LORI (LOw-Rank Interaction) model for count data with covariates
The LORI model is designed to analyse count data with covariates, using a Poisson log-linear model. In particular, it can be used to assess the effect of temporal and geographical covariates on species abundances.
Let \(Y\in\mathbb{N}^{n\times p}\) be a (incomplete) matrix of counts, and \(L\in\mathbb{R}^{np\times K}\) a matrix of covariates about the rows and columns of \(Y\). For example if \(Y\) counts the abundance of species across sites (rows) and time stamps (columns), \(L\) might contain temporal, spatial, and spatio-temporal information.
library(lori)
library(glmnet)## Warning: package 'glmnet' was built under R version 3.4.4## Loading required package: Matrix## Warning: package 'Matrix' was built under R version 3.4.4## Loading required package: foreach## Loaded glmnet 2.0-16library(gridExtra)
data("aravo")Example: Aravo data set
The {Aravo data set} measures the abundance of \(82\) species of alpine plants in \(75\) sites in France. The data consist of a contingency table collecting the abundance of species across sampling sites. Covariates about the environments and species are also available.
# Environment characteristics
head(aravo$env)## Aspect Slope Form PhysD ZoogD Snow
## AR07 7 2 1 50 no 140
## AR71 1 35 3 40 no 140
## AR26 5 0 3 20 no 140
## AR54 9 30 3 80 no 140
## AR60 9 5 1 80 no 140
## AR70 1 30 3 40 no 140# Species traits
head(aravo$traits)## Height Spread Angle Area Thick SLA N_mass Seed
## Agro.rupe 6 10 80 60.0 0.12 8.1 218.70 0.08
## Alop.alpi 5 20 20 190.9 0.20 15.1 203.85 0.21
## Anth.nipp 15 5 50 280.0 0.08 18.0 219.60 0.54
## Heli.sede 0 30 80 600.0 0.20 10.6 233.20 1.72
## Aven.vers 12 30 60 420.0 0.14 12.5 156.25 1.17
## Care.rosa 30 20 80 180.0 0.40 6.5 208.65 1.68d <- dim(aravo$spe)
n <- d[1]
p <- d[2]
# Create covariate matrix, choose quantitative variables in Row and Column covariates
# and use covmat function to replicate species/environments
# center and scale covariate matrix
cov <- scale(covmat(aravo$env[, c(1,2,4,6)], aravo$traits, n, p))lambda1 <- qut(aravo$spe, cov)##
1 / 100
2 / 100
3 / 100
4 / 100
5 / 100
6 / 100
7 / 100
8 / 100
9 / 100
10 / 100
11 / 100
12 / 100
13 / 100
14 / 100
15 / 100
16 / 100
17 / 100
18 / 100
19 / 100
20 / 100
21 / 100
22 / 100
23 / 100
24 / 100
25 / 100
26 / 100
27 / 100
28 / 100
29 / 100
30 / 100
31 / 100
32 / 100
33 / 100
34 / 100
35 / 100
36 / 100
37 / 100
38 / 100
39 / 100
40 / 100
41 / 100
42 / 100
43 / 100
44 / 100
45 / 100
46 / 100
47 / 100
48 / 100
49 / 100
50 / 100
51 / 100
52 / 100
53 / 100
54 / 100
55 / 100
56 / 100
57 / 100
58 / 100
59 / 100
60 / 100
61 / 100
62 / 100
63 / 100
64 / 100
65 / 100
66 / 100
67 / 100
68 / 100
69 / 100
70 / 100
71 / 100
72 / 100
73 / 100
74 / 100
75 / 100
76 / 100
77 / 100
78 / 100
79 / 100
80 / 100
81 / 100
82 / 100
83 / 100
84 / 100
85 / 100
86 / 100
87 / 100
88 / 100
89 / 100
90 / 100
91 / 100
92 / 100
93 / 100
94 / 100
95 / 100
96 / 100
97 / 100
98 / 100
99 / 100
100 / 100res <- lori(aravo$spe, cov, lambda1=lambda1, lambda2=0, trace.it = T)## [1] "fitting model..."
##
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
25%
26%
27%
28%
29%
30%
31%
32%
33%
34%
35%
36%
37%
38%
39%
40%
41%
42%
43%
44%
45%
46%
47%
48%
49%
50%
51%
52%
53%
54%
55%
56%
57%
58%
59%
60%
61%
62%
63%
64%
65%
66%
67%
68%
69%
70%
71%
72%
73%
74%
75%
76%
77%
78%
79%
80%
81%
82%
83%
84%
85%
86%
87%
88%
89%
90%
91%
92%
93%
94%
95%
96%
96% - iter: 10 - error: 1.026817e-05 - objective: 0.6617788
96% - iter: 20 - error: 1.025767e-05 - objective: 0.6617109
96% - iter: 30 - error: 1.024717e-05 - objective: 0.6616431
96% - iter: 40 - error: 1.023668e-05 - objective: 0.6615753
96% - iter: 50 - error: 1.022618e-05 - objective: 0.6615076
96% - iter: 60 - error: 1.021569e-05 - objective: 0.66144
96% - iter: 70 - error: 1.02052e-05 - objective: 0.6613725
96% - iter: 80 - error: 1.019472e-05 - objective: 0.661305
96% - iter: 90 - error: 1.018423e-05 - objective: 0.6612377
96% - iter: 100 - error: 1.017375e-05 - objective: 0.6611704
96% - iter: 110 - error: 1.016327e-05 - objective: 0.6611031
96% - iter: 120 - error: 1.015279e-05 - objective: 0.661036
96% - iter: 130 - error: 1.014232e-05 - objective: 0.6609689
96% - iter: 140 - error: 1.013184e-05 - objective: 0.6609019
96% - iter: 150 - error: 1.012137e-05 - objective: 0.660835
96% - iter: 160 - error: 1.01109e-05 - objective: 0.6607682
96% - iter: 170 - error: 1.010044e-05 - objective: 0.6607014
96% - iter: 180 - error: 1.008997e-05 - objective: 0.6606347
96% - iter: 190 - error: 1.007951e-05 - objective: 0.6605681
96% - iter: 200 - error: 1.006905e-05 - objective: 0.6605015
96% - iter: 210 - error: 1.00586e-05 - objective: 0.6604351
96% - iter: 220 - error: 1.004814e-05 - objective: 0.6603687
96% - iter: 230 - error: 1.003769e-05 - objective: 0.6603024
96% - iter: 240 - error: 1.002724e-05 - objective: 0.6602361
96% - iter: 250 - error: 1.001679e-05 - objective: 0.66017
96% - iter: 260 - error: 1.000635e-05 - objective: 0.6601039
97%
97% - iter: 10 - error: 1.207383e-05 - objective: 0.65981
97% - iter: 20 - error: 1.206145e-05 - objective: 0.6597304
97% - iter: 30 - error: 1.204908e-05 - objective: 0.6596509
97% - iter: 40 - error: 1.203671e-05 - objective: 0.6595715
97% - iter: 50 - error: 1.202434e-05 - objective: 0.6594921
97% - iter: 60 - error: 1.201197e-05 - objective: 0.6594129
97% - iter: 70 - error: 1.19996e-05 - objective: 0.6593337
97% - iter: 80 - error: 1.198723e-05 - objective: 0.6592547
97% - iter: 90 - error: 1.197486e-05 - objective: 0.6591757
97% - iter: 100 - error: 1.19625e-05 - objective: 0.6590968
97% - iter: 110 - error: 1.195013e-05 - objective: 0.659018
97% - iter: 120 - error: 1.193777e-05 - objective: 0.6589393
97% - iter: 130 - error: 1.192541e-05 - objective: 0.6588607
97% - iter: 140 - error: 1.191305e-05 - objective: 0.6587822
97% - iter: 150 - error: 1.190069e-05 - objective: 0.6587037
97% - iter: 160 - error: 1.188833e-05 - objective: 0.6586254
97% - iter: 170 - error: 1.187597e-05 - objective: 0.6585471
97% - iter: 180 - error: 1.186361e-05 - objective: 0.658469
97% - iter: 190 - error: 1.185126e-05 - objective: 0.6583909
97% - iter: 200 - error: 1.183891e-05 - objective: 0.6583129
97% - iter: 210 - error: 1.182655e-05 - objective: 0.6582351
97% - iter: 220 - error: 1.18142e-05 - objective: 0.6581573
97% - iter: 230 - error: 1.180185e-05 - objective: 0.6580795
97% - iter: 240 - error: 1.178951e-05 - objective: 0.6580019
97% - iter: 250 - error: 1.177716e-05 - objective: 0.6579244
97% - iter: 260 - error: 1.176481e-05 - objective: 0.657847
97% - iter: 270 - error: 1.175247e-05 - objective: 0.6577696
97% - iter: 280 - error: 1.174013e-05 - objective: 0.6576924
97% - iter: 290 - error: 1.172779e-05 - objective: 0.6576152
97% - iter: 300 - error: 1.171545e-05 - objective: 0.6575381
97% - iter: 310 - error: 1.170311e-05 - objective: 0.6574612
97% - iter: 320 - error: 1.169077e-05 - objective: 0.6573843
97% - iter: 330 - error: 1.167844e-05 - objective: 0.6573075
97% - iter: 340 - error: 1.166611e-05 - objective: 0.6572307
97% - iter: 350 - error: 1.165377e-05 - objective: 0.6571541
97% - iter: 360 - error: 1.164144e-05 - objective: 0.6570776
97% - iter: 370 - error: 1.162912e-05 - objective: 0.6570011
97% - iter: 380 - error: 1.161679e-05 - objective: 0.6569248
97% - iter: 390 - error: 1.160446e-05 - objective: 0.6568485
97% - iter: 400 - error: 1.159214e-05 - objective: 0.6567723
97% - iter: 410 - error: 1.157982e-05 - objective: 0.6566963
97% - iter: 420 - error: 1.15675e-05 - objective: 0.6566203
97% - iter: 430 - error: 1.155518e-05 - objective: 0.6565444
97% - iter: 440 - error: 1.154287e-05 - objective: 0.6564685
97% - iter: 450 - error: 1.153055e-05 - objective: 0.6563928
97% - iter: 460 - error: 1.151824e-05 - objective: 0.6563172
97% - iter: 470 - error: 1.150593e-05 - objective: 0.6562416
97% - iter: 480 - error: 1.149362e-05 - objective: 0.6561662
97% - iter: 490 - error: 1.148131e-05 - objective: 0.6560908
97% - iter: 500 - error: 1.146901e-05 - objective: 0.6560155
97% - iter: 510 - error: 1.14567e-05 - objective: 0.6559403
97% - iter: 520 - error: 1.14444e-05 - objective: 0.6558652
97% - iter: 530 - error: 1.14321e-05 - objective: 0.6557902
97% - iter: 540 - error: 1.141981e-05 - objective: 0.6557153
97% - iter: 550 - error: 1.140751e-05 - objective: 0.6556405
97% - iter: 560 - error: 1.139522e-05 - objective: 0.6555657
97% - iter: 570 - error: 1.138293e-05 - objective: 0.6554911
97% - iter: 580 - error: 1.137064e-05 - objective: 0.6554165
97% - iter: 590 - error: 1.135835e-05 - objective: 0.655342
97% - iter: 600 - error: 1.134607e-05 - objective: 0.6552677
97% - iter: 610 - error: 1.133378e-05 - objective: 0.6551934
97% - iter: 620 - error: 1.13215e-05 - objective: 0.6551191
97% - iter: 630 - error: 1.130922e-05 - objective: 0.655045
97% - iter: 640 - error: 1.129695e-05 - objective: 0.654971
97% - iter: 650 - error: 1.128467e-05 - objective: 0.654897
97% - iter: 660 - error: 1.12724e-05 - objective: 0.6548232
97% - iter: 670 - error: 1.126013e-05 - objective: 0.6547494
97% - iter: 680 - error: 1.124787e-05 - objective: 0.6546758
97% - iter: 690 - error: 1.12356e-05 - objective: 0.6546022
97% - iter: 700 - error: 1.122334e-05 - objective: 0.6545287
97% - iter: 710 - error: 1.121108e-05 - objective: 0.6544553
97% - iter: 720 - error: 1.119882e-05 - objective: 0.6543819
97% - iter: 730 - error: 1.118656e-05 - objective: 0.6543087
97% - iter: 740 - error: 1.117431e-05 - objective: 0.6542355
97% - iter: 750 - error: 1.116206e-05 - objective: 0.6541625
97% - iter: 760 - error: 1.114981e-05 - objective: 0.6540895
97% - iter: 770 - error: 1.113757e-05 - objective: 0.6540166
97% - iter: 780 - error: 1.112532e-05 - objective: 0.6539438
97% - iter: 790 - error: 1.111308e-05 - objective: 0.6538711
97% - iter: 800 - error: 1.110084e-05 - objective: 0.6537985
97% - iter: 810 - error: 1.108861e-05 - objective: 0.653726
97% - iter: 820 - error: 1.107637e-05 - objective: 0.6536536
97% - iter: 830 - error: 1.106414e-05 - objective: 0.6535812
97% - iter: 840 - error: 1.105192e-05 - objective: 0.6535089
97% - iter: 850 - error: 1.103969e-05 - objective: 0.6534368
97% - iter: 860 - error: 1.102747e-05 - objective: 0.6533647
97% - iter: 870 - error: 1.101525e-05 - objective: 0.6532927
97% - iter: 880 - error: 1.100303e-05 - objective: 0.6532208
97% - iter: 890 - error: 1.099081e-05 - objective: 0.6531489
97% - iter: 900 - error: 1.09786e-05 - objective: 0.6530772
97% - iter: 910 - error: 1.096639e-05 - objective: 0.6530055
97% - iter: 920 - error: 1.095419e-05 - objective: 0.652934
97% - iter: 930 - error: 1.094198e-05 - objective: 0.6528625
97% - iter: 940 - error: 1.092978e-05 - objective: 0.6527911
97% - iter: 950 - error: 1.091758e-05 - objective: 0.6527198
97% - iter: 960 - error: 1.090539e-05 - objective: 0.6526486
97% - iter: 970 - error: 1.08932e-05 - objective: 0.6525775
97% - iter: 980 - error: 1.088101e-05 - objective: 0.6525064
97% - iter: 990 - error: 1.086882e-05 - objective: 0.6524355
97% - iter: 1000 - error: 1.085664e-05 - objective: 0.6523646
98%
98% - iter: 10 - error: 1.298255e-05 - objective: 0.6514582
98% - iter: 20 - error: 1.296822e-05 - objective: 0.6513737
98% - iter: 30 - error: 1.29539e-05 - objective: 0.6512893
98% - iter: 40 - error: 1.293957e-05 - objective: 0.651205
98% - iter: 50 - error: 1.292524e-05 - objective: 0.6511207
98% - iter: 60 - error: 1.291092e-05 - objective: 0.6510366
98% - iter: 70 - error: 1.28966e-05 - objective: 0.6509526
98% - iter: 80 - error: 1.288227e-05 - objective: 0.6508688
98% - iter: 90 - error: 1.286795e-05 - objective: 0.650785
98% - iter: 100 - error: 1.285364e-05 - objective: 0.6507013
98% - iter: 110 - error: 1.283932e-05 - objective: 0.6506177
98% - iter: 120 - error: 1.2825e-05 - objective: 0.6505342
98% - iter: 130 - error: 1.281069e-05 - objective: 0.6504508
98% - iter: 140 - error: 1.279638e-05 - objective: 0.6503676
98% - iter: 150 - error: 1.278207e-05 - objective: 0.6502844
98% - iter: 160 - error: 1.276776e-05 - objective: 0.6502013
98% - iter: 170 - error: 1.275345e-05 - objective: 0.6501184
98% - iter: 180 - error: 1.273914e-05 - objective: 0.6500355
98% - iter: 190 - error: 1.272484e-05 - objective: 0.6499528
98% - iter: 200 - error: 1.271054e-05 - objective: 0.6498701
98% - iter: 210 - error: 1.269624e-05 - objective: 0.6497876
98% - iter: 220 - error: 1.268194e-05 - objective: 0.6497051
98% - iter: 230 - error: 1.266764e-05 - objective: 0.6496228
98% - iter: 240 - error: 1.265334e-05 - objective: 0.6495406
98% - iter: 250 - error: 1.263905e-05 - objective: 0.6494584
98% - iter: 260 - error: 1.262476e-05 - objective: 0.6493764
98% - iter: 270 - error: 1.261047e-05 - objective: 0.6492945
98% - iter: 280 - error: 1.259618e-05 - objective: 0.6492127
98% - iter: 290 - error: 1.25819e-05 - objective: 0.6491309
98% - iter: 300 - error: 1.256762e-05 - objective: 0.6490493
98% - iter: 310 - error: 1.255333e-05 - objective: 0.6489678
98% - iter: 320 - error: 1.253905e-05 - objective: 0.6488864
98% - iter: 330 - error: 1.252478e-05 - objective: 0.6488051
98% - iter: 340 - error: 1.25105e-05 - objective: 0.6487239
98% - iter: 350 - error: 1.249623e-05 - objective: 0.6486428
98% - iter: 360 - error: 1.248196e-05 - objective: 0.6485618
98% - iter: 370 - error: 1.246769e-05 - objective: 0.6484809
98% - iter: 380 - error: 1.245343e-05 - objective: 0.6484001
98% - iter: 390 - error: 1.243916e-05 - objective: 0.6483194
98% - iter: 400 - error: 1.24249e-05 - objective: 0.6482388
98% - iter: 410 - error: 1.241064e-05 - objective: 0.6481583
98% - iter: 420 - error: 1.239639e-05 - objective: 0.6480779
98% - iter: 430 - error: 1.238213e-05 - objective: 0.6479977
98% - iter: 440 - error: 1.236788e-05 - objective: 0.6479175
98% - iter: 450 - error: 1.235363e-05 - objective: 0.6478374
98% - iter: 460 - error: 1.233939e-05 - objective: 0.6477574
98% - iter: 470 - error: 1.232514e-05 - objective: 0.6476776
98% - iter: 480 - error: 1.23109e-05 - objective: 0.6475978
98% - iter: 490 - error: 1.229666e-05 - objective: 0.6475181
98% - iter: 500 - error: 1.228243e-05 - objective: 0.6474385
98% - iter: 510 - error: 1.226819e-05 - objective: 0.6473591
98% - iter: 520 - error: 1.225396e-05 - objective: 0.6472797
98% - iter: 530 - error: 1.223974e-05 - objective: 0.6472005
98% - iter: 540 - error: 1.222551e-05 - objective: 0.6471213
98% - iter: 550 - error: 1.221129e-05 - objective: 0.6470422
98% - iter: 560 - error: 1.219707e-05 - objective: 0.6469633
98% - iter: 570 - error: 1.218285e-05 - objective: 0.6468844
98% - iter: 580 - error: 1.216863e-05 - objective: 0.6468057
98% - iter: 590 - error: 1.215442e-05 - objective: 0.646727
98% - iter: 600 - error: 1.214021e-05 - objective: 0.6466485
98% - iter: 610 - error: 1.212601e-05 - objective: 0.64657
98% - iter: 620 - error: 1.211181e-05 - objective: 0.6464917
98% - iter: 630 - error: 1.209761e-05 - objective: 0.6464134
98% - iter: 640 - error: 1.208341e-05 - objective: 0.6463353
98% - iter: 650 - error: 1.206922e-05 - objective: 0.6462572
98% - iter: 660 - error: 1.205503e-05 - objective: 0.6461793
98% - iter: 670 - error: 1.204085e-05 - objective: 0.6461015
98% - iter: 680 - error: 1.202666e-05 - objective: 0.6460237
98% - iter: 690 - error: 1.201248e-05 - objective: 0.6459461
98% - iter: 700 - error: 1.199831e-05 - objective: 0.6458685
98% - iter: 710 - error: 1.198413e-05 - objective: 0.6457911
98% - iter: 720 - error: 1.196996e-05 - objective: 0.6457138
98% - iter: 730 - error: 1.19558e-05 - objective: 0.6456365
98% - iter: 740 - error: 1.194163e-05 - objective: 0.6455594
98% - iter: 750 - error: 1.192748e-05 - objective: 0.6454824
98% - iter: 760 - error: 1.191332e-05 - objective: 0.6454054
98% - iter: 770 - error: 1.189917e-05 - objective: 0.6453286
98% - iter: 780 - error: 1.188502e-05 - objective: 0.6452519
98% - iter: 790 - error: 1.187087e-05 - objective: 0.6451752
98% - iter: 800 - error: 1.185673e-05 - objective: 0.6450987
98% - iter: 810 - error: 1.184259e-05 - objective: 0.6450223
98% - iter: 820 - error: 1.182846e-05 - objective: 0.6449459
98% - iter: 830 - error: 1.181433e-05 - objective: 0.6448697
98% - iter: 840 - error: 1.18002e-05 - objective: 0.6447936
98% - iter: 850 - error: 1.178608e-05 - objective: 0.6447175
98% - iter: 860 - error: 1.177196e-05 - objective: 0.6446416
98% - iter: 870 - error: 1.175784e-05 - objective: 0.6445658
98% - iter: 880 - error: 1.174373e-05 - objective: 0.64449
98% - iter: 890 - error: 1.172962e-05 - objective: 0.6444144
98% - iter: 900 - error: 1.171551e-05 - objective: 0.6443389
98% - iter: 910 - error: 1.170141e-05 - objective: 0.6442634
98% - iter: 920 - error: 1.168732e-05 - objective: 0.6441881
98% - iter: 930 - error: 1.167322e-05 - objective: 0.6441129
98% - iter: 940 - error: 1.165914e-05 - objective: 0.6440377
98% - iter: 950 - error: 1.164505e-05 - objective: 0.6439627
98% - iter: 960 - error: 1.163097e-05 - objective: 0.6438878
98% - iter: 970 - error: 1.161689e-05 - objective: 0.6438129
98% - iter: 980 - error: 1.160282e-05 - objective: 0.6437382
98% - iter: 990 - error: 1.158875e-05 - objective: 0.6436636
98% - iter: 1000 - error: 1.157469e-05 - objective: 0.643589
99%
99% - iter: 10 - error: 1.375208e-05 - objective: 0.6420649
99% - iter: 20 - error: 1.37356e-05 - objective: 0.6419766
99% - iter: 30 - error: 1.371913e-05 - objective: 0.6418885
99% - iter: 40 - error: 1.370266e-05 - objective: 0.6418005
99% - iter: 50 - error: 1.368619e-05 - objective: 0.6417126
99% - iter: 60 - error: 1.366972e-05 - objective: 0.6416249
99% - iter: 70 - error: 1.365326e-05 - objective: 0.6415372
99% - iter: 80 - error: 1.36368e-05 - objective: 0.6414497
99% - iter: 90 - error: 1.362034e-05 - objective: 0.6413623
99% - iter: 100 - error: 1.360388e-05 - objective: 0.641275
99% - iter: 110 - error: 1.358743e-05 - objective: 0.6411878
99% - iter: 120 - error: 1.357098e-05 - objective: 0.6411008
99% - iter: 130 - error: 1.355453e-05 - objective: 0.6410138
99% - iter: 140 - error: 1.353809e-05 - objective: 0.640927
99% - iter: 150 - error: 1.352164e-05 - objective: 0.6408403
99% - iter: 160 - error: 1.350521e-05 - objective: 0.6407537
99% - iter: 170 - error: 1.348877e-05 - objective: 0.6406673
99% - iter: 180 - error: 1.347234e-05 - objective: 0.6405809
99% - iter: 190 - error: 1.345591e-05 - objective: 0.6404947
99% - iter: 200 - error: 1.343948e-05 - objective: 0.6404085
99% - iter: 210 - error: 1.342306e-05 - objective: 0.6403225
99% - iter: 220 - error: 1.340664e-05 - objective: 0.6402367
99% - iter: 230 - error: 1.339022e-05 - objective: 0.6401509
99% - iter: 240 - error: 1.337381e-05 - objective: 0.6400652
99% - iter: 250 - error: 1.33574e-05 - objective: 0.6399797
99% - iter: 260 - error: 1.334099e-05 - objective: 0.6398943
99% - iter: 270 - error: 1.332459e-05 - objective: 0.639809
99% - iter: 280 - error: 1.330819e-05 - objective: 0.6397238
99% - iter: 290 - error: 1.329179e-05 - objective: 0.6396387
99% - iter: 300 - error: 1.32754e-05 - objective: 0.6395538
99% - iter: 310 - error: 1.325901e-05 - objective: 0.6394689
99% - iter: 320 - error: 1.324263e-05 - objective: 0.6393842
99% - iter: 330 - error: 1.322624e-05 - objective: 0.6392996
99% - iter: 340 - error: 1.320987e-05 - objective: 0.6392151
99% - iter: 350 - error: 1.319349e-05 - objective: 0.6391307
99% - iter: 360 - error: 1.317712e-05 - objective: 0.6390465
99% - iter: 370 - error: 1.316076e-05 - objective: 0.6389623
99% - iter: 380 - error: 1.314439e-05 - objective: 0.6388783
99% - iter: 390 - error: 1.312803e-05 - objective: 0.6387944
99% - iter: 400 - error: 1.311168e-05 - objective: 0.6387106
99% - iter: 410 - error: 1.309533e-05 - objective: 0.6386269
99% - iter: 420 - error: 1.307898e-05 - objective: 0.6385433
99% - iter: 430 - error: 1.306264e-05 - objective: 0.6384599
99% - iter: 440 - error: 1.30463e-05 - objective: 0.6383765
99% - iter: 450 - error: 1.302997e-05 - objective: 0.6382933
99% - iter: 460 - error: 1.301364e-05 - objective: 0.6382102
99% - iter: 470 - error: 1.299731e-05 - objective: 0.6381272
99% - iter: 480 - error: 1.298099e-05 - objective: 0.6380443
99% - iter: 490 - error: 1.296468e-05 - objective: 0.6379616
99% - iter: 500 - error: 1.294837e-05 - objective: 0.6378789
99% - iter: 510 - error: 1.293206e-05 - objective: 0.6377964
99% - iter: 520 - error: 1.291576e-05 - objective: 0.637714
99% - iter: 530 - error: 1.289946e-05 - objective: 0.6376317
99% - iter: 540 - error: 1.288316e-05 - objective: 0.6375495
99% - iter: 550 - error: 1.286687e-05 - objective: 0.6374674
99% - iter: 560 - error: 1.285059e-05 - objective: 0.6373855
99% - iter: 570 - error: 1.283431e-05 - objective: 0.6373036
99% - iter: 580 - error: 1.281804e-05 - objective: 0.6372219
99% - iter: 590 - error: 1.280177e-05 - objective: 0.6371403
99% - iter: 600 - error: 1.27855e-05 - objective: 0.6370588
99% - iter: 610 - error: 1.276924e-05 - objective: 0.6369774
99% - iter: 620 - error: 1.275299e-05 - objective: 0.6368961
99% - iter: 630 - error: 1.273673e-05 - objective: 0.6368149
99% - iter: 640 - error: 1.272049e-05 - objective: 0.6367339
99% - iter: 650 - error: 1.270425e-05 - objective: 0.636653
99% - iter: 660 - error: 1.268801e-05 - objective: 0.6365721
99% - iter: 670 - error: 1.267179e-05 - objective: 0.6364914
99% - iter: 680 - error: 1.265556e-05 - objective: 0.6364108
99% - iter: 690 - error: 1.263934e-05 - objective: 0.6363304
99% - iter: 700 - error: 1.262313e-05 - objective: 0.63625
99% - iter: 710 - error: 1.260692e-05 - objective: 0.6361698
99% - iter: 720 - error: 1.259072e-05 - objective: 0.6360896
99% - iter: 730 - error: 1.257452e-05 - objective: 0.6360096
99% - iter: 740 - error: 1.255833e-05 - objective: 0.6359297
99% - iter: 750 - error: 1.254214e-05 - objective: 0.6358499
99% - iter: 760 - error: 1.252596e-05 - objective: 0.6357702
99% - iter: 770 - error: 1.250978e-05 - objective: 0.6356906
99% - iter: 780 - error: 1.249361e-05 - objective: 0.6356112
99% - iter: 790 - error: 1.247745e-05 - objective: 0.6355318
99% - iter: 800 - error: 1.246129e-05 - objective: 0.6354526
99% - iter: 810 - error: 1.244514e-05 - objective: 0.6353734
99% - iter: 820 - error: 1.242899e-05 - objective: 0.6352944
99% - iter: 830 - error: 1.241285e-05 - objective: 0.6352155
99% - iter: 840 - error: 1.239672e-05 - objective: 0.6351367
99% - iter: 850 - error: 1.238059e-05 - objective: 0.6350581
99% - iter: 860 - error: 1.236446e-05 - objective: 0.6349795
99% - iter: 870 - error: 1.234835e-05 - objective: 0.6349011
99% - iter: 880 - error: 1.233224e-05 - objective: 0.6348227
99% - iter: 890 - error: 1.231613e-05 - objective: 0.6347445
99% - iter: 900 - error: 1.230003e-05 - objective: 0.6346664
99% - iter: 910 - error: 1.228394e-05 - objective: 0.6345884
99% - iter: 920 - error: 1.226785e-05 - objective: 0.6345105
99% - iter: 930 - error: 1.225177e-05 - objective: 0.6344327
99% - iter: 940 - error: 1.22357e-05 - objective: 0.634355
99% - iter: 950 - error: 1.221963e-05 - objective: 0.6342775
99% - iter: 960 - error: 1.220357e-05 - objective: 0.6342
99% - iter: 970 - error: 1.218752e-05 - objective: 0.6341227
99% - iter: 980 - error: 1.217147e-05 - objective: 0.6340455
99% - iter: 990 - error: 1.215543e-05 - objective: 0.6339684
99% - iter: 1000 - error: 1.21394e-05 - objective: 0.6338914
100%
100% - iter: 10 - error: 1.434754e-05 - objective: 0.6317776
100% - iter: 20 - error: 1.432882e-05 - objective: 0.631687
100% - iter: 30 - error: 1.431011e-05 - objective: 0.6315966
100% - iter: 40 - error: 1.42914e-05 - objective: 0.6315062
100% - iter: 50 - error: 1.42727e-05 - objective: 0.6314161
100% - iter: 60 - error: 1.4254e-05 - objective: 0.631326
100% - iter: 70 - error: 1.423531e-05 - objective: 0.6312361
100% - iter: 80 - error: 1.421662e-05 - objective: 0.6311463
100% - iter: 90 - error: 1.419794e-05 - objective: 0.6310567
100% - iter: 100 - error: 1.417926e-05 - objective: 0.6309671
100% - iter: 110 - error: 1.416059e-05 - objective: 0.6308777
100% - iter: 120 - error: 1.414193e-05 - objective: 0.6307885
100% - iter: 130 - error: 1.412327e-05 - objective: 0.6306993
100% - iter: 140 - error: 1.410461e-05 - objective: 0.6306103
100% - iter: 150 - error: 1.408596e-05 - objective: 0.6305215
100% - iter: 160 - error: 1.406732e-05 - objective: 0.6304327
100% - iter: 170 - error: 1.404868e-05 - objective: 0.6303441
100% - iter: 180 - error: 1.403005e-05 - objective: 0.6302556
100% - iter: 190 - error: 1.401143e-05 - objective: 0.6301673
100% - iter: 200 - error: 1.399281e-05 - objective: 0.630079
100% - iter: 210 - error: 1.39742e-05 - objective: 0.6299909
100% - iter: 220 - error: 1.395559e-05 - objective: 0.629903
100% - iter: 230 - error: 1.393699e-05 - objective: 0.6298151
100% - iter: 240 - error: 1.39184e-05 - objective: 0.6297274
100% - iter: 250 - error: 1.389981e-05 - objective: 0.6296399
100% - iter: 260 - error: 1.388123e-05 - objective: 0.6295524
100% - iter: 270 - error: 1.386265e-05 - objective: 0.6294651
100% - iter: 280 - error: 1.384408e-05 - objective: 0.6293779
100% - iter: 290 - error: 1.382552e-05 - objective: 0.6292908
100% - iter: 300 - error: 1.380697e-05 - objective: 0.6292039
100% - iter: 310 - error: 1.378842e-05 - objective: 0.6291171
100% - iter: 320 - error: 1.376988e-05 - objective: 0.6290304
100% - iter: 330 - error: 1.375134e-05 - objective: 0.6289439
100% - iter: 340 - error: 1.373281e-05 - objective: 0.6288575
100% - iter: 350 - error: 1.371429e-05 - objective: 0.6287712
100% - iter: 360 - error: 1.369578e-05 - objective: 0.628685
100% - iter: 370 - error: 1.367727e-05 - objective: 0.628599
100% - iter: 380 - error: 1.365877e-05 - objective: 0.6285131
100% - iter: 390 - error: 1.364028e-05 - objective: 0.6284273
100% - iter: 400 - error: 1.362179e-05 - objective: 0.6283417
100% - iter: 410 - error: 1.360331e-05 - objective: 0.6282561
100% - iter: 420 - error: 1.358484e-05 - objective: 0.6281707
100% - iter: 430 - error: 1.356638e-05 - objective: 0.6280855
100% - iter: 440 - error: 1.354792e-05 - objective: 0.6280003
100% - iter: 450 - error: 1.352947e-05 - objective: 0.6279153
100% - iter: 460 - error: 1.351103e-05 - objective: 0.6278304
100% - iter: 470 - error: 1.34926e-05 - objective: 0.6277457
100% - iter: 480 - error: 1.347417e-05 - objective: 0.6276611
100% - iter: 490 - error: 1.345575e-05 - objective: 0.6275766
100% - iter: 500 - error: 1.343734e-05 - objective: 0.6274922
100% - iter: 510 - error: 1.341894e-05 - objective: 0.6274079
100% - iter: 520 - error: 1.340054e-05 - objective: 0.6273238
100% - iter: 530 - error: 1.338216e-05 - objective: 0.6272398
100% - iter: 540 - error: 1.336378e-05 - objective: 0.627156
100% - iter: 550 - error: 1.334541e-05 - objective: 0.6270722
100% - iter: 560 - error: 1.332704e-05 - objective: 0.6269886
100% - iter: 570 - error: 1.330869e-05 - objective: 0.6269051
100% - iter: 580 - error: 1.329034e-05 - objective: 0.6268217
100% - iter: 590 - error: 1.327201e-05 - objective: 0.6267385
100% - iter: 600 - error: 1.325368e-05 - objective: 0.6266554
100% - iter: 610 - error: 1.323536e-05 - objective: 0.6265724
100% - iter: 620 - error: 1.321704e-05 - objective: 0.6264895
100% - iter: 630 - error: 1.319874e-05 - objective: 0.6264068
100% - iter: 640 - error: 1.318044e-05 - objective: 0.6263242
100% - iter: 650 - error: 1.316216e-05 - objective: 0.6262417
100% - iter: 660 - error: 1.314388e-05 - objective: 0.6261594
100% - iter: 670 - error: 1.312561e-05 - objective: 0.6260771
100% - iter: 680 - error: 1.310735e-05 - objective: 0.625995
100% - iter: 690 - error: 1.308909e-05 - objective: 0.625913
100% - iter: 700 - error: 1.307085e-05 - objective: 0.6258312
100% - iter: 710 - error: 1.305262e-05 - objective: 0.6257494
100% - iter: 720 - error: 1.303439e-05 - objective: 0.6256678
100% - iter: 730 - error: 1.301618e-05 - objective: 0.6255864
100% - iter: 740 - error: 1.299797e-05 - objective: 0.625505
100% - iter: 750 - error: 1.297977e-05 - objective: 0.6254238
100% - iter: 760 - error: 1.296158e-05 - objective: 0.6253427
100% - iter: 770 - error: 1.29434e-05 - objective: 0.6252617
100% - iter: 780 - error: 1.292523e-05 - objective: 0.6251808
100% - iter: 790 - error: 1.290707e-05 - objective: 0.6251001
100% - iter: 800 - error: 1.288892e-05 - objective: 0.6250195
100% - iter: 810 - error: 1.287078e-05 - objective: 0.624939
100% - iter: 820 - error: 1.285265e-05 - objective: 0.6248586
100% - iter: 830 - error: 1.283453e-05 - objective: 0.6247784
100% - iter: 840 - error: 1.281641e-05 - objective: 0.6246982
100% - iter: 850 - error: 1.279831e-05 - objective: 0.6246182
100% - iter: 860 - error: 1.278022e-05 - objective: 0.6245384
100% - iter: 870 - error: 1.276214e-05 - objective: 0.6244586
100% - iter: 880 - error: 1.274406e-05 - objective: 0.624379
100% - iter: 890 - error: 1.2726e-05 - objective: 0.6242995
100% - iter: 900 - error: 1.270795e-05 - objective: 0.6242201
100% - iter: 910 - error: 1.26899e-05 - objective: 0.6241408
100% - iter: 920 - error: 1.267187e-05 - objective: 0.6240617
100% - iter: 930 - error: 1.265385e-05 - objective: 0.6239827
100% - iter: 940 - error: 1.263583e-05 - objective: 0.6239038
100% - iter: 950 - error: 1.261783e-05 - objective: 0.623825
100% - iter: 960 - error: 1.259984e-05 - objective: 0.6237464
100% - iter: 970 - error: 1.258186e-05 - objective: 0.6236679
100% - iter: 980 - error: 1.256389e-05 - objective: 0.6235895
100% - iter: 990 - error: 1.254592e-05 - objective: 0.6235112
100% - iter: 1000 - error: 1.252797e-05 - objective: 0.623433res$alpha## Aspect Slope PhysD Snow Height Spread
## 0.03531235 0.06928402 -0.01650697 -0.07819410 0.09606974 -0.23143505
## Angle Area Thick SLA N_mass Seed
## -0.17350092 -0.18790596 -0.09952458 -0.15620022 0.17531840 -0.11302239plot(svd(res$theta)$d)