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變量選擇，使用 glmmLasso 包中的 glmmLasso() 函數處理多重共線性

[英]Variable Selection, dealing with multicollinearity using glmmLasso() function from glmmLasso package

 原文  2020-08-29 08:48:55  9   1    r

問題描述

我基本上要做的是用其他變量預測“度數”，ID 是隨機效應。

E0 到 E5 都是問卷的項目，它們之間似乎有一些重疊。 我懷疑最好放棄一個或另一個或找到其他方法來處理多重共線性（=因此用套索來幫助選擇變量）。 請幫助我使用glmmLasso包中的glmmLasso()函數。

這是我的數據

structure(list(ID = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 
3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 
6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 
10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 
12, 14, 14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 15, 15, 15, 
15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 
18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 
20), Age = c(23, 23, 23, 23, 23, 23, 20, 20, 20, 20, 20, 20, 
22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 21, 21, 21, 21, 
21, 21, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 24, 24, 
24, 24, 24, 24, 22, 22, 22, 22, 22, 22, 20, 20, 20, 20, 20, 20, 
20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 20, 20, 20, 20, 
20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 19, 19, 
19, 19, 19, 19, 22, 22, 22, 22, 22, 22, 32, 32, 32, 32, 32, 32, 
21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21), Gender = c("female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"male", "male", "male", "male", "male", "male", "female", "female", 
"female", "female", "female", "female", "male", "male", "male", 
"male", "male", "male", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"male", "male", "male", "male", "male", "male", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female"), Order = c(0, 
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 
1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 
0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 
1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1), Condition = c("Synch", 
"Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", 
"Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", 
"Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", 
"Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", 
"Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", 
"Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", 
"Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", 
"Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", 
"Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", 
"Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", 
"Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", 
"Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", 
"Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", 
"Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", 
"Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", 
"Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", 
"Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch"
), Repetition = c(1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3
), Degrees = c(40.1, 41.9, 43.1, 40.4, 41.9, 43.3, 34.8, 35.4, 
36.3, 35.5, 39.3, 39.9, 43.9, 45.7, 46.5, 42.9, 45.8, 46, 47.4, 
49, 49.5, 47.5, 49.1, 50.1, 45.2, 46.6, 46.7, 45.1, 47.5, 48.3, 
44.7, 46.6, 47.2, 45.9, 48.1, 48.8, 41.3, 43, 44.3, 41.7, 43.3, 
45.4, 36.7, 37.4, 37, 34.5, 35, 35.8, 42.3, 44.8, 45.5, 44.1, 
44, 46, 34.7, 35.8, 36.4, 35, 38.5, 38.1, 42.4, 45.4, 46.6, 46.7, 
48.9, 49.3, 37.1, 39.4, 41.4, 35.4, 36.9, 37.5, 45.7, 49.1, 49.8, 
45.2, 48, 49.2, 43.4, 43.9, 46.7, 42.3, 42.3, 44.2, 43.1, 46.2, 
46.8, 42.2, 44.5, 46.4, 43.7, 45.7, 46.2, 42.6, 44.4, 44.9, 33.8, 
35.7, 36.6, 40, 42.8, 44.8, 40.4, 42.2, 41.2, 42.5, 44.5, 45.8, 
36.5, 37.5, 37.2, 39.4, 39.7, 40.1, 36.9, 38.8, 40.5, 36.5, 37.4, 
37.2), E0 = c(0.0768868, 0.0768868, 0.0768868, 0.2271815, 0.2271815, 
0.2271815, 0.03119651, 0.03119651, 0.03119651, 0.02528191, 0.02528191, 
0.02528191, 0.3195968, 0.3195968, 0.3195968, 0.8617448, 0.8617448, 
0.8617448, 0.016712, 0.016712, 0.016712, 0.192138, 0.192138, 
0.192138, 0.5702031, 0.5702031, 0.5702031, 0.6742166, 0.6742166, 
0.6742166, 0.5429105, 0.5429105, 0.5429105, 0.6398613, 0.6398613, 
0.6398613, 0.131432, 0.131432, 0.131432, 0.3017955, 0.3017955, 
0.3017955, 0.3942284, 0.3942284, 0.3942284, 0.639801, 0.639801, 
0.639801, 0.03173056, 0.03173056, 0.03173056, 0.6359394, 0.6359394, 
0.6359394, 0.04259072, 0.04259072, 0.04259072, 0.4833971, 0.4833971, 
0.4833971, 0.08142848, 0.08142848, 0.08142848, 0.6650531, 0.6650531, 
0.6650531, 0.5650839, 0.5650839, 0.5650839, 0.7032156, 0.7032156, 
0.7032156, 0.320466, 0.320466, 0.320466, 0.640702, 0.640702, 
0.640702, 0.6469789, 0.6469789, 0.6469789, 0.1677248, 0.1677248, 
0.1677248, 0.3414678, 0.3414678, 0.3414678, 0.8929449, 0.8929449, 
0.8929449, 0.01605268, 0.01605268, 0.01605268, 0.294402, 0.294402, 
0.294402, 0.2365988, 0.2365988, 0.2365988, 0.8268939, 0.8268939, 
0.8268939, 0.06308042, 0.06308042, 0.06308042, 0.1803928, 0.1803928, 
0.1803928, 0.2218148, 0.2218148, 0.2218148, 0.6628052, 0.6628052, 
0.6628052, 0.3121818, 0.3121818, 0.3121818, 0.6094786, 0.6094786, 
0.6094786), E1 = c(0.01999379, 0.01999379, 0.01999379, 0.1853924, 
0.1853924, 0.1853924, 0.02456413, 0.02456413, 0.02456413, 0.2393895, 
0.2393895, 0.2393895, 0.5738584, 0.5738584, 0.5738584, 0.07511263, 
0.07511263, 0.07511263, 0.03833967, 0.03833967, 0.03833967, 0.2184013, 
0.2184013, 0.2184013, 0.6612324, 0.6612324, 0.6612324, 0.8205952, 
0.8205952, 0.8205952, 0.4550764, 0.4550764, 0.4550764, 0.6707836, 
0.6707836, 0.6707836, 0.1181969, 0.1181969, 0.1181969, 0.335041, 
0.335041, 0.335041, 0.1621491, 0.1621491, 0.1621491, 0.621815, 
0.621815, 0.621815, 0.02165118, 0.02165118, 0.02165118, 0.7052947, 
0.7052947, 0.7052947, 0.09274998, 0.09274998, 0.09274998, 0.3174826, 
0.3174826, 0.3174826, 0.06511536, 0.06511536, 0.06511536, 0.3064937, 
0.3064937, 0.3064937, 0.3812979, 0.3812979, 0.3812979, 0.7456663, 
0.7456663, 0.7456663, 0.2002029, 0.2002029, 0.2002029, 0.5376665, 
0.5376665, 0.5376665, 0.6580499, 0.6580499, 0.6580499, 0.133816, 
0.133816, 0.133816, 0.2279951, 0.2279951, 0.2279951, 0.9042466, 
0.9042466, 0.9042466, 0.0306675, 0.0306675, 0.0306675, 0.2003181, 
0.2003181, 0.2003181, 0.5605861, 0.5605861, 0.5605861, 0.8692495, 
0.8692495, 0.8692495, 0.06655293, 0.06655293, 0.06655293, 0.2035956, 
0.2035956, 0.2035956, 0.4324917, 0.4324917, 0.4324917, 0.7667023, 
0.7667023, 0.7667023, 0.342127, 0.342127, 0.342127, 0.622084, 
0.622084, 0.622084), E2 = c(0.02998782, 0.02998782, 0.02998782, 
0.4065087, 0.4065087, 0.4065087, 0.01831246, 0.01831246, 0.01831246, 
0.01373025, 0.01373025, 0.01373025, 0.04794903, 0.04794903, 0.04794903, 
0.710304, 0.710304, 0.710304, 0.01402579, 0.01402579, 0.01402579, 
0.0208993, 0.0208993, 0.0208993, 0.3167048, 0.3167048, 0.3167048, 
0.8881705, 0.8881705, 0.8881705, 0.6375082, 0.6375082, 0.6375082, 
0.7259912, 0.7259912, 0.7259912, 0.3311014, 0.3311014, 0.3311014, 
0.6063731, 0.6063731, 0.6063731, 0.2870846, 0.2870846, 0.2870846, 
0.8522398, 0.8522398, 0.8522398, 0.02177463, 0.02177463, 0.02177463, 
0.1213144, 0.1213144, 0.1213144, 0.1349742, 0.1349742, 0.1349742, 
0.7028073, 0.7028073, 0.7028073, 0.6833739, 0.6833739, 0.6833739, 
0.9032798, 0.9032798, 0.9032798, 0.7020537, 0.7020537, 0.7020537, 
0.926264, 0.926264, 0.926264, 0.383186, 0.383186, 0.383186, 0.4550786, 
0.4550786, 0.4550786, 0.756362, 0.756362, 0.756362, 0.6544293, 
0.6544293, 0.6544293, 0.2980719, 0.2980719, 0.2980719, 0.8489144, 
0.8489144, 0.8489144, 0.02421351, 0.02421351, 0.02421351, 0.2058944, 
0.2058944, 0.2058944, 0.6240092, 0.6240092, 0.6240092, 0.9023253, 
0.9023253, 0.9023253, 0.06995097, 0.06995097, 0.06995097, 0.03501845, 
0.03501845, 0.03501845, 0.04382497, 0.04382497, 0.04382497, 0.3723554, 
0.3723554, 0.3723554, 0.4634022, 0.4634022, 0.4634022, 0.525814, 
0.525814, 0.525814), E3 = c(0.01915932, 0.01915932, 0.01915932, 
0.5782945, 0.5782945, 0.5782945, 0.02180086, 0.02180086, 0.02180086, 
0.00840865, 0.00840865, 0.00840865, 0.06862031, 0.06862031, 0.06862031, 
0.2257261, 0.2257261, 0.2257261, 0.01627846, 0.01627846, 0.01627846, 
0.00919124, 0.00919124, 0.00919124, 0.07538968, 0.07538968, 0.07538968, 
0.7273877, 0.7273877, 0.7273877, 0.5896595, 0.5896595, 0.5896595, 
0.6200206, 0.6200206, 0.6200206, 0.433723, 0.433723, 0.433723, 
0.6501525, 0.6501525, 0.6501525, 0.02401429, 0.02401429, 0.02401429, 
0.1286855, 0.1286855, 0.1286855, 0.02497416, 0.02497416, 0.02497416, 
0.08344417, 0.08344417, 0.08344417, 0.1233322, 0.1233322, 0.1233322, 
0.4747348, 0.4747348, 0.4747348, 0.9421821, 0.9421821, 0.9421821, 
0.978715, 0.978715, 0.978715, 0.6047539, 0.6047539, 0.6047539, 
0.9446791, 0.9446791, 0.9446791, 0.6467746, 0.6467746, 0.6467746, 
0.9648757, 0.9648757, 0.9648757, 0.3449726, 0.3449726, 0.3449726, 
0.247598, 0.247598, 0.247598, 0.277001, 0.277001, 0.277001, 0.7794862, 
0.7794862, 0.7794862, 0.02448922, 0.02448922, 0.02448922, 0.1051826, 
0.1051826, 0.1051826, 0.6608064, 0.6608064, 0.6608064, 0.9313511, 
0.9313511, 0.9313511, 0.2042655, 0.2042655, 0.2042655, 0.3983715, 
0.3983715, 0.3983715, 0.1561849, 0.1561849, 0.1561849, 0.4790193, 
0.4790193, 0.4790193, 0.2808366, 0.2808366, 0.2808366, 0.3224252, 
0.3224252, 0.3224252), E4 = c(0.9847589, 0.9847589, 0.9847589, 
0.7891661, 0.7891661, 0.7891661, 0.6799378, 0.6799378, 0.6799378, 
0.1813519, 0.1813519, 0.1813519, 0.947698, 0.947698, 0.947698, 
0.2316942, 0.2316942, 0.2316942, 0.9853715, 0.9853715, 0.9853715, 
0.856954, 0.856954, 0.856954, 0.972347, 0.972347, 0.972347, 0.6260341, 
0.6260341, 0.6260341, 0.7341723, 0.7341723, 0.7341723, 0.5199851, 
0.5199851, 0.5199851, 0.4800602, 0.4800602, 0.4800602, 0.4135151, 
0.4135151, 0.4135151, 0.9886117, 0.9886117, 0.9886117, 0.3622957, 
0.3622957, 0.3622957, 0.9717241, 0.9717241, 0.9717241, 0.3430836, 
0.3430836, 0.3430836, 0.6693761, 0.6693761, 0.6693761, 0.2278465, 
0.2278465, 0.2278465, 0.9591872, 0.9591872, 0.9591872, 0.02147499, 
0.02147499, 0.02147499, 0.8326513, 0.8326513, 0.8326513, 0.4311295, 
0.4311295, 0.4311295, 0.9624056, 0.9624056, 0.9624056, 0.3675235, 
0.3675235, 0.3675235, 0.8383142, 0.8383142, 0.8383142, 0.8542646, 
0.8542646, 0.8542646, 0.7963936, 0.7963936, 0.7963936, 0.8244256, 
0.8244256, 0.8244256, 0.9263281, 0.9263281, 0.9263281, 0.6535487, 
0.6535487, 0.6535487, 0.6641843, 0.6641843, 0.6641843, 0.5970008, 
0.5970008, 0.5970008, 0.9235346, 0.9235346, 0.9235346, 0.746903, 
0.746903, 0.746903, 0.8027389, 0.8027389, 0.8027389, 0.6307229, 
0.6307229, 0.6307229, 0.6779547, 0.6779547, 0.6779547, 0.7031775, 
0.7031775, 0.7031775), E5 = c(0.01855536, 0.01855536, 0.01855536, 
0.02507306, 0.02507306, 0.02507306, 0.02327319, 0.02327319, 0.02327319, 
0.03142696, 0.03142696, 0.03142696, 0.04486647, 0.04486647, 0.04486647, 
0.5009657, 0.5009657, 0.5009657, 0.01553736, 0.01553736, 0.01553736, 
0.1872279, 0.1872279, 0.1872279, 0.04081627, 0.04081627, 0.04081627, 
0.1493435, 0.1493435, 0.1493435, 0.3854077, 0.3854077, 0.3854077, 
0.5490297, 0.5490297, 0.5490297, 0.2929604, 0.2929604, 0.2929604, 
0.2464589, 0.2464589, 0.2464589, 0.1885217, 0.1885217, 0.1885217, 
0.3307694, 0.3307694, 0.3307694, 0.03378974, 0.03378974, 0.03378974, 
0.05832682, 0.05832682, 0.05832682, 0.2188185, 0.2188185, 0.2188185, 
0.2639117, 0.2639117, 0.2639117, 0.07256842, 0.07256842, 0.07256842, 
0.8385035, 0.8385035, 0.8385035, 0.1420448, 0.1420448, 0.1420448, 
0.2386608, 0.2386608, 0.2386608, 0.2327594, 0.2327594, 0.2327594, 
0.6836823, 0.6836823, 0.6836823, 0.01668616, 0.01668616, 0.01668616, 
0.06372214, 0.06372214, 0.06372214, 0.2240552, 0.2240552, 0.2240552, 
0.4487696, 0.4487696, 0.4487696, 0.01916614, 0.01916614, 0.01916614, 
0.1628296, 0.1628296, 0.1628296, 0.218945, 0.218945, 0.218945, 
0.8990987, 0.8990987, 0.8990987, 0.06771775, 0.06771775, 0.06771775, 
0.1452569, 0.1452569, 0.1452569, 0.1618602, 0.1618602, 0.1618602, 
0.3947573, 0.3947573, 0.3947573, 0.2672102, 0.2672102, 0.2672102, 
0.3518078, 0.3518078, 0.3518078)), row.names = c(NA, -120L), class = c("tbl_df", 
"tbl", "data.frame"))

1 個解決方案

解決方案1
 1 已采納  2020-08-29 11:08:50

對於您的數據，我已運行以下代碼

library(glmmLasso)

str(df) #To see the variable types (numeric, character, factor etc.) 

#Fit the model
lm <- glmmLasso(Degrees ~ Age + as.factor(Gender) + Order +
          as.factor(Condition) + Repetition + 
          E0 + E1 + E2 + E3 + E4 + E5, 
          rnd= list(ID=~1),#Taking ID as the random effect
          data = df, lambda=100, final.re=TRUE,
          control = list(print.iter=TRUE,print.iter.final=TRUE))

#To see the summary of the model
summary(lm)

從總結中可以說，重要的變量可以作為重要變量保留。

數據

df <-structure(list(ID = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 
3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 
6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 
10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 
12, 14, 14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 15, 15, 15, 
15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 
18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 
20), Age = c(23, 23, 23, 23, 23, 23, 20, 20, 20, 20, 20, 20, 
22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 21, 21, 21, 21, 
21, 21, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 24, 24, 
24, 24, 24, 24, 22, 22, 22, 22, 22, 22, 20, 20, 20, 20, 20, 20, 
20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 20, 20, 20, 20, 
20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 19, 19, 
19, 19, 19, 19, 22, 22, 22, 22, 22, 22, 32, 32, 32, 32, 32, 32, 
21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21), Gender = c("female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"male", "male", "male", "male", "male", "male", "female", "female", 
"female", "female", "female", "female", "male", "male", "male", 
"male", "male", "male", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"male", "male", "male", "male", "male", "male", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female", "female", "female", 
"female", "female", "female", "female", "female"), Order = c(0, 
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 
1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 
0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 
1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1), Condition = c("Synch", 
"Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", 
"Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", 
"Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", 
"Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", 
"Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", 
"Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", 
"Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", 
"Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", 
"Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", 
"Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", 
"Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", 
"Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", 
"Synch", "Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", 
"Synch", "Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", 
"Asynch", "Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", 
"Asynch", "Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", 
"Asynch", "Synch", "Synch", "Synch", "Asynch", "Asynch", "Asynch"
), Repetition = c(1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3
), Degrees = c(40.1, 41.9, 43.1, 40.4, 41.9, 43.3, 34.8, 35.4, 
36.3, 35.5, 39.3, 39.9, 43.9, 45.7, 46.5, 42.9, 45.8, 46, 47.4, 
49, 49.5, 47.5, 49.1, 50.1, 45.2, 46.6, 46.7, 45.1, 47.5, 48.3, 
44.7, 46.6, 47.2, 45.9, 48.1, 48.8, 41.3, 43, 44.3, 41.7, 43.3, 
45.4, 36.7, 37.4, 37, 34.5, 35, 35.8, 42.3, 44.8, 45.5, 44.1, 
44, 46, 34.7, 35.8, 36.4, 35, 38.5, 38.1, 42.4, 45.4, 46.6, 46.7, 
48.9, 49.3, 37.1, 39.4, 41.4, 35.4, 36.9, 37.5, 45.7, 49.1, 49.8, 
45.2, 48, 49.2, 43.4, 43.9, 46.7, 42.3, 42.3, 44.2, 43.1, 46.2, 
46.8, 42.2, 44.5, 46.4, 43.7, 45.7, 46.2, 42.6, 44.4, 44.9, 33.8, 
35.7, 36.6, 40, 42.8, 44.8, 40.4, 42.2, 41.2, 42.5, 44.5, 45.8, 
36.5, 37.5, 37.2, 39.4, 39.7, 40.1, 36.9, 38.8, 40.5, 36.5, 37.4, 
37.2), E0 = c(0.0768868, 0.0768868, 0.0768868, 0.2271815, 0.2271815, 
0.2271815, 0.03119651, 0.03119651, 0.03119651, 0.02528191, 0.02528191, 
0.02528191, 0.3195968, 0.3195968, 0.3195968, 0.8617448, 0.8617448, 
0.8617448, 0.016712, 0.016712, 0.016712, 0.192138, 0.192138, 
0.192138, 0.5702031, 0.5702031, 0.5702031, 0.6742166, 0.6742166, 
0.6742166, 0.5429105, 0.5429105, 0.5429105, 0.6398613, 0.6398613, 
0.6398613, 0.131432, 0.131432, 0.131432, 0.3017955, 0.3017955, 
0.3017955, 0.3942284, 0.3942284, 0.3942284, 0.639801, 0.639801, 
0.639801, 0.03173056, 0.03173056, 0.03173056, 0.6359394, 0.6359394, 
0.6359394, 0.04259072, 0.04259072, 0.04259072, 0.4833971, 0.4833971, 
0.4833971, 0.08142848, 0.08142848, 0.08142848, 0.6650531, 0.6650531, 
0.6650531, 0.5650839, 0.5650839, 0.5650839, 0.7032156, 0.7032156, 
0.7032156, 0.320466, 0.320466, 0.320466, 0.640702, 0.640702, 
0.640702, 0.6469789, 0.6469789, 0.6469789, 0.1677248, 0.1677248, 
0.1677248, 0.3414678, 0.3414678, 0.3414678, 0.8929449, 0.8929449, 
0.8929449, 0.01605268, 0.01605268, 0.01605268, 0.294402, 0.294402, 
0.294402, 0.2365988, 0.2365988, 0.2365988, 0.8268939, 0.8268939, 
0.8268939, 0.06308042, 0.06308042, 0.06308042, 0.1803928, 0.1803928, 
0.1803928, 0.2218148, 0.2218148, 0.2218148, 0.6628052, 0.6628052, 
0.6628052, 0.3121818, 0.3121818, 0.3121818, 0.6094786, 0.6094786, 
0.6094786), E1 = c(0.01999379, 0.01999379, 0.01999379, 0.1853924, 
0.1853924, 0.1853924, 0.02456413, 0.02456413, 0.02456413, 0.2393895, 
0.2393895, 0.2393895, 0.5738584, 0.5738584, 0.5738584, 0.07511263, 
0.07511263, 0.07511263, 0.03833967, 0.03833967, 0.03833967, 0.2184013, 
0.2184013, 0.2184013, 0.6612324, 0.6612324, 0.6612324, 0.8205952, 
0.8205952, 0.8205952, 0.4550764, 0.4550764, 0.4550764, 0.6707836, 
0.6707836, 0.6707836, 0.1181969, 0.1181969, 0.1181969, 0.335041, 
0.335041, 0.335041, 0.1621491, 0.1621491, 0.1621491, 0.621815, 
0.621815, 0.621815, 0.02165118, 0.02165118, 0.02165118, 0.7052947, 
0.7052947, 0.7052947, 0.09274998, 0.09274998, 0.09274998, 0.3174826, 
0.3174826, 0.3174826, 0.06511536, 0.06511536, 0.06511536, 0.3064937, 
0.3064937, 0.3064937, 0.3812979, 0.3812979, 0.3812979, 0.7456663, 
0.7456663, 0.7456663, 0.2002029, 0.2002029, 0.2002029, 0.5376665, 
0.5376665, 0.5376665, 0.6580499, 0.6580499, 0.6580499, 0.133816, 
0.133816, 0.133816, 0.2279951, 0.2279951, 0.2279951, 0.9042466, 
0.9042466, 0.9042466, 0.0306675, 0.0306675, 0.0306675, 0.2003181, 
0.2003181, 0.2003181, 0.5605861, 0.5605861, 0.5605861, 0.8692495, 
0.8692495, 0.8692495, 0.06655293, 0.06655293, 0.06655293, 0.2035956, 
0.2035956, 0.2035956, 0.4324917, 0.4324917, 0.4324917, 0.7667023, 
0.7667023, 0.7667023, 0.342127, 0.342127, 0.342127, 0.622084, 
0.622084, 0.622084), E2 = c(0.02998782, 0.02998782, 0.02998782, 
0.4065087, 0.4065087, 0.4065087, 0.01831246, 0.01831246, 0.01831246, 
0.01373025, 0.01373025, 0.01373025, 0.04794903, 0.04794903, 0.04794903, 
0.710304, 0.710304, 0.710304, 0.01402579, 0.01402579, 0.01402579, 
0.0208993, 0.0208993, 0.0208993, 0.3167048, 0.3167048, 0.3167048, 
0.8881705, 0.8881705, 0.8881705, 0.6375082, 0.6375082, 0.6375082, 
0.7259912, 0.7259912, 0.7259912, 0.3311014, 0.3311014, 0.3311014, 
0.6063731, 0.6063731, 0.6063731, 0.2870846, 0.2870846, 0.2870846, 
0.8522398, 0.8522398, 0.8522398, 0.02177463, 0.02177463, 0.02177463, 
0.1213144, 0.1213144, 0.1213144, 0.1349742, 0.1349742, 0.1349742, 
0.7028073, 0.7028073, 0.7028073, 0.6833739, 0.6833739, 0.6833739, 
0.9032798, 0.9032798, 0.9032798, 0.7020537, 0.7020537, 0.7020537, 
0.926264, 0.926264, 0.926264, 0.383186, 0.383186, 0.383186, 0.4550786, 
0.4550786, 0.4550786, 0.756362, 0.756362, 0.756362, 0.6544293, 
0.6544293, 0.6544293, 0.2980719, 0.2980719, 0.2980719, 0.8489144, 
0.8489144, 0.8489144, 0.02421351, 0.02421351, 0.02421351, 0.2058944, 
0.2058944, 0.2058944, 0.6240092, 0.6240092, 0.6240092, 0.9023253, 
0.9023253, 0.9023253, 0.06995097, 0.06995097, 0.06995097, 0.03501845, 
0.03501845, 0.03501845, 0.04382497, 0.04382497, 0.04382497, 0.3723554, 
0.3723554, 0.3723554, 0.4634022, 0.4634022, 0.4634022, 0.525814, 
0.525814, 0.525814), E3 = c(0.01915932, 0.01915932, 0.01915932, 
0.5782945, 0.5782945, 0.5782945, 0.02180086, 0.02180086, 0.02180086, 
0.00840865, 0.00840865, 0.00840865, 0.06862031, 0.06862031, 0.06862031, 
0.2257261, 0.2257261, 0.2257261, 0.01627846, 0.01627846, 0.01627846, 
0.00919124, 0.00919124, 0.00919124, 0.07538968, 0.07538968, 0.07538968, 
0.7273877, 0.7273877, 0.7273877, 0.5896595, 0.5896595, 0.5896595, 
0.6200206, 0.6200206, 0.6200206, 0.433723, 0.433723, 0.433723, 
0.6501525, 0.6501525, 0.6501525, 0.02401429, 0.02401429, 0.02401429, 
0.1286855, 0.1286855, 0.1286855, 0.02497416, 0.02497416, 0.02497416, 
0.08344417, 0.08344417, 0.08344417, 0.1233322, 0.1233322, 0.1233322, 
0.4747348, 0.4747348, 0.4747348, 0.9421821, 0.9421821, 0.9421821, 
0.978715, 0.978715, 0.978715, 0.6047539, 0.6047539, 0.6047539, 
0.9446791, 0.9446791, 0.9446791, 0.6467746, 0.6467746, 0.6467746, 
0.9648757, 0.9648757, 0.9648757, 0.3449726, 0.3449726, 0.3449726, 
0.247598, 0.247598, 0.247598, 0.277001, 0.277001, 0.277001, 0.7794862, 
0.7794862, 0.7794862, 0.02448922, 0.02448922, 0.02448922, 0.1051826, 
0.1051826, 0.1051826, 0.6608064, 0.6608064, 0.6608064, 0.9313511, 
0.9313511, 0.9313511, 0.2042655, 0.2042655, 0.2042655, 0.3983715, 
0.3983715, 0.3983715, 0.1561849, 0.1561849, 0.1561849, 0.4790193, 
0.4790193, 0.4790193, 0.2808366, 0.2808366, 0.2808366, 0.3224252, 
0.3224252, 0.3224252), E4 = c(0.9847589, 0.9847589, 0.9847589, 
0.7891661, 0.7891661, 0.7891661, 0.6799378, 0.6799378, 0.6799378, 
0.1813519, 0.1813519, 0.1813519, 0.947698, 0.947698, 0.947698, 
0.2316942, 0.2316942, 0.2316942, 0.9853715, 0.9853715, 0.9853715, 
0.856954, 0.856954, 0.856954, 0.972347, 0.972347, 0.972347, 0.6260341, 
0.6260341, 0.6260341, 0.7341723, 0.7341723, 0.7341723, 0.5199851, 
0.5199851, 0.5199851, 0.4800602, 0.4800602, 0.4800602, 0.4135151, 
0.4135151, 0.4135151, 0.9886117, 0.9886117, 0.9886117, 0.3622957, 
0.3622957, 0.3622957, 0.9717241, 0.9717241, 0.9717241, 0.3430836, 
0.3430836, 0.3430836, 0.6693761, 0.6693761, 0.6693761, 0.2278465, 
0.2278465, 0.2278465, 0.9591872, 0.9591872, 0.9591872, 0.02147499, 
0.02147499, 0.02147499, 0.8326513, 0.8326513, 0.8326513, 0.4311295, 
0.4311295, 0.4311295, 0.9624056, 0.9624056, 0.9624056, 0.3675235, 
0.3675235, 0.3675235, 0.8383142, 0.8383142, 0.8383142, 0.8542646, 
0.8542646, 0.8542646, 0.7963936, 0.7963936, 0.7963936, 0.8244256, 
0.8244256, 0.8244256, 0.9263281, 0.9263281, 0.9263281, 0.6535487, 
0.6535487, 0.6535487, 0.6641843, 0.6641843, 0.6641843, 0.5970008, 
0.5970008, 0.5970008, 0.9235346, 0.9235346, 0.9235346, 0.746903, 
0.746903, 0.746903, 0.8027389, 0.8027389, 0.8027389, 0.6307229, 
0.6307229, 0.6307229, 0.6779547, 0.6779547, 0.6779547, 0.7031775, 
0.7031775, 0.7031775), E5 = c(0.01855536, 0.01855536, 0.01855536, 
0.02507306, 0.02507306, 0.02507306, 0.02327319, 0.02327319, 0.02327319, 
0.03142696, 0.03142696, 0.03142696, 0.04486647, 0.04486647, 0.04486647, 
0.5009657, 0.5009657, 0.5009657, 0.01553736, 0.01553736, 0.01553736, 
0.1872279, 0.1872279, 0.1872279, 0.04081627, 0.04081627, 0.04081627, 
0.1493435, 0.1493435, 0.1493435, 0.3854077, 0.3854077, 0.3854077, 
0.5490297, 0.5490297, 0.5490297, 0.2929604, 0.2929604, 0.2929604, 
0.2464589, 0.2464589, 0.2464589, 0.1885217, 0.1885217, 0.1885217, 
0.3307694, 0.3307694, 0.3307694, 0.03378974, 0.03378974, 0.03378974, 
0.05832682, 0.05832682, 0.05832682, 0.2188185, 0.2188185, 0.2188185, 
0.2639117, 0.2639117, 0.2639117, 0.07256842, 0.07256842, 0.07256842, 
0.8385035, 0.8385035, 0.8385035, 0.1420448, 0.1420448, 0.1420448, 
0.2386608, 0.2386608, 0.2386608, 0.2327594, 0.2327594, 0.2327594, 
0.6836823, 0.6836823, 0.6836823, 0.01668616, 0.01668616, 0.01668616, 
0.06372214, 0.06372214, 0.06372214, 0.2240552, 0.2240552, 0.2240552, 
0.4487696, 0.4487696, 0.4487696, 0.01916614, 0.01916614, 0.01916614, 
0.1628296, 0.1628296, 0.1628296, 0.218945, 0.218945, 0.218945, 
0.8990987, 0.8990987, 0.8990987, 0.06771775, 0.06771775, 0.06771775, 
0.1452569, 0.1452569, 0.1452569, 0.1618602, 0.1618602, 0.1618602, 
0.3947573, 0.3947573, 0.3947573, 0.2672102, 0.2672102, 0.2672102, 
0.3518078, 0.3518078, 0.3518078)), row.names = c(NA, -120L), class = c("tbl_df", 
"tbl", "data.frame"))

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