问题描述
如果系数使用t检验等效，我想在两个回归之间进行比较，我该如何处理这个问题，R中是否有一个函数，这对于看似无关的回归是否有用？线性假设函数仅支持卡方检验和f检验。
structure(list(Mkt.RF = c(-3.58,-2.06,2.13,4.26,3.45,-0.74,0.66,-5.11,-5.98,-4.32,2.3,-3.91,4.66,-1.52,3.27,3.09,2.31,2.93,4.39,1.91),SMB = c(3.4,-0.72,0.27,-1.6,-1.07,0.55,-0.76,0.06,0.08,-2.52,0.4,-0.93,4.36,0.7,0.63,-0.59,2.24,-0.24,0.47,1.19),HML = c(2.78,-0.73,-0.47,-1.51,-2.05,0.01,0.38,-0.45,0.88,-1.83,-2.9,-1.71,4.23,0.28,-0.92,1.46,-0.35,0.5,3.12,0.29),RF = c(0.27,0.24,0.23,0.25,0.26,0.3,0.29,0.12,0.09,0.11,0.03,0.07,0.04),Mom = c(-3.05,0.31,-0.18,0.96,0.44,0.77,-0.07,0.49,0.62,1.94,1.24,7.79,-7.63,3.75,-1.85,1.85,-1.82,-0.87,-3.62,0.28),ST_Rev = c(3.64,-0.12,1.08,-0.54,0.2,-0.83,0.59,-4.04,-3.54,-0.16,-1.2,5.46,1.79,1.15,-0.44,1.19,1.96,2.7,1.71),LT_Rev = c(4.96,1.11,-0.63,-1.9,-1.56,-0.56,2.1,2.47,-0.14,-0.82,1.66,2.5,0.82,-0.69,1.13,-0.68,-2.12,0.65),SMALL.LoBM = c(-0.2503,2.9079,-2.7574,0.0526,6.5715,-2.9304,10.823,-3.7417,-8.4998,-9.134,2.3031,-10.7934,22.6559,-8.0991,0.0122,3.9872,8.0196,2.8676,0.9155,3.6121),ME1.BM2 = c(1.1499,-2.684,0.4626,0.712,-0.3634,1.7096,-3.2747,-3.2251,-2.4005,-10.0789,-2.5086,-5.2028,9.4805,0.5592,5.8376,5.6991,4.7564,1.8046,7.0892,-0.4536),ME1.BM3 = c(0.3391,-2.9947,3.0314,2.66,-2.005,-0.6318,0.0214,-3.7985,-4.0396,-6.2716,0.7112,-4.4564,9.2809,-1.7363,4.1581,2.3189,4.1872,1.2225,7.3031,3.1771
),ME1.BM4 = c(2.3947,-2.7768,2.5032,1.8131,0.6916,1.0397,-0.0338,-4.9373,-4.2979,-6.7299,0.7121,-6.0009,11.4808,-1.4308,4.6421,3.3693,3.8889,3.225,6.2092,2.8972),SMALL.HiBM = c(3.0661,-1.9227,0.616,2.8892,-0.1074,1.5065,-0.1177,-4.2014,-4.7744,-9.7825,1.1377,-5.4893,14.1829,-0.9943,2.7984,3.6832,3.9037,3.247,5.5628,4.5524),ME2.BM1 = c(1.7551,-5.7328,2.3007,2.2013,3.297,-0.3559,-1.8405,-4.774,-6.8747,-6.8879,1.458,-5.9069,12.2022,0.5558,8.1202,4.8782,4.2682,0.2252,2.1459,3.9586),ME2.BM2 = c(-0.9705,-1.8677,0.7317,-1.0295,4.1267,-0.7306,0.2541,-3.6977,-4.6924,-6.7164,2.2514,-3.128,10.4595,-0.0779,2.3431,3.8102,3.3286,4.95,2.744,3.2929),ME2.BM3 = c(1.4035,-3.6199,1.6266,3.6103,0.4984,-0.5925,0.3072,-4.2721,-3.8077,-5.3892,1.0828,-1.5308,8.6883,-0.6165,3.1584,2.746,2.757,2.2907,5.4909,2.0368),ME2.BM4 = c(-0.2011,-3.6209,1.9333,0.8332,0.5706,-2.2377,0.8313,-5.3742,-4.3962,-6.4608,-1.6069,-7.2318,10.738,-0.1293,2.7462,2.1808,3.6956,3.4065,5.033,2.1134),ME2.BM5 = c(2.0711,-1.8232,2.8456,4.0999,2.7381,1.3955,0.405,-6.2742,-7.0585,-9.4413,0.3334,-7.2297,12.7326,0.3038,3.561,4.8341,5.7237,2.9956,7.3176,4.6113),ME3.BM1 = c(-0.1804,-2.8882,1.352,2.9007,2.782,1.1381,0.4867,-6.2306,-5.7554,-7.6683,3.8579,-4.5266,7.913,-0.4997,3.1115,2.7842,6.7293,2.9003,2.5795,4.0556),ME3.BM2 = c(-0.7311,-2.9647,3.2335,1.3674,1.6556,-2.206,-0.6753,-4.4656,-7.6589,-5.5316,3.1475,-2.6196,8.4187,-0.1565,4.58,0.798,4.7252,2.4181,5.6894,3.4092),ME3.BM3 = c(-1.4191,-2.7309,2.89,3.2702,3.0169,-2.3016,-0.3286,-5.2077,-4.643,-5.6728,2.0126,-5.0963,10.1059,-0.6968,3.0432,1.7961,3.8527,2.8335,6.8058,3.3262
),ME3.BM4 = c(-0.5254,-2.7913,1.6405,1.4421,1.5075,-0.5878,1.1964,-5.8299,-5.3617,-6.2945,1.7535,-7.0812,12.6428,-0.7669,3.2638,0.8487,4.3544,1.708,7.1502,4.1152),ME3.BM5 = c(1.4049,-3.8607,1.5727,0.7456,1.9912,-1.1459,0.8075,-6.2397,-4.5381,-7.5731,3.4239,-4.1991,10.9095,0.1019,4.1297,4.7065,4.3938,3.4303,10.057,1.8304),ME4.BM1 = c(-1.7133,-1.0446,2.7137,4.259,2.8387,-1.6461,-0.2418,-7.7127,-5.2005,-6.3393,3.8992,-3.7172,6.9502,-1.4509,5.7128,3.7283,2.5366,3.3355,3.7266,3.213),ME4.BM2 = c(-1.2759,-1.3582,1.2222,1.8649,1.9799,-2.6201,-0.2497,-5.8088,-5.3128,-2.6377,3.6378,-2.8932,7.9308,-0.6119,2.7065,2.58,2.3185,1.9882,3.9238,1.8505
),ME4.BM3 = c(-1.216,-2.5053,3.1187,2.4602,0.4411,-2.2538,-0.0837,-4.3101,-3.3985,-3.3454,1.5862,-0.8756,7.309,0.7886,3.2176,2.0817,2.7693,2.8197,5.6228,3.8941),ME4.BM4 = c(-2.2442,-3.8999,2.0182,3.5898,1.2033,-2.6227,1.0005,-5.9218,-7.1044,-7.2683,1.3216,-7.3886,13.209,-1.8963,1.8581,3.2885,3.0029,3.0511,5.3104,1.8811),ME4.BM5 = c(-1.9603,-2.9296,1.4486,0.1516,3.6732,0.0404,1.0588,-5.8241,-8.7229,-10.6485,-0.906,-5.8981,13.5529,-2.6018,3.0886,6.0737,2.1082,4.763,9.537,3.8238),BIG.LoBM = c(-5.1549,-1.8637,2.3957,5.3741,4.8306,0.1678,1.2408,-5.6726,-7.1147,-3.9227,2.5652,-3.8819,2.6308,-2.0986,3.1063,2.9589,1.7297,2.9227,5.0309,1.7733),ME5.BM2 = c(-4.7384,-1.4001,1.9731,5.4208,2.9949,-2.0476,0.8084,-4.9762,-5.2956,-3.702,2.7913,-4.5086,3.4779,-1.3382,3.1628,3.3917,2.6598,3.2409,2.1203,0.6962),ME5.BM3 = c(-2.3125,-1.9445,2.0115,2.8931,2.7253,-0.7017,-0.2,-2.5243,-4.2654,-3.6365,1.4897,-1.76,5.0131,-0.8321,3.7127,3.1274,1.792,2.9392,3.729,2.1507),ME5.BM4 = c(-4.6173,-4.2998,0.8601,4.602,2.0774,-2.303,0.7922,-5.4849,-5.6303,-5.7929,1.7485,-7.3657,6.9289,-3.2758,2.9054,2.5705,3.3908,2.7507,5.463,1.784),BIG.HiBM = c(-0.9533,-4.2776,1.9959,1.6504,2.5779,0.0725,0.9071,-5.1901,-8.6878,-7.8173,-4.4356,-7.0048,11.5797,-3.4114,1.2488,6.2048,3.9438,3.1976,7.7579,2.0333)),row.names = c(NA,20L),class = "data.frame")
*编辑：我现在添加了数据框
解决方法
我创建了两个任意方程：
eq1 = ME1.BM2 ~ Mkt.RF + SMB
eq2 = ME1.BM3 ~ Mkt.RF + HML
mod = summary(systemfit::systemfit(list(eq1,eq2),data=df))
现在，我们计算该帖子中显示的Z统计量：
为此，我们获取mod的系数并手动进行计算：
coef1 = mod$eq[[1]]$coefficients[3,] #The 3 is for getting the HML coef
coef2 = mod$eq[[2]]$coefficients[3,] #The 3 is for getting the SMB coef
Z = (coef1[1]-coef2[1])/sqrt(coef1[2]^2-coef2[2]^2) #[2] is the estimate,[2] is the sd
然后，您可以将Z与标准正态分布的临界值进行比较，以获取所需的有效值。
我找不到执行此测试的程序包，但我认为这是正确的。