我已经读过一些有趣的替代品来解释plot(mymodel)函数从一个gam适合像这个答案 https://stats.stackexchange.com/questions/430606/make-nonlinear-smooth-interpretable-in-logistic-gam-regression.
# I included just a sample of the data used to plot, as the whole data set would be too big to include.
dd <- structure(list(GDP = c(16611, 24179, 18778, 9073, 27862, 17305,
17589, 61296, 21710, 64943, 29712, 22933, 35383, 33914, 23072,
44636, 27595, 21360, 60916, 26049, 30951, 35601, 13934, 8478,
21746, 21755, 22938, 34007, 39754, 32381, 14986, 31116, 35653,
26818, 21497, 19523, 29436, 30486, 44443, 14725, 42390, 45663,
24552, 37524, 16210, 54907, 28196, 18720, 11902, 20436, 33176,
25109, 38894, 9849, 10060, 18619, 6352, 24327, 30614, 27727,
33828, 24515, 29958, 25189, 23625, 16210, 25939, 43761, 12674,
56371, 32373, 46967, 12606, 33503, 42224, 50624, 17152, 28638,
47319, 32437, 22464, 18868, 19725, 31049, 17977, 19789, 17941,
34454, 20324, 28674, 15523, 22464, 27073, 30940, 21320, 32283,
81505, 11768, 34292, 16904, 15095, 16730, 10452, 27749, 24383,
45458, 25288, 35601, 27850, 36042, 16318, 16263, 39112, 17725,
43552, 8478, 23072, 77617, 41175, 22329, 23031, 20412, 28597,
35894, 20693, 80181, 9887, 18235, 18778, 30614, 18688, 18578,
31002, 25024, 25749, 24338, 24515, 16355, 23329, 37361, 68933,
18526, 29956, 30153, 20355, 31116, 10154, 17960, 34298, 16810,
46402, 23767, 82208, 69645, 15095, 23075, 9528, 32848, 30839,
35383, 15132, 30219, 17560, 42116, 23551, 34631, 21755, 24045,
14269, 19725, 34641, 16781, 26779, 44587, 33029, 33828, 27081,
21552, 24671, 34454, 32970, 31988, 62974, 31094, 31021, 34454,
27216, 20492, 76563, 16862, 19653, 17941, 23625, 17152, 24515,
24515, 39754, 25039, 24774, 15523), Wage = c(0,
66602.2565076336, 19216.5395599364, 0, 0, 5721.51105263158, 0,
22024.8925267783, 0, 23024.8771684222, 0, 0, 35821.580462963,
0, 44957.0372533334, 17110.1706479156, 18332.8264626248, 19286.6876140043,
3868.9808, 0, 6742.64953952618, 30958.5393530612, 16921.2017315598,
21123.0720965993, 0, 11686.5098276762, 24268.300841235, 27858.6084894319,
18982.3275540713, 29078.1949916726, 0, 135229.170095384, 0, 42043.6862104972,
17514.6624249231, 25831.393328, 24516.4927762963, 0, 28017.9849961773,
0, 0, 32707.0561021505, 0, 27494.12116768, 9611.99634331974,
32370.357599471, 31055.5665115, 421993.176, 0, 0, 31263.1240312159,
9851.74454063882, 25423.9521292758, 0, 0, 91380.0180109091, 0,
13538.9139074839, 21672.6845580472, 27101.4878951333, 120560.601746666,
19284.5609535135, 0, 23700.4572205275, 0, 8116.11754901099, 0,
0, 27985.6914888647, 15965.5314217098, 30726.1238836003, 12505.5044732891,
0, 0, 153757.45372, 29353.1834862035, 0, 0, 19499.5308406846,
22646.471631356, 0, 0, 0, 18056.2380448589, 0, 0, 9056.55403077858,
32787.2002382827, 32525.7860641758, 15624.6092833745, 19878.7632243161,
0, 408947.141986666, 16385.4151221607, 0, 21613.7889501624, 81047.846376,
0, 31657.6492790697, 0, 0, 16536.2706710009, 43176.06188, 0,
14930.805379836, 7758.583, 17722.3549873251, 23034.4775943992,
13617.1922205303, 20953.1594540603, 16338.1106, 0, 30683.715600926,
7171.93619768519, 5482.74768047337, 0, 22787.2578523466, 104196.074399216,
20249.5401310861, 6647.56457232858, 0, 0, 25031.3770292917, 29907.2141204229,
0, 2687.2923, 22632.6973589655, 17618.1251776923, 19313.9108723404,
20361.5500836544, 0, 13508.1738694762, 21353.1996631231, 7951.11867047619,
0, 0, 0, 0, 0, 0, 17680.2982901078, 0, 0, 0, 19970.8752175553,
42446.4695569812, 12913.0598686629, 0, 21689.8852722289, 12859.0235435979,
4435.205225, 13927.4983508064, 22776.0627369469, 24493.2365310016,
0, 15584.3064931477, 0, 0, 0, 33418.937017192, 0, 0, 0, 15541.0730786026,
34273.8917989071, 0, 11572.6891313559, 0, 17556.1824878261, 0,
25576.4592603334, 0, 0, 0, 19637.083866971, 52579.0440135065,
0, 15533.1754333333, 17478.2808835487, 37346.9720513089, 11001.6379534907,
14948.8790488501, 2579.6373062069, 0, 0, 0, 18479.6474883721,
0, 135170.882619529, 417972.61976, 0, 9331.93045208609, 0, 0,
18765.9212547729, 22982.3656916937, 0, 86846.914, 23779.771692395,
0), Impostos = c(232664.557057, 3530226.1995, 4161857.678264,
72295.526989, 12152.633423, 0, 81507.664206, 14708828.766756,
15769.690384, 32933757.532485, 209116.513305, 15797.776863, 2019102.652875,
168567.293125, 0, 7077441.931609, 3102780.678438, 48846.597684,
391597.461504, 107138.387888, 876890.138586, 6510880.57854, 332443.0835,
2170686.675542, 5998.24005, 1644142.7277, 1764766.052373, 6920124.525103,
2650584.442635, 5678743.047908, 0, 111399.905589, 222079.463375,
9612984.739155, 160750.553885, 3640.803141, 4901830.9957, 220114.4819,
11104163.28175, 0, 407097.8065, 4734294.18, 2421061.226073, 16552.643899,
781082.590995, 9380558.776098, 197996.343837, 0, 1034010.912088,
1788.810853, 104737934.0823, 937352.477685, 9471664.846957, 247.061522,
0, 33089.171395, 0, 3384749.661656, 6077916.607471, 54698435.8485,
191109.153862, 3087915.421624, 0, 6175891.538784, 0, 1947206.919609,
20090.32025, 18268.75023, 1612764.944034, 11352494.069689, 6146126.826958,
6068097.31275, 42774.207855, 10299.797294, 232874.92998, 7294100.376346,
0, 139153.219966, 54179292.394857, 517729.799125, 48332.300222,
4000.7068, 0, 11058001.60327, 0, 0, 1946654.148202, 3801469.851,
-6978472.744936, 7935352.308324, 178316.056032, 44060.521756,
0, 297441.430034, 375351.421063, 749753.389345, 1324929.539352,
0, 5164601.75, 6926.642895, 95849.3184, 6455516.254896, 1790.910163,
191109.153862, 5400542.827929, -2006.2735, 1483048.940481, 5137589.237205,
19648210.482247, 3252207.442942, 72871.686048, 183157.899205,
454227.32697, 1034.491323, -4749367.250458, 349.713712, 62756859.66,
1124309.586451, 5588312.92745, 483140.411864, 1576276.2015, 136098.67159,
-6820362.198144, 1510507.742201, 77468.294464, 310518.18875,
2451866.291469, 517260.951893, 3553509.9303, 5587374.731822,
24371.831533, 1853842.915983, 5682789.587699, 0, 22407.841904,
0, 40462.97585, 0, 10546.207868, 0, 21796324.291819, 232874.92998,
0, 29794.274125, 38922987.8401, 320840.867347, 424607.849337,
0, 513084.828196, 1986282.763612, 454954.02975, 3026976.5735,
25962961.560054, 67459659.86375, 0, 926744.526451, 90827.457477,
5006.299375, 656457.179548, 5733215.4495, 90784.561846, 141791.204286,
4782.995884, 12787661.71375, 18209387.049057, 501898.121985,
2365044.6325, 237034.698833, 175374.182494, 23403.52685, 1872496.824345,
1124309.586451, 3135.135254, 54088.93473, 13983838.95278, 320863.989283,
0, 1104374.279799, 5457707.132157, 916062.9081, 3408576.497621,
2876435.611908, 206343.844042, 409405.91025, 19771.560761, 372256.64541,
6148657.88515, 70457.29152, 1561224.230828, 0, 341115.8817, 1395379.229263,
659.22175, 0, 2715282.94455, 113652.089848, 0, 75328.7612, 1607178.5761,
0)), row.names = c(118L, 563L, 193L, 56L, 365L, 156L, 93L, 435L,
366L, 491L, 354L, 304L, 560L, 584L, 224L, 313L, 325L, 72L, 303L,
337L, 321L, 508L, 147L, 14L, 182L, 143L, 452L, 437L, 515L, 447L,
96L, 334L, 602L, 367L, 73L, 102L, 368L, 459L, 558L, 94L, 581L,
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144L, 199L, 588L, 343L, 249L, 372L, 236L, 608L, 75L, 330L, 132L,
379L, 49L, 74L, 253L, 400L, 351L, 338L, 171L, 350L, 355L, 220L,
323L, 528L, 521L, 593L, 7L, 317L, 25L, 411L, 392L, 13L, 181L,
130L, 445L, 552L, 166L, 65L, 117L, 610L, 484L, 572L, 99L, 397L,
472L, 573L, 245L, 545L, 146L, 276L, 6L, 153L, 309L, 405L, 298L,
534L, 451L, 378L, 37L, 4L, 257L, 499L, 79L, 393L, 364L, 523L,
412L, 537L, 131L, 215L, 463L, 89L, 179L, 85L, 176L, 155L, 145L,
194L, 530L, 151L, 246L, 88L), class = "data.frame")
我有一个gam模型与一个Gamma链接功能：
library(mgcv)
m2 <- gam(GDP ~ s(Wage) +
s(Impostos),
data = dd,
select = T,
family = Gamma(link = "log"),
method = "REML")
我用这个函数绘制了它：
plot(m2, shade = T, se = T, select = 1,
xlab = "Wage",
ylab = "Change in log of GDP")
我可以这样解释：直到工资100,000，GDP的对数增加，之后减少到300,000，之后没有变化（因为0穿过阴影区域）。
不过，我能说一下增加了多少吗？比如，工资达到 100,000 之前，GDP 对数的累计增长接近 0.5（y 轴的值）？我正在寻找类似解释的回归系数。
如果我对 y 轴求幂，我会得到：
plot(m2, shade = T, se = T, select = 3,
trans = exp,
xlab = "Wage",
ylab = "Change of GDP")
我能说工资到10万的时候几乎增加了50%吗？
