select 具有最佳预测能力的向量组合的自动程序
Automatic procedure to select combination of vectors with best predictive power
我有一个包含 23 个元素 (Var01-Var23)、增长和年份的时间序列的矩阵 （参见下面的数据）。
然后，我想知道是哪一组化学元素阻止了我的树的生长。
当我将每个单独的元素与 growth 变量相关联时，结果非常低。但是当我计算所有元素的 mean 并将其与 growth 变量相关联时，相关性会增加。或者，当我将增长与选定元素的 mean 相关联时，相关性会增加更多（例如，Var02、Var04 和 Var09 到 Var13 的平均值）。我有几棵树的数据，然后我需要一些脚本来自动执行我的计算，因为目前我正在以手动方式进行。
# Example:
# My data
data <- read.delim("clipboard")
# Correlation with Mean of all variables (r= -0.64)
cor.test(data$growth, rowMeans(data[,3:25]))
# Correlation with Mean of seven variables (r= -0.65)
cor.test(data$growth, rowMeans(data[,c(4,6,11:15)]))
基于 PCA 和层次聚类分析，我正在计算某些元素（具有所有可能的元素组组合）的 growth 和 mean 之间的相关性。在这一点上，当我添加一个或多个元素时，我的相关性增加或减少，反之亦然。此外，我将growth与所有变量相关联，我只选择了第一个高相关元素，但这并不是我想要的。
我想知道与 growth 变量具有最高相关性的元素的精确组合。
我已经看到与 dplR 包的函数 strip.rwl() 的类似计算。此函数丢弃所有无助于改善某种相关性 (EPS) 的时间序列。此函数为您提供具有最高系列间相关性的精确变量。
类似，但我想知道给我最好的 mean 来计算与增长的最高相关性的变量的精确组合是什么？
是否已经有一个函数可以计算这个，或者你能给我一些指导吗？
数据：
year growth var01 var02 var03 var04 var05 var06 var07 var08 var09 var10 var11 var12 var13 var14 var15 var16 var17 var18 var19 var20 var21 var22 var23
2015 0.7355 -1.5093 -0.4718 0.4724 -1.2182 1.2762 2.1297 -0.3869 2.5204 0.5939 0.4910 -0.6156 -0.7688 -0.7586 -1.3430 2.0780 -1.5219 -1.2929 -0.6673 -1.2759 -1.3003 -1.1383 -1.0050 -1.0538
2014 1.0499 -1.5731 -0.8291 0.3671 -1.2009 1.2957 1.5425 -0.5630 1.3536 1.9637 0.4473 -0.5620 -0.6266 -0.6508 -1.4364 1.5605 -1.6061 -0.9849 -0.4060 -1.4001 -0.5928 -0.9355 -0.9086 -1.1744
2013 0.3023 -1.3480 -0.9086 1.0562 -1.4676 1.6038 1.6197 -0.9654 0.8675 -0.5802 0.3953 -0.6743 -1.2814 -0.9289 -1.7962 1.6508 -1.6769 -1.2483 -0.4202 -1.7725 -0.5117 -0.8456 -1.1292 -1.1822
2012 0.4691 -1.4137 -1.3467 0.8196 -0.9280 1.5524 1.6472 -0.6955 1.2168 0.3453 0.4625 -0.4587 -0.8154 -0.4288 -1.8088 1.5263 -1.5974 -1.2437 -0.6041 -1.9023 -0.4178 -0.7794 -1.0962 -1.4127
2011 1.5789 -1.3981 -0.9584 1.1080 -1.5778 1.3515 1.4592 -1.2458 1.2315 -0.8985 0.3111 -0.7732 -1.5045 -1.3703 -1.8152 1.4385 -1.5522 -1.3145 -0.5637 -1.7576 -0.8766 -1.0122 -1.5530 -1.3255
2010 1.2607 -1.3424 -0.8443 1.1052 -1.1118 1.3660 1.3892 -1.0938 1.2785 -0.9152 0.3842 -0.4285 -0.5272 -0.5904 -1.7213 1.4067 -1.4321 -0.2067 -0.3469 -1.7433 -0.1480 -0.2845 -0.7672 0.7892
2009 -0.5909 -0.7340 -0.5030 0.1297 -0.9245 1.3174 1.2938 -0.4455 1.0780 -0.5008 0.3727 -0.3743 -0.6238 -0.6003 -1.8261 1.3141 -0.9217 -0.3761 -0.4310 -1.8382 -0.3053 -0.5241 -0.7800 0.2114
2008 -0.6983 -1.1673 -0.1231 0.5825 -1.2651 1.6569 1.3955 -0.7211 0.9760 -0.7845 0.3861 0.0815 -0.3776 -0.6394 -1.7565 1.4102 -1.1523 -0.4078 -0.3300 -1.8786 -0.4062 -0.4016 -0.4600 -0.0071
2007 0.1183 -1.3682 -0.9443 -0.0971 -1.3220 1.3293 1.2750 -0.8371 1.0943 -1.0089 0.3398 -0.4498 -1.2298 -1.2716 -1.6478 1.3486 -1.3283 -0.7784 -0.2968 -1.5428 -0.1280 -0.7084 -0.9944 -0.5956
2006 0.5534 -1.2314 -0.7071 -0.7115 -1.2178 1.0437 1.1603 -0.8700 1.0272 -0.7154 0.3785 -0.7280 -0.8290 -0.7931 -1.4326 1.2680 -1.2664 -1.1744 -0.3001 -1.2794 -0.2198 -0.3347 -0.7982 -0.8576
2005 -0.1290 -0.6186 -0.7554 -0.8953 -0.7179 0.8193 1.2671 0.0563 1.1459 -0.3939 0.5788 -0.4018 -0.4051 -0.0909 -0.3482 1.1628 -0.6649 -0.5135 -0.1499 -0.5293 1.7077 1.3397 -0.5928 -0.3255
2004 -1.3960 -0.7433 3.3826 0.0168 0.6878 2.3632 2.0095 1.4930 1.1984 1.6115 0.9325 6.0082 3.4345 4.0293 -0.7450 1.8678 -1.1456 1.7131 -0.0351 -0.8672 -1.1172 0.6631 1.9708 1.3615
2003 -1.2024 -1.1421 1.4662 0.1289 -0.2702 1.5784 1.8177 0.4645 1.0738 0.3043 0.6369 0.1920 0.5853 0.6188 -0.9899 1.7807 -1.1835 0.8453 -0.3640 -0.8570 -0.2409 -0.7386 0.7062 0.1594
2002 -1.2695 -1.2228 -0.7048 -0.5232 -0.6171 1.9463 1.6148 0.2365 0.7777 1.1024 0.6519 0.3360 0.8234 0.8263 -0.7476 1.6094 -1.3752 1.7203 -0.2869 -0.9334 0.3433 0.2585 0.9249 0.3958
2001 2.2805 -2.0591 -0.8628 -3.9804 -1.5726 0.1381 0.5142 -0.6226 0.3808 -1.2949 0.7876 -0.5202 -0.4475 -0.2446 -1.7901 0.7399 -2.4933 0.4975 0.3481 -1.8721 2.6124 2.2446 -0.6788 0.8185
2000 1.2243 -0.3546 -0.3555 -0.9080 0.6723 0.7487 1.2527 0.2992 1.7156 1.4165 2.3882 -0.1943 -0.5190 -0.0279 -0.9017 1.3534 -0.8618 -0.0725 1.9422 -0.8831 2.9700 2.1966 -0.3275 0.5609
1999 1.1170 -1.0957 -0.5224 -0.9462 -0.8757 0.8819 1.2233 -0.1417 1.4077 0.3444 0.7656 -0.5936 -0.5658 -0.5246 1.7319 1.2449 -0.9524 0.1268 0.5618 1.6841 2.6959 2.1735 -0.6886 -0.0353
1998 1.5080 -0.9427 -0.5292 -1.9068 -0.9694 0.5602 0.9686 -0.5317 0.9646 -0.5927 0.5123 -0.5573 -0.6479 -0.6202 -1.2297 1.1412 -1.0400 -0.3132 -0.1830 -1.1215 2.2558 2.0275 -0.7357 -0.2513
1997 1.2109 -1.2957 -0.2941 -1.7398 -0.4912 0.4444 0.7539 -0.4458 0.7561 -0.3942 0.4130 -0.6011 -0.5307 -0.1443 -1.0119 0.8553 -1.2888 -1.1635 -0.2902 -1.0984 -0.3384 -0.7099 -0.7028 -0.6451
1996 1.9374 -0.9590 -0.5634 -1.1346 -0.8146 0.1582 0.5529 -0.7560 0.3428 -0.7315 0.3842 -0.9918 -1.1590 -0.8275 -1.0101 0.6369 -0.9615 -1.1021 -0.2902 -1.0126 -0.3163 -0.3251 -1.0070 -0.8537
1995 -0.0906 -0.6876 -0.5482 -0.7573 -0.8502 0.0115 0.3705 -0.8278 0.3808 -0.4898 0.4215 -0.7297 -0.9322 -0.9299 -0.4233 0.2834 -0.5797 -0.7969 0.0192 -0.4001 -0.0401 -0.2343 -0.8086 -0.4427
1994 -0.6005 -0.0975 -0.6942 -0.5902 -0.0880 0.3175 0.1632 0.7675 0.5207 1.0282 0.5350 0.0978 0.7515 0.6528 0.2238 0.1230 0.0881 -0.4784 0.2601 0.2429 0.1688 0.1807 0.9592 0.0418
1993 -0.6331 -0.1956 0.0405 -0.8816 -0.7516 -0.2010 -0.1611 -0.4313 0.3369 1.1248 0.4827 -0.8354 -0.7042 -0.9057 0.2060 -0.1867 0.1458 -0.7784 -0.0915 0.3305 -0.0211 -0.3948 -0.2624 -0.1793
1992 -1.4688 0.9073 3.1301 0.8338 2.5185 1.8601 0.5797 2.6687 1.9719 4.6638 1.2484 2.0706 2.6003 2.8108 1.4070 0.3997 0.9439 2.4897 1.1890 1.3518 1.0730 0.8020 3.1918 2.0749
1991 0.1202 -0.0531 -0.0162 0.0803 -0.1292 -0.2617 0.1123 -0.2343 0.1041 0.1202 0.5609 -0.2215 0.2995 0.3069 0.1439 0.1829 0.2389 1.6160 -0.0490 0.4088 0.8250 -0.1432 0.4282 2.4041
1990 0.7739 0.1974 -0.2758 -0.2005 -0.4915 -0.4294 -0.1930 -0.3400 -0.1200 -0.6279 0.4248 -0.5160 -0.3597 -0.2878 0.1752 -0.2011 0.5998 -0.2399 -0.3001 0.3875 0.4752 -0.2927 -0.4844 0.4067
1989 1.4409 -0.1443 -0.4217 -0.7657 -1.0045 -1.0412 -0.4217 -0.8033 -0.1983 -0.6299 0.4042 -0.6739 -0.4189 -0.2231 -0.0075 -0.4847 0.1006 -1.2786 -0.2707 0.0786 -0.0884 -0.3562 -0.5116 -0.9430
1988 0.0627 0.0790 -0.3464 -0.9041 -1.0201 -0.6182 -0.5480 -0.4564 -0.2100 -0.9290 0.4112 -0.8355 -0.7661 -0.8463 0.1953 -0.5956 0.2049 -0.5149 0.0899 0.2429 0.2949 -0.3993 -0.4629 -1.6034
1987 -0.0772 0.3881 -0.1524 -0.5225 0.1709 -0.6857 -0.4846 0.3772 -0.2441 0.0915 -0.7341 -0.1923 0.1421 1.1470 0.5189 -0.6089 0.6509 0.1051 -0.1116 0.5543 -0.3053 0.2307 -0.0151 1.7381
1986 0.9272 0.1445 -0.0866 -0.5388 -0.2163 -0.9456 -0.5572 -0.6548 -0.2948 -1.0206 -0.9377 -0.5081 -0.0798 -0.4386 0.3222 -0.6297 0.4495 -0.5263 -0.2200 0.2290 -1.2341 -0.6906 -0.2357 0.2041
1985 1.1131 0.0253 -0.4906 -0.5509 -0.2975 -0.9225 -0.6997 -0.6370 -0.0884 -0.3245 -1.1308 -0.7209 -0.8256 -0.9482 0.2401 -0.7110 0.2473 -0.7735 -0.4202 0.3121 -1.2059 -0.7069 -0.8015 -0.2975
1984 1.8013 0.2284 -0.5440 -0.1447 -0.4211 -0.8235 -0.6575 -0.7925 -0.1492 -0.9069 -1.1281 -0.7848 -0.6862 -0.7732 0.4834 -0.6695 0.5650 -1.0714 -0.4167 0.4992 -0.8736 -0.3715 -0.8133 -0.7442
1983 0.9502 0.0912 -0.3639 -0.6158 -0.3501 -0.8718 -0.7431 -0.8826 -0.8025 -1.1922 -1.1150 -0.4250 0.2337 -0.0468 0.4108 -0.7577 0.3113 -0.5710 -0.3989 0.3311 -1.8749 -1.9467 0.0756 -0.6873
1982 -0.9436 0.9775 0.7716 0.2479 0.9319 -0.1762 -0.6461 -0.1360 -1.8662 -0.3247 -1.1207 -0.1339 1.3616 0.7641 0.7340 -0.7842 0.7577 1.3445 -0.4060 0.5994 0.1340 0.3584 1.7261 0.3133
1981 -0.9666 0.4902 -0.6478 -0.4053 0.9247 -0.2615 -0.8484 -0.2314 -1.6397 -0.8245 -1.3230 0.5140 1.0220 1.1154 0.6691 -0.8737 0.4194 0.8998 -0.7992 0.5904 0.1163 0.3389 0.8467 -0.1124
1980 -1.2541 1.7357 1.7745 1.7795 1.6191 0.5960 -0.7116 1.6093 -1.5534 0.7996 -0.6887 1.5322 2.6049 2.8926 1.2064 -0.6855 1.1873 1.7319 -0.0972 1.1336 0.1602 0.3776 2.4082 0.2887
1979 0.9234 0.3475 -0.4153 -0.5224 0.1081 -0.8532 -0.9357 -0.0814 -0.5229 -1.0353 -1.0966 -0.1029 0.0437 -0.0171 0.4097 -0.7625 0.3251 1.0325 -0.3744 0.3936 -0.8812 -0.3848 -0.2112 2.3548
1978 0.5477 0.3268 -0.4658 -0.4173 -0.2025 -0.9164 -0.8704 -0.6012 -0.4608 -1.0767 -0.9210 -0.3823 -0.1133 -0.5651 0.3620 -0.7968 0.4289 -0.2014 -0.2075 0.4020 -1.1600 -0.8439 -0.2556 0.4952
1977 0.2065 0.4730 -0.1826 0.0941 -0.1233 -0.9184 -0.7367 -0.0390 -0.6020 -0.5310 -0.8984 0.0119 0.1358 0.2026 0.7328 -0.7439 0.6711 -0.1219 -0.1921 0.7615 -0.4529 -0.1719 -0.1456 0.0670
1976 0.9004 0.3434 -0.3918 0.7682 0.1170 -0.7074 -0.5424 -0.7441 -0.1253 -0.0578 -1.0464 -0.4098 -0.9362 0.0920 1.0475 -0.7216 0.9563 -0.6707 -0.3166 0.8140 -0.5776 -0.0814 -0.7861 -0.4623
1975 0.6972 0.1800 -0.8167 0.1120 -0.1196 -0.8904 -0.8327 -0.1215 -0.4762 -0.4726 0.3593 -0.3703 -0.2568 -0.2583 0.7316 -0.8034 0.5018 -1.0593 -0.5518 0.6697 -1.2341 -0.7069 -0.5976 -0.8553
1974 -1.2120 1.1185 1.5724 0.8716 0.7787 0.1795 -0.8420 0.6933 -1.9117 0.0430 -1.2172 0.1498 -0.1294 -0.4590 1.3863 -0.7974 1.0743 1.1988 -0.5597 1.3714 0.9767 1.0511 0.4705 0.4016
1973 -0.9628 0.4276 -0.0410 0.1087 0.2920 -0.2293 -0.9448 -0.2077 -1.0053 -0.5260 -0.9422 -0.1569 -0.8008 -0.5443 0.4898 -0.8743 0.4793 -0.7277 -0.2231 0.5532 0.1515 0.3713 -0.4173 -0.1950
1972 -0.3417 0.5028 -0.0892 0.1256 0.2009 -0.8769 -0.9136 -0.4308 -1.1777 -0.5572 -1.3502 0.0552 0.2952 -0.0647 0.4340 -0.8732 0.5752 -0.7586 -0.8786 0.4637 0.1074 0.3324 0.1065 -0.7151
1971 -1.0663 1.4514 0.7596 1.0064 1.4265 -0.1857 -0.6966 0.0646 -1.5851 -0.1682 -0.9928 0.8045 1.2418 1.5867 1.0944 -0.7248 1.0222 0.3959 -0.2643 1.1645 0.1427 0.3649 1.0996 -0.4215
1970 -0.1731 0.2830 -0.2867 0.3696 0.1652 -0.7090 -0.8112 -0.3736 -0.3142 -0.5996 0.4910 0.0731 -0.0576 0.2005 0.6857 -0.6739 0.5739 1.4645 0.1127 0.8136 -0.9955 -0.3454 -0.2405 2.7218
1969 0.5496 0.0708 -1.1229 -0.2215 -0.0224 -1.1272 -1.0123 -0.2998 0.0002 0.7823 -1.2852 -0.4108 -0.6424 -0.0993 0.4756 -0.9020 0.2522 0.0435 -0.7023 0.4398 -1.7905 -1.7240 -0.7576 0.4713
1968 0.4557 0.3754 -0.1914 0.0782 -0.0442 -1.0424 -0.8591 -0.5058 -0.0528 -0.6357 -0.8632 -0.2303 -0.0315 -0.4494 0.8054 -0.8174 0.4188 -0.1702 -0.1709 0.8400 0.1515 0.3713 -0.0779 0.1860
1967 -0.0331 0.4082 -0.1135 0.3716 0.3029 -0.8140 -0.8333 -0.3632 -0.3441 -0.6185 -0.8795 -0.0115 0.4341 -0.2016 0.5365 -0.8199 0.6325 0.4662 -0.1799 0.5568 0.1515 0.3713 0.3658 0.0823
1966 -1.3091 2.4265 1.9120 3.5159 1.7204 0.3925 -0.3358 4.0710 -1.1894 1.1428 -0.7170 1.0888 2.2487 1.3671 1.8517 -0.4379 2.4150 2.5052 -0.1059 1.8671 0.1602 0.3776 2.4620 1.4373
1965 -0.3865 0.6265 0.4303 0.2184 0.2952 -0.5675 -0.8397 -0.5385 -0.4155 0.8830 0.1583 0.2678 0.6830 0.5453 0.7177 -0.8522 0.7218 0.2577 -0.0269 0.6639 0.1688 0.3840 0.4992 -0.2566
1964 0.0761 0.2908 -0.2917 0.0262 0.8445 -0.8938 -0.9006 -0.4216 -0.4443 0.3291 -0.7933 -0.2331 0.0098 -0.4144 0.2669 -0.7975 0.4580 -0.4564 -0.1351 0.3079 -1.7992 -4.0357 -0.1313 -0.7129
1963 -0.5091 0.3587 -0.3000 0.2313 0.6458 -0.8484 -0.8979 0.2260 -0.5598 0.7006 -0.9991 -0.1602 -0.2566 -0.6252 0.3226 -0.9419 0.5258 0.0035 -0.2707 0.2862 0.1427 0.3649 -0.1694 -1.1526
1962 -1.1161 0.7858 0.1291 0.9148 0.5731 -0.5193 -0.7648 0.1396 -0.5341 0.1245 -1.0139 1.0248 0.4818 0.6698 0.7706 -0.7147 0.9169 0.3912 -0.2837 0.8386 0.1427 0.3642 0.2324 -1.1177
1961 -0.9015 0.5666 0.1987 0.3679 0.9936 -0.8241 -0.7050 0.9734 -0.6841 0.1911 -1.0430 0.0148 0.1850 -0.2893 0.4734 -0.8045 0.6152 -0.3412 -0.3133 0.3074 0.1427 0.3649 0.1296 -1.4248
1960 -1.0433 0.5102 0.4145 0.5807 0.9967 -0.7398 -0.7065 1.4128 -0.4794 1.3586 0.5110 -0.0877 -0.4572 -0.5883 0.6178 -0.6754 0.7916 0.3395 0.1253 0.5598 -0.2515 0.0197 -0.2512 2.0852
1959 -0.8593 0.4067 -0.3155 0.3043 0.1448 -0.9809 -0.7874 0.0866 -0.6011 -0.3097 -0.8248 -0.2912 -0.7388 -0.0724 0.3642 -0.7552 0.6715 -0.2708 -0.1499 0.3971 0.1515 0.3713 -0.4288 0.4693
1958 -1.3883 1.4330 0.6080 0.7613 2.0997 -0.0061 -0.8815 0.6944 -0.7064 1.4439 0.4042 0.3192 0.0227 -0.1728 1.2644 -0.7873 1.5796 0.5583 0.5341 1.2738 0.2201 0.4340 0.4769 0.8129
1957 -0.1501 0.0788 -0.6378 0.5301 -0.0052 -1.4811 -0.7726 -0.5773 -0.1142 -0.3035 0.3192 -0.3458 -0.2647 -0.3562 0.4415 -0.8422 0.7440 -1.1722 0.0219 0.2437 0.1688 0.3840 -0.4811 -0.7914
1956 -1.1660 0.9024 0.9387 -0.4486 0.7415 -0.7435 -0.9087 0.5561 -1.5628 -0.0826 3.3428 0.8977 0.0357 -0.6959 0.0996 -0.8731 0.1990 1.3175 5.4730 -0.0201 1.4525 1.4838 0.7398 0.2129
1955 -1.2810 2.6427 3.0556 1.7682 2.6251 -0.2087 -0.3884 2.1850 -1.2176 1.1117 2.8520 1.7799 2.3472 1.9516 0.9034 -0.6220 1.4277 1.9119 4.3493 1.1407 1.0612 1.1603 2.8571 0.6604
1954 -0.9513 1.7707 1.0759 -0.4117 1.8763 -0.7741 -0.9430 2.8715 -0.9605 0.0427 0.9580 0.7628 -0.5342 0.0212 -0.2429 -0.9756 0.4455 0.4704 0.5851 -0.1011 0.2286 0.4340 0.1032 -0.4706
1953 -0.7213 0.3247 0.8136 -0.1111 0.2263 -1.6928 -0.7778 0.1082 -0.5078 -0.6086 -0.8420 0.6116 0.8281 -0.0156 0.0789 -0.8039 0.2684 -0.2745 -0.1588 -0.0194 0.1515 0.3713 0.7915 -0.9210
首先，对于 23 个变量，您有大约 8,388,607 种可能的组合 (2^23 - 1)。可能你不想去那里。
你可以做的是尝试找到一种算法，让你的组合越来越好。我依靠 stepwise regression 中向后消除背后的逻辑来做到这一点。基本上，我从所有变量的行均值开始，然后一次删除每个变量，计算每个 n-1 组合的行均值和相关性，然后选择最好的一个并重新做一遍整个过程：查看所有可能的 n-2 组合，计算相关性等。您已经明白了。
现在，不能保证这可以找到最佳组合，但结果 (r = -0.76) 是一个很大的改进。
如果您尝试向前选择，看看会发生什么会很有趣。
代码如下：
vars <- data[,-1:-2] #create data frame with only the variables in it
best <- NA # stores the best correlation in any given iteration
var_names <- NULL #stores variables in the given iteration
while(ncol(vars) > 2 ){
temp_mean <- NULL #stores rowmeans
temp_cor <- NULL #stores correlations
var_names <- c(var_names, list(names(vars))) #updates list with variable names
for(i in 1:ncol(vars)){
low_vars <- vars[,-i] #drop each variable one-by-one
temp_mean <- rowMeans(low_vars[,1:ncol(low_vars)]) #calculate means
temp_cor <- c(temp_cor, cor(temp_mean, data$growth)) #calculate correlation
}
best <- c(best, min(temp_cor)) #best correlation of given iteration stored
vars <- vars[, -which.min(temp_cor)] #update vars to best combination
}
min(best, na.rm = T) #check what is the best correlation found
var_names[[which.min(best)]] #check what combination lead to it
我有一个包含 23 个元素 (Var01-Var23)、增长和年份的时间序列的矩阵 （参见下面的数据）。 然后，我想知道是哪一组化学元素阻止了我的树的生长。
当我将每个单独的元素与 growth 变量相关联时，结果非常低。但是当我计算所有元素的 mean 并将其与 growth 变量相关联时，相关性会增加。或者，当我将增长与选定元素的 mean 相关联时，相关性会增加更多（例如，Var02、Var04 和 Var09 到 Var13 的平均值）。我有几棵树的数据，然后我需要一些脚本来自动执行我的计算，因为目前我正在以手动方式进行。
# Example:
# My data
data <- read.delim("clipboard")
# Correlation with Mean of all variables (r= -0.64)
cor.test(data$growth, rowMeans(data[,3:25]))
# Correlation with Mean of seven variables (r= -0.65)
cor.test(data$growth, rowMeans(data[,c(4,6,11:15)]))
基于 PCA 和层次聚类分析，我正在计算某些元素（具有所有可能的元素组组合）的 growth 和 mean 之间的相关性。在这一点上，当我添加一个或多个元素时，我的相关性增加或减少，反之亦然。此外，我将growth与所有变量相关联，我只选择了第一个高相关元素，但这并不是我想要的。
我想知道与 growth 变量具有最高相关性的元素的精确组合。
我已经看到与 dplR 包的函数 strip.rwl() 的类似计算。此函数丢弃所有无助于改善某种相关性 (EPS) 的时间序列。此函数为您提供具有最高系列间相关性的精确变量。
类似，但我想知道给我最好的 mean 来计算与增长的最高相关性的变量的精确组合是什么？
是否已经有一个函数可以计算这个，或者你能给我一些指导吗？
数据：
year growth var01 var02 var03 var04 var05 var06 var07 var08 var09 var10 var11 var12 var13 var14 var15 var16 var17 var18 var19 var20 var21 var22 var23
2015 0.7355 -1.5093 -0.4718 0.4724 -1.2182 1.2762 2.1297 -0.3869 2.5204 0.5939 0.4910 -0.6156 -0.7688 -0.7586 -1.3430 2.0780 -1.5219 -1.2929 -0.6673 -1.2759 -1.3003 -1.1383 -1.0050 -1.0538
2014 1.0499 -1.5731 -0.8291 0.3671 -1.2009 1.2957 1.5425 -0.5630 1.3536 1.9637 0.4473 -0.5620 -0.6266 -0.6508 -1.4364 1.5605 -1.6061 -0.9849 -0.4060 -1.4001 -0.5928 -0.9355 -0.9086 -1.1744
2013 0.3023 -1.3480 -0.9086 1.0562 -1.4676 1.6038 1.6197 -0.9654 0.8675 -0.5802 0.3953 -0.6743 -1.2814 -0.9289 -1.7962 1.6508 -1.6769 -1.2483 -0.4202 -1.7725 -0.5117 -0.8456 -1.1292 -1.1822
2012 0.4691 -1.4137 -1.3467 0.8196 -0.9280 1.5524 1.6472 -0.6955 1.2168 0.3453 0.4625 -0.4587 -0.8154 -0.4288 -1.8088 1.5263 -1.5974 -1.2437 -0.6041 -1.9023 -0.4178 -0.7794 -1.0962 -1.4127
2011 1.5789 -1.3981 -0.9584 1.1080 -1.5778 1.3515 1.4592 -1.2458 1.2315 -0.8985 0.3111 -0.7732 -1.5045 -1.3703 -1.8152 1.4385 -1.5522 -1.3145 -0.5637 -1.7576 -0.8766 -1.0122 -1.5530 -1.3255
2010 1.2607 -1.3424 -0.8443 1.1052 -1.1118 1.3660 1.3892 -1.0938 1.2785 -0.9152 0.3842 -0.4285 -0.5272 -0.5904 -1.7213 1.4067 -1.4321 -0.2067 -0.3469 -1.7433 -0.1480 -0.2845 -0.7672 0.7892
2009 -0.5909 -0.7340 -0.5030 0.1297 -0.9245 1.3174 1.2938 -0.4455 1.0780 -0.5008 0.3727 -0.3743 -0.6238 -0.6003 -1.8261 1.3141 -0.9217 -0.3761 -0.4310 -1.8382 -0.3053 -0.5241 -0.7800 0.2114
2008 -0.6983 -1.1673 -0.1231 0.5825 -1.2651 1.6569 1.3955 -0.7211 0.9760 -0.7845 0.3861 0.0815 -0.3776 -0.6394 -1.7565 1.4102 -1.1523 -0.4078 -0.3300 -1.8786 -0.4062 -0.4016 -0.4600 -0.0071
2007 0.1183 -1.3682 -0.9443 -0.0971 -1.3220 1.3293 1.2750 -0.8371 1.0943 -1.0089 0.3398 -0.4498 -1.2298 -1.2716 -1.6478 1.3486 -1.3283 -0.7784 -0.2968 -1.5428 -0.1280 -0.7084 -0.9944 -0.5956
2006 0.5534 -1.2314 -0.7071 -0.7115 -1.2178 1.0437 1.1603 -0.8700 1.0272 -0.7154 0.3785 -0.7280 -0.8290 -0.7931 -1.4326 1.2680 -1.2664 -1.1744 -0.3001 -1.2794 -0.2198 -0.3347 -0.7982 -0.8576
2005 -0.1290 -0.6186 -0.7554 -0.8953 -0.7179 0.8193 1.2671 0.0563 1.1459 -0.3939 0.5788 -0.4018 -0.4051 -0.0909 -0.3482 1.1628 -0.6649 -0.5135 -0.1499 -0.5293 1.7077 1.3397 -0.5928 -0.3255
2004 -1.3960 -0.7433 3.3826 0.0168 0.6878 2.3632 2.0095 1.4930 1.1984 1.6115 0.9325 6.0082 3.4345 4.0293 -0.7450 1.8678 -1.1456 1.7131 -0.0351 -0.8672 -1.1172 0.6631 1.9708 1.3615
2003 -1.2024 -1.1421 1.4662 0.1289 -0.2702 1.5784 1.8177 0.4645 1.0738 0.3043 0.6369 0.1920 0.5853 0.6188 -0.9899 1.7807 -1.1835 0.8453 -0.3640 -0.8570 -0.2409 -0.7386 0.7062 0.1594
2002 -1.2695 -1.2228 -0.7048 -0.5232 -0.6171 1.9463 1.6148 0.2365 0.7777 1.1024 0.6519 0.3360 0.8234 0.8263 -0.7476 1.6094 -1.3752 1.7203 -0.2869 -0.9334 0.3433 0.2585 0.9249 0.3958
2001 2.2805 -2.0591 -0.8628 -3.9804 -1.5726 0.1381 0.5142 -0.6226 0.3808 -1.2949 0.7876 -0.5202 -0.4475 -0.2446 -1.7901 0.7399 -2.4933 0.4975 0.3481 -1.8721 2.6124 2.2446 -0.6788 0.8185
2000 1.2243 -0.3546 -0.3555 -0.9080 0.6723 0.7487 1.2527 0.2992 1.7156 1.4165 2.3882 -0.1943 -0.5190 -0.0279 -0.9017 1.3534 -0.8618 -0.0725 1.9422 -0.8831 2.9700 2.1966 -0.3275 0.5609
1999 1.1170 -1.0957 -0.5224 -0.9462 -0.8757 0.8819 1.2233 -0.1417 1.4077 0.3444 0.7656 -0.5936 -0.5658 -0.5246 1.7319 1.2449 -0.9524 0.1268 0.5618 1.6841 2.6959 2.1735 -0.6886 -0.0353
1998 1.5080 -0.9427 -0.5292 -1.9068 -0.9694 0.5602 0.9686 -0.5317 0.9646 -0.5927 0.5123 -0.5573 -0.6479 -0.6202 -1.2297 1.1412 -1.0400 -0.3132 -0.1830 -1.1215 2.2558 2.0275 -0.7357 -0.2513
1997 1.2109 -1.2957 -0.2941 -1.7398 -0.4912 0.4444 0.7539 -0.4458 0.7561 -0.3942 0.4130 -0.6011 -0.5307 -0.1443 -1.0119 0.8553 -1.2888 -1.1635 -0.2902 -1.0984 -0.3384 -0.7099 -0.7028 -0.6451
1996 1.9374 -0.9590 -0.5634 -1.1346 -0.8146 0.1582 0.5529 -0.7560 0.3428 -0.7315 0.3842 -0.9918 -1.1590 -0.8275 -1.0101 0.6369 -0.9615 -1.1021 -0.2902 -1.0126 -0.3163 -0.3251 -1.0070 -0.8537
1995 -0.0906 -0.6876 -0.5482 -0.7573 -0.8502 0.0115 0.3705 -0.8278 0.3808 -0.4898 0.4215 -0.7297 -0.9322 -0.9299 -0.4233 0.2834 -0.5797 -0.7969 0.0192 -0.4001 -0.0401 -0.2343 -0.8086 -0.4427
1994 -0.6005 -0.0975 -0.6942 -0.5902 -0.0880 0.3175 0.1632 0.7675 0.5207 1.0282 0.5350 0.0978 0.7515 0.6528 0.2238 0.1230 0.0881 -0.4784 0.2601 0.2429 0.1688 0.1807 0.9592 0.0418
1993 -0.6331 -0.1956 0.0405 -0.8816 -0.7516 -0.2010 -0.1611 -0.4313 0.3369 1.1248 0.4827 -0.8354 -0.7042 -0.9057 0.2060 -0.1867 0.1458 -0.7784 -0.0915 0.3305 -0.0211 -0.3948 -0.2624 -0.1793
1992 -1.4688 0.9073 3.1301 0.8338 2.5185 1.8601 0.5797 2.6687 1.9719 4.6638 1.2484 2.0706 2.6003 2.8108 1.4070 0.3997 0.9439 2.4897 1.1890 1.3518 1.0730 0.8020 3.1918 2.0749
1991 0.1202 -0.0531 -0.0162 0.0803 -0.1292 -0.2617 0.1123 -0.2343 0.1041 0.1202 0.5609 -0.2215 0.2995 0.3069 0.1439 0.1829 0.2389 1.6160 -0.0490 0.4088 0.8250 -0.1432 0.4282 2.4041
1990 0.7739 0.1974 -0.2758 -0.2005 -0.4915 -0.4294 -0.1930 -0.3400 -0.1200 -0.6279 0.4248 -0.5160 -0.3597 -0.2878 0.1752 -0.2011 0.5998 -0.2399 -0.3001 0.3875 0.4752 -0.2927 -0.4844 0.4067
1989 1.4409 -0.1443 -0.4217 -0.7657 -1.0045 -1.0412 -0.4217 -0.8033 -0.1983 -0.6299 0.4042 -0.6739 -0.4189 -0.2231 -0.0075 -0.4847 0.1006 -1.2786 -0.2707 0.0786 -0.0884 -0.3562 -0.5116 -0.9430
1988 0.0627 0.0790 -0.3464 -0.9041 -1.0201 -0.6182 -0.5480 -0.4564 -0.2100 -0.9290 0.4112 -0.8355 -0.7661 -0.8463 0.1953 -0.5956 0.2049 -0.5149 0.0899 0.2429 0.2949 -0.3993 -0.4629 -1.6034
1987 -0.0772 0.3881 -0.1524 -0.5225 0.1709 -0.6857 -0.4846 0.3772 -0.2441 0.0915 -0.7341 -0.1923 0.1421 1.1470 0.5189 -0.6089 0.6509 0.1051 -0.1116 0.5543 -0.3053 0.2307 -0.0151 1.7381
1986 0.9272 0.1445 -0.0866 -0.5388 -0.2163 -0.9456 -0.5572 -0.6548 -0.2948 -1.0206 -0.9377 -0.5081 -0.0798 -0.4386 0.3222 -0.6297 0.4495 -0.5263 -0.2200 0.2290 -1.2341 -0.6906 -0.2357 0.2041
1985 1.1131 0.0253 -0.4906 -0.5509 -0.2975 -0.9225 -0.6997 -0.6370 -0.0884 -0.3245 -1.1308 -0.7209 -0.8256 -0.9482 0.2401 -0.7110 0.2473 -0.7735 -0.4202 0.3121 -1.2059 -0.7069 -0.8015 -0.2975
1984 1.8013 0.2284 -0.5440 -0.1447 -0.4211 -0.8235 -0.6575 -0.7925 -0.1492 -0.9069 -1.1281 -0.7848 -0.6862 -0.7732 0.4834 -0.6695 0.5650 -1.0714 -0.4167 0.4992 -0.8736 -0.3715 -0.8133 -0.7442
1983 0.9502 0.0912 -0.3639 -0.6158 -0.3501 -0.8718 -0.7431 -0.8826 -0.8025 -1.1922 -1.1150 -0.4250 0.2337 -0.0468 0.4108 -0.7577 0.3113 -0.5710 -0.3989 0.3311 -1.8749 -1.9467 0.0756 -0.6873
1982 -0.9436 0.9775 0.7716 0.2479 0.9319 -0.1762 -0.6461 -0.1360 -1.8662 -0.3247 -1.1207 -0.1339 1.3616 0.7641 0.7340 -0.7842 0.7577 1.3445 -0.4060 0.5994 0.1340 0.3584 1.7261 0.3133
1981 -0.9666 0.4902 -0.6478 -0.4053 0.9247 -0.2615 -0.8484 -0.2314 -1.6397 -0.8245 -1.3230 0.5140 1.0220 1.1154 0.6691 -0.8737 0.4194 0.8998 -0.7992 0.5904 0.1163 0.3389 0.8467 -0.1124
1980 -1.2541 1.7357 1.7745 1.7795 1.6191 0.5960 -0.7116 1.6093 -1.5534 0.7996 -0.6887 1.5322 2.6049 2.8926 1.2064 -0.6855 1.1873 1.7319 -0.0972 1.1336 0.1602 0.3776 2.4082 0.2887
1979 0.9234 0.3475 -0.4153 -0.5224 0.1081 -0.8532 -0.9357 -0.0814 -0.5229 -1.0353 -1.0966 -0.1029 0.0437 -0.0171 0.4097 -0.7625 0.3251 1.0325 -0.3744 0.3936 -0.8812 -0.3848 -0.2112 2.3548
1978 0.5477 0.3268 -0.4658 -0.4173 -0.2025 -0.9164 -0.8704 -0.6012 -0.4608 -1.0767 -0.9210 -0.3823 -0.1133 -0.5651 0.3620 -0.7968 0.4289 -0.2014 -0.2075 0.4020 -1.1600 -0.8439 -0.2556 0.4952
1977 0.2065 0.4730 -0.1826 0.0941 -0.1233 -0.9184 -0.7367 -0.0390 -0.6020 -0.5310 -0.8984 0.0119 0.1358 0.2026 0.7328 -0.7439 0.6711 -0.1219 -0.1921 0.7615 -0.4529 -0.1719 -0.1456 0.0670
1976 0.9004 0.3434 -0.3918 0.7682 0.1170 -0.7074 -0.5424 -0.7441 -0.1253 -0.0578 -1.0464 -0.4098 -0.9362 0.0920 1.0475 -0.7216 0.9563 -0.6707 -0.3166 0.8140 -0.5776 -0.0814 -0.7861 -0.4623
1975 0.6972 0.1800 -0.8167 0.1120 -0.1196 -0.8904 -0.8327 -0.1215 -0.4762 -0.4726 0.3593 -0.3703 -0.2568 -0.2583 0.7316 -0.8034 0.5018 -1.0593 -0.5518 0.6697 -1.2341 -0.7069 -0.5976 -0.8553
1974 -1.2120 1.1185 1.5724 0.8716 0.7787 0.1795 -0.8420 0.6933 -1.9117 0.0430 -1.2172 0.1498 -0.1294 -0.4590 1.3863 -0.7974 1.0743 1.1988 -0.5597 1.3714 0.9767 1.0511 0.4705 0.4016
1973 -0.9628 0.4276 -0.0410 0.1087 0.2920 -0.2293 -0.9448 -0.2077 -1.0053 -0.5260 -0.9422 -0.1569 -0.8008 -0.5443 0.4898 -0.8743 0.4793 -0.7277 -0.2231 0.5532 0.1515 0.3713 -0.4173 -0.1950
1972 -0.3417 0.5028 -0.0892 0.1256 0.2009 -0.8769 -0.9136 -0.4308 -1.1777 -0.5572 -1.3502 0.0552 0.2952 -0.0647 0.4340 -0.8732 0.5752 -0.7586 -0.8786 0.4637 0.1074 0.3324 0.1065 -0.7151
1971 -1.0663 1.4514 0.7596 1.0064 1.4265 -0.1857 -0.6966 0.0646 -1.5851 -0.1682 -0.9928 0.8045 1.2418 1.5867 1.0944 -0.7248 1.0222 0.3959 -0.2643 1.1645 0.1427 0.3649 1.0996 -0.4215
1970 -0.1731 0.2830 -0.2867 0.3696 0.1652 -0.7090 -0.8112 -0.3736 -0.3142 -0.5996 0.4910 0.0731 -0.0576 0.2005 0.6857 -0.6739 0.5739 1.4645 0.1127 0.8136 -0.9955 -0.3454 -0.2405 2.7218
1969 0.5496 0.0708 -1.1229 -0.2215 -0.0224 -1.1272 -1.0123 -0.2998 0.0002 0.7823 -1.2852 -0.4108 -0.6424 -0.0993 0.4756 -0.9020 0.2522 0.0435 -0.7023 0.4398 -1.7905 -1.7240 -0.7576 0.4713
1968 0.4557 0.3754 -0.1914 0.0782 -0.0442 -1.0424 -0.8591 -0.5058 -0.0528 -0.6357 -0.8632 -0.2303 -0.0315 -0.4494 0.8054 -0.8174 0.4188 -0.1702 -0.1709 0.8400 0.1515 0.3713 -0.0779 0.1860
1967 -0.0331 0.4082 -0.1135 0.3716 0.3029 -0.8140 -0.8333 -0.3632 -0.3441 -0.6185 -0.8795 -0.0115 0.4341 -0.2016 0.5365 -0.8199 0.6325 0.4662 -0.1799 0.5568 0.1515 0.3713 0.3658 0.0823
1966 -1.3091 2.4265 1.9120 3.5159 1.7204 0.3925 -0.3358 4.0710 -1.1894 1.1428 -0.7170 1.0888 2.2487 1.3671 1.8517 -0.4379 2.4150 2.5052 -0.1059 1.8671 0.1602 0.3776 2.4620 1.4373
1965 -0.3865 0.6265 0.4303 0.2184 0.2952 -0.5675 -0.8397 -0.5385 -0.4155 0.8830 0.1583 0.2678 0.6830 0.5453 0.7177 -0.8522 0.7218 0.2577 -0.0269 0.6639 0.1688 0.3840 0.4992 -0.2566
1964 0.0761 0.2908 -0.2917 0.0262 0.8445 -0.8938 -0.9006 -0.4216 -0.4443 0.3291 -0.7933 -0.2331 0.0098 -0.4144 0.2669 -0.7975 0.4580 -0.4564 -0.1351 0.3079 -1.7992 -4.0357 -0.1313 -0.7129
1963 -0.5091 0.3587 -0.3000 0.2313 0.6458 -0.8484 -0.8979 0.2260 -0.5598 0.7006 -0.9991 -0.1602 -0.2566 -0.6252 0.3226 -0.9419 0.5258 0.0035 -0.2707 0.2862 0.1427 0.3649 -0.1694 -1.1526
1962 -1.1161 0.7858 0.1291 0.9148 0.5731 -0.5193 -0.7648 0.1396 -0.5341 0.1245 -1.0139 1.0248 0.4818 0.6698 0.7706 -0.7147 0.9169 0.3912 -0.2837 0.8386 0.1427 0.3642 0.2324 -1.1177
1961 -0.9015 0.5666 0.1987 0.3679 0.9936 -0.8241 -0.7050 0.9734 -0.6841 0.1911 -1.0430 0.0148 0.1850 -0.2893 0.4734 -0.8045 0.6152 -0.3412 -0.3133 0.3074 0.1427 0.3649 0.1296 -1.4248
1960 -1.0433 0.5102 0.4145 0.5807 0.9967 -0.7398 -0.7065 1.4128 -0.4794 1.3586 0.5110 -0.0877 -0.4572 -0.5883 0.6178 -0.6754 0.7916 0.3395 0.1253 0.5598 -0.2515 0.0197 -0.2512 2.0852
1959 -0.8593 0.4067 -0.3155 0.3043 0.1448 -0.9809 -0.7874 0.0866 -0.6011 -0.3097 -0.8248 -0.2912 -0.7388 -0.0724 0.3642 -0.7552 0.6715 -0.2708 -0.1499 0.3971 0.1515 0.3713 -0.4288 0.4693
1958 -1.3883 1.4330 0.6080 0.7613 2.0997 -0.0061 -0.8815 0.6944 -0.7064 1.4439 0.4042 0.3192 0.0227 -0.1728 1.2644 -0.7873 1.5796 0.5583 0.5341 1.2738 0.2201 0.4340 0.4769 0.8129
1957 -0.1501 0.0788 -0.6378 0.5301 -0.0052 -1.4811 -0.7726 -0.5773 -0.1142 -0.3035 0.3192 -0.3458 -0.2647 -0.3562 0.4415 -0.8422 0.7440 -1.1722 0.0219 0.2437 0.1688 0.3840 -0.4811 -0.7914
1956 -1.1660 0.9024 0.9387 -0.4486 0.7415 -0.7435 -0.9087 0.5561 -1.5628 -0.0826 3.3428 0.8977 0.0357 -0.6959 0.0996 -0.8731 0.1990 1.3175 5.4730 -0.0201 1.4525 1.4838 0.7398 0.2129
1955 -1.2810 2.6427 3.0556 1.7682 2.6251 -0.2087 -0.3884 2.1850 -1.2176 1.1117 2.8520 1.7799 2.3472 1.9516 0.9034 -0.6220 1.4277 1.9119 4.3493 1.1407 1.0612 1.1603 2.8571 0.6604
1954 -0.9513 1.7707 1.0759 -0.4117 1.8763 -0.7741 -0.9430 2.8715 -0.9605 0.0427 0.9580 0.7628 -0.5342 0.0212 -0.2429 -0.9756 0.4455 0.4704 0.5851 -0.1011 0.2286 0.4340 0.1032 -0.4706
1953 -0.7213 0.3247 0.8136 -0.1111 0.2263 -1.6928 -0.7778 0.1082 -0.5078 -0.6086 -0.8420 0.6116 0.8281 -0.0156 0.0789 -0.8039 0.2684 -0.2745 -0.1588 -0.0194 0.1515 0.3713 0.7915 -0.9210
首先，对于 23 个变量，您有大约 8,388,607 种可能的组合 (2^23 - 1)。可能你不想去那里。
你可以做的是尝试找到一种算法，让你的组合越来越好。我依靠 stepwise regression 中向后消除背后的逻辑来做到这一点。基本上，我从所有变量的行均值开始，然后一次删除每个变量，计算每个 n-1 组合的行均值和相关性，然后选择最好的一个并重新做一遍整个过程：查看所有可能的 n-2 组合，计算相关性等。您已经明白了。
现在，不能保证这可以找到最佳组合，但结果 (r = -0.76) 是一个很大的改进。
如果您尝试向前选择，看看会发生什么会很有趣。
代码如下：
vars <- data[,-1:-2] #create data frame with only the variables in it
best <- NA # stores the best correlation in any given iteration
var_names <- NULL #stores variables in the given iteration
while(ncol(vars) > 2 ){
temp_mean <- NULL #stores rowmeans
temp_cor <- NULL #stores correlations
var_names <- c(var_names, list(names(vars))) #updates list with variable names
for(i in 1:ncol(vars)){
low_vars <- vars[,-i] #drop each variable one-by-one
temp_mean <- rowMeans(low_vars[,1:ncol(low_vars)]) #calculate means
temp_cor <- c(temp_cor, cor(temp_mean, data$growth)) #calculate correlation
}
best <- c(best, min(temp_cor)) #best correlation of given iteration stored
vars <- vars[, -which.min(temp_cor)] #update vars to best combination
}
min(best, na.rm = T) #check what is the best correlation found
var_names[[which.min(best)]] #check what combination lead to it