我想通过计算单个组mean并从平均值中删除相应的个体来手动计算面板数据中的固定效果或时间不变效果。因此，我只想运行一个没有时间不变效应的简单线性模型：
library(plm)
library(data.table)
df <- head(Grunfeld,nrow(Grunfeld[1:60,]))
Given 3 individuals:
firm year inv value capital
1 1 1935 317.6 3078.5 2.8
2 1 1936 391.8 4661.7 52.6
3 1 1937 410.6 5387.1 156.9
4 1 1938 257.7 2792.2 209.2
5 1 1939 330.8 4313.2 203.4
6 1 1940 461.2 4643.9 207.2
7 1 1941 512.0 4551.2 255.2
8 1 1942 448.0 3244.1 303.7
9 1 1943 499.6 4053.7 264.1
10 1 1944 547.5 4379.3 201.6
11 1 1945 561.2 4840.9 265.0
12 1 1946 688.1 4900.9 402.2
13 1 1947 568.9 3526.5 761.5
14 1 1948 529.2 3254.7 922.4
15 1 1949 555.1 3700.2 1020.1
16 1 1950 642.9 3755.6 1099.0
17 1 1951 755.9 4833.0 1207.7
18 1 1952 891.2 4924.9 1430.5
19 1 1953 1304.4 6241.7 1777.3
20 1 1954 1486.7 5593.6 2226.3
21 2 1935 209.9 1362.4 53.8
22 2 1936 355.3 1807.1 50.5
23 2 1937 469.9 2676.3 118.1
24 2 1938 262.3 1801.9 260.2
25 2 1939 230.4 1957.3 312.7
26 2 1940 361.6 2202.9 254.2
27 2 1941 472.8 2380.5 261.4
28 2 1942 445.6 2168.6 298.7
29 2 1943 361.6 1985.1 301.8
30 2 1944 288.2 1813.9 279.1
31 2 1945 258.7 1850.2 213.8
32 2 1946 420.3 2067.7 132.6
33 2 1947 420.5 1796.7 264.8
34 2 1948 494.5 1625.8 306.9
35 2 1949 405.1 1667.0 351.1
36 2 1950 418.8 1677.4 357.8
37 2 1951 588.2 2289.5 342.1
38 2 1952 645.5 2159.4 444.2
39 2 1953 641.0 2031.3 623.6
40 2 1954 459.3 2115.5 669.7
41 3 1935 33.1 1170.6 97.8
42 3 1936 45.0 2015.8 104.4
43 3 1937 77.2 2803.3 118.0
44 3 1938 44.6 2039.7 156.2
45 3 1939 48.1 2256.2 172.6
46 3 1940 74.4 2132.2 186.6
47 3 1941 113.0 1834.1 220.9
48 3 1942 91.9 1588.0 287.8
49 3 1943 61.3 1749.4 319.9
50 3 1944 56.8 1687.2 321.3
51 3 1945 93.6 2007.7 319.6
52 3 1946 159.9 2208.3 346.0
53 3 1947 147.2 1656.7 456.4
54 3 1948 146.3 1604.4 543.4
55 3 1949 98.3 1431.8 618.3
56 3 1950 93.5 1610.5 647.4
57 3 1951 135.2 1819.4 671.3
58 3 1952 157.3 2079.7 726.1
59 3 1953 179.5 2371.6 800.3
60 3 1954 189.6 2759.9 888.9
I would generally do the following:
# First I caluclate the group mean
setDT(df)[, al_mean := mean(capital), by = firm]
setDT(df)[, all_mean := mean(value), by = firm]
#Then I subtrac each indidiual from group mean
df$Y_fix <- df$capital-df$al_mean
df$X_fix <- df$value-df$all_mean
firm year inv value capital al_mean Y_fix all_mean X_fix
1: 1 1935 317.6 3078.5 2.8 648.435 -645.635 4333.845 -1255.345
2: 1 1936 391.8 4661.7 52.6 648.435 -595.835 4333.845 327.855
3: 1 1937 410.6 5387.1 156.9 648.435 -491.535 4333.845 1053.255
4: 1 1938 257.7 2792.2 209.2 648.435 -439.235 4333.845 -1541.645
5: 1 1939 330.8 4313.2 203.4 648.435 -445.035 4333.845 -20.645
6: 1 1940 461.2 4643.9 207.2 648.435 -441.235 4333.845 310.055
7: 1 1941 512.0 4551.2 255.2 648.435 -393.235 4333.845 217.355
8: 1 1942 448.0 3244.1 303.7 648.435 -344.735 4333.845 -1089.745
9: 1 1943 499.6 4053.7 264.1 648.435 -384.335 4333.845 -280.145
10: 1 1944 547.5 4379.3 201.6 648.435 -446.835 4333.845 45.455
11: 1 1945 561.2 4840.9 265.0 648.435 -383.435 4333.845 507.055
12: 1 1946 688.1 4900.9 402.2 648.435 -246.235 4333.845 567.055
13: 1 1947 568.9 3526.5 761.5 648.435 113.065 4333.845 -807.345
14: 1 1948 529.2 3254.7 922.4 648.435 273.965 4333.845 -1079.145
15: 1 1949 555.1 3700.2 1020.1 648.435 371.665 4333.845 -633.645
16: 1 1950 642.9 3755.6 1099.0 648.435 450.565 4333.845 -578.245
17: 1 1951 755.9 4833.0 1207.7 648.435 559.265 4333.845 499.155
18: 1 1952 891.2 4924.9 1430.5 648.435 782.065 4333.845 591.055
19: 1 1953 1304.4 6241.7 1777.3 648.435 1128.865 4333.845 1907.855
20: 1 1954 1486.7 5593.6 2226.3 648.435 1577.865 4333.845 1259.755
21: 2 1935 209.9 1362.4 53.8 294.855 -241.055 1971.825 -609.425
22: 2 1936 355.3 1807.1 50.5 294.855 -244.355 1971.825 -164.725
23: 2 1937 469.9 2676.3 118.1 294.855 -176.755 1971.825 704.475
24: 2 1938 262.3 1801.9 260.2 294.855 -34.655 1971.825 -169.925
25: 2 1939 230.4 1957.3 312.7 294.855 17.845 1971.825 -14.525
26: 2 1940 361.6 2202.9 254.2 294.855 -40.655 1971.825 231.075
27: 2 1941 472.8 2380.5 261.4 294.855 -33.455 1971.825 408.675
28: 2 1942 445.6 2168.6 298.7 294.855 3.845 1971.825 196.775
29: 2 1943 361.6 1985.1 301.8 294.855 6.945 1971.825 13.275
30: 2 1944 288.2 1813.9 279.1 294.855 -15.755 1971.825 -157.925
31: 2 1945 258.7 1850.2 213.8 294.855 -81.055 1971.825 -121.625
32: 2 1946 420.3 2067.7 132.6 294.855 -162.255 1971.825 95.875
33: 2 1947 420.5 1796.7 264.8 294.855 -30.055 1971.825 -175.125
34: 2 1948 494.5 1625.8 306.9 294.855 12.045 1971.825 -346.025
35: 2 1949 405.1 1667.0 351.1 294.855 56.245 1971.825 -304.825
36: 2 1950 418.8 1677.4 357.8 294.855 62.945 1971.825 -294.425
37: 2 1951 588.2 2289.5 342.1 294.855 47.245 1971.825 317.675
38: 2 1952 645.5 2159.4 444.2 294.855 149.345 1971.825 187.575
39: 2 1953 641.0 2031.3 623.6 294.855 328.745 1971.825 59.475
40: 2 1954 459.3 2115.5 669.7 294.855 374.845 1971.825 143.675
41: 3 1935 33.1 1170.6 97.8 400.160 -302.360 1941.325 -770.725
42: 3 1936 45.0 2015.8 104.4 400.160 -295.760 1941.325 74.475
43: 3 1937 77.2 2803.3 118.0 400.160 -282.160 1941.325 861.975
44: 3 1938 44.6 2039.7 156.2 400.160 -243.960 1941.325 98.375
45: 3 1939 48.1 2256.2 172.6 400.160 -227.560 1941.325 314.875
46: 3 1940 74.4 2132.2 186.6 400.160 -213.560 1941.325 190.875
47: 3 1941 113.0 1834.1 220.9 400.160 -179.260 1941.325 -107.225
48: 3 1942 91.9 1588.0 287.8 400.160 -112.360 1941.325 -353.325
49: 3 1943 61.3 1749.4 319.9 400.160 -80.260 1941.325 -191.925
50: 3 1944 56.8 1687.2 321.3 400.160 -78.860 1941.325 -254.125
51: 3 1945 93.6 2007.7 319.6 400.160 -80.560 1941.325 66.375
52: 3 1946 159.9 2208.3 346.0 400.160 -54.160 1941.325 266.975
53: 3 1947 147.2 1656.7 456.4 400.160 56.240 1941.325 -284.625
54: 3 1948 146.3 1604.4 543.4 400.160 143.240 1941.325 -336.925
55: 3 1949 98.3 1431.8 618.3 400.160 218.140 1941.325 -509.525
56: 3 1950 93.5 1610.5 647.4 400.160 247.240 1941.325 -330.825
57: 3 1951 135.2 1819.4 671.3 400.160 271.140 1941.325 -121.925
58: 3 1952 157.3 2079.7 726.1 400.160 325.940 1941.325 138.375
59: 3 1953 179.5 2371.6 800.3 400.160 400.140 1941.325 430.275
60: 3 1954 189.6 2759.9 888.9 400.160 488.740 1941.325 818.575
现在我可以为面板数据固定效果运行plm或使用新变量运行简单lm：
summary(plm(capital ~ value,df, index=c("firm", "year"), na.action=na.omit, model="within"))
summary(lm(Y_fix ~ X_fix,df))
但是我不确定如何手动计算给出几十个变量。是否有保留预期结构的捷径X_fix和Y_fix以及Z_fix等等？