, 8L, 14L, 20L, 25L, 19L, 135L, 91L, 171L, 88L, 59L,
1L, 1L, 1L, 2L, 1L, 11L, 9L, 34L, 15L, 32L, 21L, 33L, 43L, 39L,
20L, 6L, 3L, 9L, 9L, 28L, 16L, 15L, 2L, 1L, 1L, 34L, 16L, 19L,
35L, 32L, 7L, 2L, 30L, 29L, 25L, 28L, 11L, 31L, 31L, 28L, 27L,
34L, 110L, 87L, 103L, 72L, 19L, 46L, 43L, 107L, 32L, 26L, 31L,
12L, 29L, 23L, 40L, 50L, 23L, 34L, 11L, 9L, 4L, 24L, 55L, 14L,
16L, 51L, 43L, 2L, 13L, 8L, 96L, 52L, 118L, 32L, 1L, 8L, 17L,
34L, 29L, 38L, 15L, 4L, 38L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 3L,
4L, 6L, 4L, 4L, 10L, 6L, 7L, 9L, 15L, 30L, 25L, 36L, 13L, 17L,
43L, 36L, 60L, 50L, 26L, 13L, 13L, 27L, 18L, 56L, 96L, 16L, 54L,
2L, 2L, 9L, 5L, 5L, 6L, 2L, 6L, 2L, 3L, 4L, 3L, 136L, 71L, 116L,
28L, 23L, 76L, 64L, 98L, 58L, 26L, 13L, 13L, 13L, 18L, 19L, 24L,
18L, 17L, 3L, 23L, 19L, 9L, 11L, 13L, 20L, 29L, 29L, 17L, 20L,
26L, 71L, 63L, 53L, 54L, 20L, 22L, 18L, 93L, 50L, 18L, 12L, 12L,
31L), LogCount = c(1.908385019, 1.653212514, 1.982271233, 1.643462676,
1.380211242, 0.903089987, 1.447158031, 1.505109978, 1.591064607,
1.462397998, 1.602059991, 1.230448921, 0.602059991, 1.079181206,
1.255272505, 1.041392685, 1.799340549, 1.991226076, 1.892094603,
1.880813592, 1.826074803, 1.556302501, 1.748188027, 1.633468456,
1.908485019, 0.903089987, 1.146128035, 1.301029996, 1.397940009,
1.278753601, 2.130333768, 1.95904139, 2.2329961, 1.94448267,
1.770852012, 0, 0, 0, 0.30102999, 0, 1.0411392685, 0.954242509,
1.531478917, 1.176031259, 1.505149978, 1.322219295, 1.51851394,
1.6334684456, 1.591064607, 1.301029996, 0.77815125, 0.477121255,
0.954242509, 0.954242509, 1.447158031, 1.204119983, 1.176091259,
0.301029996, 0, 0, 1.531478917, 1.204119983, 1.278753501, 1.544068044,
1.505149978, 0.084509804, 0.301029996, 1.477121255, 1.462397998,
1.397940009, 1.447158031, 1.041392685, 1.491361694, 1.491361694,
1.447158031, 1.431363754, 1.531478917, 2.041392685, 1.939519253,
2.012837225, 1.857332495, 1.278753601, 1.662757382, 1.633468456,
2.029383778, 1.505149978, 1.414973348, 1.491361594, 1.079181245,
1.462397998, 1.361727835, 1.602059991, 1.698970004, 1.361727836,
1.531478917, 1.041392685, 0.954242509, 0.602059991, 1.380211242,
1.740362689, 1.146128036, 1.204119983, 1.707570176, 1.633468456,
0.301029996, 1.113943352, 0.903089987, 1.982271233, 1.716003344,
2.071882007, 1.50514997, 0, 0.903089987, 1.230448921, 1.53147891,
1.2397998, 1.57978359, 1.176091259, 0.602059991, 1.57978359,
0.301029996, 0, 0, 0, 0, 0, 0.477121255, 0.477121255, 0.602059991,
0.77815125, 0.602059991, 0.602059991, 1, 0.77815125, 0.84509804,
0.95424509, 1.176091259, 1.477121255, 1.39790009, 1.555302501,
1.113943352, 1.230448921, 1.633468456, 1.555302501, 1.77815125,
1.698970004, 1.414973348, 1.113943352, 1.113943352, 1.431353754,
1.255272505, 1.748188027, 1.982271233, 1.204119983, 1.73239376,
1.431363754, 1.361727835, 0.954242509, 0.698970004, 0.698970004,
0.77815125, 0.301029996, 0.77815125, 0.301029996, 0.477121255,
0.602059991, 0.477121255, 2.133538908, 1.851258349, 2.064457989,
1.447158031, 1.361727836, 1.880813592, 1.806179974, 1.991226076,
1.763427994, 1.414973348, 1.113943352, 1.113943352, 1.113943352,
1.255272505, 1.278753601, 1.380211242, 1.255272505, 1.230446921,
0.477121255, 1.361727835, 1.278753601, 0.954242509, 1.0411392685,
1.113943352, 1.301029996, 1.462397998, 1.462397998, 1.230448921,
1.301029995, 1.414973348, 1.851258349, 1.799340549, 1.72427587,
1.73239376, 1.301029996, 1.342422681, 1.255272505, 1.968482949,
1.698970004, 1.255272505, 1.079181246, 1.079181246, 1.491361694
), Diff = c(-0.255272505, 0.329058719, -0.338818557, -0.263241434,
-0.077121255, 0.544068044, 0.057991947, 0.085910629, -0.128666609,
0.139661993, -0.37161107, -0.62838893, 0.477121255, 0.176091259,
-0.21387982, 0.757947864, 0.191885527, -0.099131473, -0.011281011,
-0.054738789, -0.269772302, 0.191885526, -0.114719571, 0.275016563,
-1.005395032, 0.243038049, 0.15490196, 0.096910013, -0.119186408,
NA, -0.171292376, 0.273954718, -0.288513438, -0.17363066, -1.770852012,
0, 0, 0.301029996, -0.301029996, 1.041392685, -0.087150176, 0.577235408,
-0.355387658, 0.329058719, -0.182930683, 0.196294545, 0.110954516,
-0.042403849, -0.290034611, -0.522878746, -0.301029995, 0.477121254,
0, 0.492915522, -0.243038048, -0.028028724, -0.875061263, -0.301029996,
0, 1.531078917, -0.32735893, 0.070633618, 0.265310043, -0.038918066,
-0.660051938, -0.544068044, 1.176091259, -0.014723257, -0.064457989,
0.049218022, -0.405765346, 0.449969009, 0, -0.044203663, -0.015794267,
0.100115153, 0.509913768, -0.101873432, 0.073317972, -0.155504729,
-0.578578895, 0.384054231, -0.029289376, 0.395915322, -0.5202338,
-0.09017663, 0.076388346, -0.412180448, 0.383216752, -0.100670162,
0.240332155, 0.096910013, -0.337242168, 0.169751081, -0.490086232,
-0.087150176, -0.352182518, 0.778151251, 0.360151447, -0.594234653,
0.057991947, 0.503450193, -0.07410172, -1.33243846, 0.812913356,
-0.210853365, 1.079181246, -0.266267889, 0.355878663, -0.566732029,
-1.505149978, 0.903089987, 0.327358934, 0.301029996, -0.069080919,
0.117385599, -0.403692338, -0.574031268, 0.977723606, -1.278753601,
-0.301029996, 0, 0, 0, 0, 0.477121255, 0, 0.124938736, 0.176091259,
-0.176091259, 0, 0.397490009, -0.2218485, 0.06690679, 0.10914469,
0.22184875, 0.301029996, -0.079181206, 0.158362092, -0.442359149,
0.116505569, 0.403019535, -0.077165955, 0.221848749, -0.079181206,
-0.283996656, -0.301029996, 0, 0.317420412, -0.176091259, 0.492915522,
0.23483206, -0.77815125, 0.528273777, -0.301029996, -0.069635928,
-0.407485327, -0.255272505, 0, 0.079181246, -0.477121254, 0.477121254,
-0.477121254, 0.176091259, 0.124938736, -0.124938736, 1.656417653,
-0.282280559, 0.21319964, -0.617299958, -0.085430195, 0.5191085756,
-0.074533518, 0.185045102, -0.227798082, -0.348454546, -0.301029996,
0, 0, 0.141329153, 0.023481096, 0.101457641, -0.124938737, -0.024823584,
-0.753327666, 0.884606581, -0.082974235, -0.324511092, 0.087150176,
0.072550667, 0.187086644, 0.161368002, 0, -0.231949077, 0.070581075,
0.113903352, 0.436285001, -0.00519178, -0.075054679, 0.00811789,
-0.431363764, 0.041392685, -0.087150176, 0.713210444, -0.269512945,
-0.443697499, -0.176091259, 0, 0.412180448, -0.148939013)), class = "data.frame", row.names = c(NA,
-210L))
Code:
for(f in 1:11){
for(b in 1:5){
for (c in 1:5){
#To select test sets 1,2,3,4, and 5 years beyond the training set:
#Calculate the mean of abundance for the training set years.
Model1<-lm(mean~1, data=DD1)
#
Output2:
2 3 0.676209994477288 1.9365051784348e-09 4.44089209850063e-16
3 53 11.9236453578109 2.06371097988267e-09 1.13686837721616e-13
4 31 1.94583877614293 1.11022302462516e-15 1.99840144432528e-15
5 4 8.06660449042397 1.48071350736245e-08 3.19744231092045e-14
6 5 10.5321102149558 9.31706267692789e-10 1.4210854715202e-14
..

Answer 1

First, please see the time series graph of counts for different species and plots below.
library(ggplot2)
ggplot(DD, aes(Year, Count)) +
geom_point() +
geom_line() +
facet_grid(Plot ~ Species) +
scale_y_log10()
It is seen that there is no obvious trend which can be fitted by power or log-power function using nls.
Second, as I understand you are trying to use nls to predict outside the training data set. Usually it is not quite an effective to use least square models because of auto-correlated nature of time-series.
Third, the simplest prediction algorithm is Holt-Winters (see "dirty" implementation below). You can use as well a ton of other algorithms like ARIMA, exponential smoothing state space etc.
x <- ts(DD[DD$Species == "BG" & DD$Plot == "elq1a3", ]$LogCount)
m <- HoltWinters(x, gamma = FALSE)
library(forecast)
f <- forecast(m, 2)
plot(f, main = "elq1a3 at BG")
Fourth, about your algorithm in question, it throws
Error in qr.solve(QR.B, cc) : singular matrix 'a' in solve.
The reason is that in the first step of for-loop (at f = b = c = 1 DD2 data frame contains just one row. And executing
Model6<-nls(Diff~1+Count^T,start=list(T=1),trace=TRUE,algorithm ="plinear",data=DD2)
means that you are trying to fit a curve using only one data point, which is impossible.
However if you change f value in for-loop from 1:11 to 2:11 another error thrown:
Error in nls(Diff ~ 1 + Count^T, start = list(T = 1), trace = TRUE,
algorithm = "plinear", : step factor 0.000488281 reduced below
minFactor 0.000976562.
In this case you cannot use "naive" approach used by plinear algorithm with self-starting inital value and, e.g. nls.control(min.factor = 1e-5). You must feed all initial coefficients explicitely with default Gauss-Newton algorithm. Quite exausting, please try yourself :)