繪制來自 GAM {mgcv} r 的未轉換的、可解釋的輸出和原始數據

Question

我正在嘗試使用 GAM {mgcv} 了解 NDVI 和海拔之間的關系。

ndvi=c(0.37284458, 0.36299109, 0.34534124, 0.35626486, 0.33304086, 
0.34456021, 0.34147954, 0.37136942, 0.34765118, 0.31762186, 0.31168666, 
0.36252472, 0.37283841, 0.33449343, 0.34287873, 0.35803697, 0.29003596, 
0.38974261, 0.37898183, 0.33467904, 0.37784857, 0.4082346, 0.34065819, 
0.33835235, 0.34296334, 0.36620009, 0.38511008, 0.48989189, 0.38676593, 
0.35365942, 0.44366336, 0.48514673, 0.49109551, 0.52452511, 0.39972124, 
0.40625861, 0.43465778, 0.44273201, 0.40738371, 0.44018745, 0.49735194, 
0.53355908, 0.44059527, 0.49126968, 0.4331325, 0.50643468, 0.49381891, 
0.43036473, 0.41900063, 0.46537551, 0.38005379, 0.59700656, 0.50228047, 
0.45391369, 0.49698669, 0.38300833, 0.40035707, 0.50576973, 0.34738368, 
0.29102421, 0.38579389, 0.40881836, 0.32830772, 0.31917784, 0.38334072, 
0.44629705, 0.55095547, 0.45162645, 0.44459134, 0.60119373, 0.5148682, 
0.33612376, 0.36213681, 0.28747568, 0.29177585, 0.32551974, 0.35665748, 
0.3745077, 0.40644151, 0.29654002, 0.35043341, 0.31480816, 0.3203741, 
0.38690963, 0.37501845, 0.44434533, 0.42677853, 0.39572114, 0.33268374, 
0.36218885, 0.45128649, 0.48611939, 0.36604273, 0.35607538, 0.40648854, 
0.51214248, 0.42073068, 0.41392553, 0.43328416, 0.39342898, 0.43975314, 
0.43961406, 0.56884927, 0.54535288, 0.66552502, 0.59507757, 0.35456958, 
0.29807517, 0.28920445, 0.2994661, 0.29049689, 0.32402208, 0.35077614, 
0.36170107, 0.35779324, 0.37913361, 0.35802785, 0.3657203, 0.37261558, 
0.30806249, 0.29533851, 0.29045367, 0.30271557, 0.3270824, 0.36809677, 
0.32528841, 0.40088555, 0.51367378, 0.53471488, 0.49363512, 0.42806908, 
0.35330164, 0.31458119, 0.38571393, 0.33384511, 0.34088102, 0.38640618, 
0.46462426, 0.46435356, 0.43860245, 0.45624161, 0.46190062, 0.45900786, 
0.43069631, 0.42575583, 0.47714207, 0.39718044, 0.40318352, 0.2497917, 
0.25269625, 0.47882196, 0.5320223, 0.5435406, 0.37848091, 0.20995587, 
0.39205831, 0.51161075, 0.45779061, 0.26454785, 0.30714244, 0.33823466, 
0.39386562, 0.39106974, 0.36486822, 0.23709562, 0.49485436, 0.3659955, 
0.25378579, 0.42694312, 0.42897266, 0.46190798, 0.45739591, 0.28146976, 
0.3088598, 0.30763069, 0.44386092, 0.261134, 0.23552018, 0.21810713, 
0.19807275, 0.1983645, 0.20088004, 0.31146958, 0.2289221, 0.2640928, 
0.18468697, 0.18130147, 0.18427111, 0.28448355, 0.21563233, 0.24098049, 
0.22049443, 0.23217815, 0.24867195, 0.30727732, 0.37952852, 0.39026323, 
0.3106921, 0.27072188, 0.40688464, 0.24761118, 0.23710926, 0.23490097, 
0.20989761, 0.19913878, 0.22746462, 0.27149725, 0.23974811, 0.24351674, 
0.21835253, 0.23701255, 0.2642346, 0.35599774, 0.38883707, 0.51227754, 
0.52291566, 0.42694929, 0.31988204, 0.34567946, 0.28045416, 0.28074971, 
0.3015548, 0.3018271, 0.33375728, 0.3026112, 0.36266547, 0.4212667, 
0.37581727, 0.36138797, 0.42702183, 0.42004678, 0.48225939, 0.4645187, 
0.48628905, 0.35416839, 0.42213014, 0.22399676, 0.20081049, 0.21593477, 
0.18973792, 0.23069827, 0.23390402, 0.20583794, 0.42624232, 0.22057733, 
0.21734384, 0.1978067, 0.38804373, 0.22859769, 0.21575791, 0.20370759, 
0.35803479, 0.22058661, 0.20311546, 0.39473101, 0.25248429, 0.29062492, 
0.18886448, 0.28385413, 0.43893406, 0.36858734, 0.1738556, 0.48782307, 
0.38708588, 0.40135667, 0.27829349, 0.42564583, 0.39994976, 0.23983358, 
0.29697156, 0.44519106, 0.32593229, 0.46419907, 0.31740955, 0.47189832, 
0.33024263, 0.39319688, 0.37098923, 0.35016385, 0.36154863, 0.42523682, 
0.38669956, 0.36397356, 0.36762711, 0.37823507, 0.31974643, 0.27281806, 
0.28012297, 0.34467915, 0.42085385, 0.37235492, 0.35309508, 0.45293796, 
0.39240688, 0.41030771, 0.3528643, 0.40271956, 0.4757368, 0.36223486, 
0.41054854, 0.41387588, 0.38983357, 0.4167802, 0.35918111, 0.50965786, 
0.39109153, 0.49194288, 0.55038857, 0.39720327, 0.43226415, 0.56539428,0.45440963, 0.34884879, 0.41057199, 0.38644075, 0.47156903, 0.33063081, 
0.32137984, 0.35716292, 0.38749653, 0.42357811, 0.46679774, 0.44854486, 
0.30482626, 0.27483031, 0.35759008, 0.42913625, 0.46651256, 0.28502983, 
0.39216331, 0.40816534, 0.27440724, 0.3111816, 0.37306091, 0.38279143, 
0.3264704, 0.44179216, 0.38299596, 0.29607165, 0.30998632, 0.46233353, 
0.33230495, 0.32675204, 0.24098285, 0.20409316, 0.30174595, 0.21717471, 
0.23586701, 0.21025825, 0.2350591, 0.51234818, 0.30030167, 0.17971739, 
0.52621692, 0.52366912, 0.40064591, 0.57194382, 0.63093466, 0.48751017, 
0.52511013, 0.50126761, 0.37541237, 0.42792675, 0.31729576, 0.37768126, 
0.52844834, 0.31242937, 0.39442217, 0.40255255, 0.40193877, 0.36440474, 
0.41571805, 0.315835, 0.31166464, 0.35319975, 0.50620955, 0.50272065, 
0.45752475, 0.40692955, 0.37109366, 0.36725962, 0.36716217, 0.33104709, 
0.41383833, 0.37535995, 0.41239858, 0.39627686, 0.42360836, 0.3887102, 
0.44936863, 0.33351886, 0.48855564, 0.41484746, 0.47105169, 0.39093614, 
0.40007663, 0.49453706, 0.48607925, 0.3932541, 0.44774082, 0.42149165, 
0.3819266, 0.36476272, 0.36824036, 0.41211739, 0.36111835, 0.41108459, 
0.36994269, 0.34518829, 0.34582183, 0.3388541, 0.36861211, 0.40138465, 
0.38365835, 0.43873557, 0.43879241, 0.49522537, 0.52001029, 0.46294218, 
0.43171886, 0.12007371, 0.4836823, 0.46957007, 0.10998849, 0.42262775, 
0.44603577, 0.10697274, 0.47638127, 0.50140697, 0.48923677, 0.10984974, 
0.49029085, 0.45691997, 0.42762986, 0.11285156, 0.39055535, 0.35207632, 
0.40831631, 0.44256192, 0.50568485, 0.54724079, 0.11433452, 0.54162121, 
0.11548679, 0.12456147, 0.55419147, 0.5490337, 0.1308123, 0.5958755, 
0.37515038, 0.61899012, 0.54582655, 0.12366795, 0.53331429, 0.54886377, 
0.12084137, 0.54416335, 0.33218127, 0.12337033, 0.57192695, 0.54615563, 
0.12288751, 0.47263604, 0.3987166, 0.42566201, 0.41175276, 0.12040752, 
0.59236515, 0.52589303, 0.55943716, 0.42766839, 0.5547722, 0.11845382, 
0.56455755, 0.59910047, 0.5679692, 0.43171248, 0.12218402, 0.5436691, 
0.56641918, 0.12743743, 0.55414909, 0.14656784, 0.52954382, 0.42851776, 
0.14594139, 0.60023719, 0.12003227, 0.59396029, 0.62594134, 0.16057645, 
0.3776767, 0.67848641, 0.21419135, 0.6850282, 0.58143109, 0.15435438, 
0.54788327, 0.15782964, 0.58817184, 0.19433907, 0.2134172, 0.46749261, 
0.54181325, 0.41827089, 0.42650056, 0.1875321, 0.46528313, 0.4021, 
0.50298762, 0.48612255, 0.43469813, 0.16945361, 0.17312884, 0.5417611, 
0.15071063, 0.57286531, 0.5541805, 0.32761294, 0.56888014, 0.11994911, 
0.5775314, 0.55209744, 0.5880518, 0.5298745, 0.53949076, 0.43877628, 
0.48537695, 0.38416794, 0.49095127, 0.56465995, 0.4470818, 0.56394529, 
0.11755586, 0.57454139, 0.11578638, 0.5672397, 0.57609165, 0.5380218, 
0.58232319, 0.59500247, 0.60516119, 0.45734581, 0.48618528, 0.51702631, 
0.55027866, 0.37871492, 0.31339511, 0.34899774, 0.39584169, 0.34440562, 
0.55272824, 0.38057595, 0.40194014, 0.37820032, 0.35338613, 0.4434987, 
0.47183508, 0.50089973, 0.56338143, 0.35097095, 0.47634727, 0.29248065, 
0.35980406, 0.30520365, 0.51648533, 0.5068593, 0.31666866, 0.32031479, 
0.37659955, 0.26569951, 0.26894692, 0.43952745, 0.44224274, 0.46047512, 
0.28328276, 0.40928012, 0.37350893, 0.39134952, 0.48740214, 0.36256111, 
0.33733693, 0.50880104, 0.36416224, 0.46596181, 0.43892652, 0.37539759, 
0.49673808, 0.44390601, 0.44054565, 0.47481841, 0.5103085, 0.51133341, 
0.57967305, 0.57180786, 0.53124815, 0.41183549, 0.46823403, 0.33697557, 
0.50546753, 0.55019134, 0.59541911, 0.52273095, 0.63234776, 0.54289067, 
0.6559633, 0.44042417, 0.52003521, 0.69010967, 0.45370963, 0.40090004, 
0.32907081, 0.44446883, 0.18390173, 0.17358142, 0.27948725, 0.32681823, 0.17034216, 0.17107487, 0.30296239, 0.1622318, 0.16486378, 0.28758663, 
0.16008918, 0.47051576, 0.39771613, 0.20432511, 0.30118409, 0.18917, 
0.16774413, 0.19803287, 0.31669104, 0.28809702, 0.27116156, 0.32019755, 
0.47789127, 0.22356878, 0.33761221, 0.2071128, 0.45098323, 0.43004736, 
0.46809581, 0.19979469, 0.20777245, 0.40051672, 0.24367467, 0.17879868, 
0.47685167, 0.40548974, 0.20904543, 0.18480691, 0.22970232, 0.25320169, 
0.34040126, 0.1866201, 0.3197476, 0.29494119, 0.23753925, 0.2466726, 
0.33789754, 0.19939244, 0.20041303, 0.2025224, 0.19561875, 0.27618363, 
0.30849349, 0.22153169, 0.55085963, 0.3131991, 0.3583152, 0.20948842, 
0.20855463, 0.31315297, 0.28010854, 0.25264174, 0.39960471, 0.4657588, 
0.28375575, 0.25989574, 0.31080499, 0.467841, 0.41235253, 0.45717904, 
0.5812813, 0.56274688, 0.48186132, 0.39704716, 0.42959207, 0.46030018, 
0.40959281, 0.57361746, 0.51162231, 0.48982546, 0.4931736, 0.48223504, 
0.53471524, 0.52804619, 0.49133918, 0.5440793, 0.49828768, 0.52568519, 
0.52009314, 0.55978638, 0.54395258, 0.41577986, 0.38484025, 0.4419764, 
0.44596735, 0.44326246, 0.39296818, 0.42032951, 0.50332654, 0.44751549, 
0.39300203, 0.44557381, 0.52650803, 0.49614227, 0.42115286, 0.49260482, 
0.44385687, 0.5635072, 0.32846645, 0.50394791, 0.46008989, 0.58905828, 
0.53291762, 0.32630342, 0.61202854, 0.41473407, 0.58198237, 0.35745674, 
0.34939414, 0.38247347, 0.62988394, 0.57093704, 0.48079449, 0.36502972, 
0.41322416, 0.45119342, 0.46854448, 0.46846315, 0.64025593, 0.42413765, 
0.51297534, 0.59165025, 0.51079077, 0.49969929, 0.6184572, 0.55338889, 
0.58190191, 0.55547076, 0.59358573, 0.63075489, 0.51425701, 0.63361824, 
0.49662313, 0.47938466, 0.49662527, 0.51538551, 0.48033077, 0.65019745, 
0.49855691, 0.50957841, 0.46327689, 0.52606738, 0.54897904, 0.54415298, 
0.53295821, 0.48907343, 0.5813539, 0.5791558, 0.56734169, 0.50948626, 
0.61064368, 0.63390613, 0.54600215, 0.54012775, 0.54547435, 0.53523856, 
0.47844616, 0.54452389, 0.61522639, 0.66612244, 0.54486001, 0.55848712, 
0.57533371, 0.59418201, 0.57968897, 0.55798745, 0.43673918, 0.59824342, 
0.61019611, 0.56767529, 0.23656663, 0.49716783, 0.42394811, 0.49415183, 
0.48858669, 0.56280184, 0.53211331, 0.570948, 0.44651186, 0.55828547, 
0.44064161, 0.52318674, 0.50507104, 0.56085426, 0.62119055, 0.52611685, 
0.43739846, 0.56699002, 0.48123884, 0.44280618, 0.49389672, 0.57842433, 
0.60003191, 0.59438759, 0.60395777, 0.52329993, 0.58154529, 0.50001037, 
0.53997809, 0.42599022, 0.40334904, 0.5300926, 0.47504365, 0.61598688, 
0.5307219, 0.54195917, 0.36586505, 0.52503568, 0.58194685, 0.56088555, 
0.43736571, 0.44608584, 0.49466795, 0.46879953, 0.38689315, 0.37443966, 
0.48397902, 0.50784773, 0.38129795, 0.53752059, 0.3884064, 0.43738136, 
0.56364578, 0.67537719, 0.59310961, 0.38332301, 0.4207001, 0.6113413, 
0.37628123, 0.58488911, 0.30617586, 0.50850123, 0.58645731, 0.3069602, 
0.32366791, 0.57885045, 0.57523584, 0.48794562, 0.45338526, 0.4764891, 
0.51286817, 0.56180888, 0.43689296, 0.51353568, 0.60581577, 0.40476534, 
0.55250001, 0.61904049, 0.54644275, 0.56612611, 0.56348616, 0.58739144, 
0.55728227, 0.49260241, 0.48701286, 0.54145378, 0.53963166, 0.4933565, 
0.45025027, 0.42232114, 0.47838867, 0.58416939, 0.56239808, 0.37954712, 
0.56743282, 0.39150637, 0.53962982, 0.60306382, 0.46025828, 0.49077743, 
0.60236579, 0.47457057, 0.47792545, 0.57731998, 0.447983, 0.44238743, 
0.45048851, 0.4277384, 0.38526028, 0.45638478, 0.42012143, 0.46913737, 
0.44282815, 0.52651328, 0.4475337, 0.47447568, 0.4499096, 0.57560682, 
0.46730033, 0.49862021, 0.35509562, 0.53960955, 0.50024015, 0.59349477, 
0.38186911, 0.44112691, 0.36592636, 0.64959121, 0.48866126, 0.41112146, 
0.59468359, 0.40227708, 0.46466774, 0.52884471, 0.54625285, 0.3591285, 0.46930903, 0.59036058, 0.48719868, 0.58185583, 0.58928138, 0.4725737, 
0.47224933, 0.48249629, 0.51947838, 0.50547099, 0.49053812, 0.58460832, 
0.56633383, 0.54741734, 0.55866396, 0.56510276, 0.54703504, 0.50296366, 
0.59481162, 0.39838254, 0.49417058, 0.55508375, 0.44624022, 0.40848476, 
0.47220662, 0.41816965, 0.35065037, 0.5417226, 0.3843298, 0.57464051, 
0.33038601, 0.35658485, 0.40679565, 0.36484152, 0.54721773, 0.39360908, 
0.48341459, 0.5437758, 0.45842963, 0.53718525, 0.56601614, 0.37139726, 
0.43007621, 0.58927023, 0.31203148, 0.49183467, 0.43646091, 0.29040816, 
0.42643794, 0.44335389, 0.3266508, 0.47064027, 0.4330571, 0.32086417, 
0.52630913, 0.3401593, 0.58157116, 0.55650526, 0.40066051, 0.53089213, 
0.51907247, 0.52990496, 0.50308192, 0.41526651, 0.41932482, 0.49954349, 
0.40952563, 0.54189724, 0.43167049, 0.38867795, 0.32555526)

Elevation=c(1871.92, 1875.38, 1878.28, 1878.54, 1878.33, 1879.2, 1880.51, 
1883.78, 1884.6, 1884.85, 1885.46, 1888.72, 1890.94, 1897.19, 
1901.95, 1902.47, 1902.81, 1903.49, 1906.62, 1908.73, 1909.4, 
1910.65, 1913.44, 1915, 1915.81, 1918.06, 1920.01, 1921.53, 1925.48, 
1926.66, 1927.64, 1931.02, 1932.8, 1935.27, 1938.33, 1941.19, 
1945.71, 1948.68, 1951.52, 1951.83, 1955.76, 1961.02, 1963.92, 
1963.25, 1969.53, 1972.56, 1977.92, 1978.93, 1981.54, 1985.64, 
1987.6, 1987.62, 1988.78, 1991.92, 1997.03, 1998.06, 1998.98, 
2001.26, 2006.97, 2009.56, 2009.81, 2011.55, 2017.92, 2021.75, 
2023.42, 2024.91, 2028.15, 2032.83, 2032.83, 2033.5, 2035.75, 
2037.44, 2045.51, 2047.38, 2049.85, 2052.33, 2059.36, 2069.27, 
2071.41, 2071.83, 2074.15, 2081.55, 2083.52, 2086.3, 2090.5, 
2095.57, 2096.69, 2100.65, 2108.06, 2110.48, 2113.45, 2121.78, 
2124.82, 2133.54, 2137.54, 2146.43, 2150.53, 2156.63, 2160.05, 
2168.57, 2174.68, 2183.42, 2188.54, 2194.25, 2204.1, 2214.74, 
1629.73, 1634.59, 1635.31, 1637.06, 1638.47, 1639.57, 1641.11, 
1643.07, 1644.68, 1646.96, 1648.51, 1650.56, 1652.34, 1654.67, 
1658.78, 1660.71, 1662.58, 1663.67, 1664.53, 1665.73, 1667.21, 
1668.69, 1669.68, 1670.13, 1671.99, 1673.73, 1674.78, 1676.91, 
1678.96, 1685.13, 1686.78, 1688.51, 1690.57, 1692.54, 1694.26, 
1696.56, 1702.03, 1703.58, 1705.62, 1707.59, 1709.36, 1711.76, 
2121.37, 2132.33, 2139.32, 2039.39, 2147.19, 2037.25, 2116.11, 
2036.77, 2047.41, 2032.13, 2100.15, 2024.77, 2048.57, 2095.7, 
2156.29, 2023.25, 2056.88, 2090.25, 2021.07, 2060.16, 2012.3, 
2064.89, 2011.73, 2085.58, 2072.01, 2076.73, 2082.98, 2010.81, 
2007.68, 2001.07, 2000.23, 1999.18, 1996.75, 1993.55, 1988.19, 
1987.55, 1986.94, 1982.81, 1977.24, 1976.09, 1964.42, 1972.47, 
1975.41, 1974.17, 1960.14, 1954.49, 1951.47, 1951.95, 1953.25, 
1951.26, 1945.84, 1714.37, 1942.2, 1939.7, 1939.43, 1937.78, 
1930.15, 1927.88, 1927.52, 1927.48, 1927.41, 1927.3, 1925.13, 
1923.31, 1922.32, 1716.56, 1922.9, 1923.41, 1921.9, 1916.1, 1914.31, 
1914.32, 1914.47, 1914.54, 1914.67, 1914.95, 1916.91, 1914.58, 
1914.79, 1914.31, 1915.26, 1915.35, 1913.95, 1913.92, 1913.46, 
1913.56, 1718.82, 1912.73, 1926.81, 1927.11, 1927.06, 1928.72, 
1926.95, 1926.98, 1927, 1907.55, 1926.84, 1930.71, 1926.89, 1904.94, 
1922.97, 1931.07, 1916.23, 1904.11, 1931.5, 1917.11, 1907.87, 
1932.36, 1932.87, 1914.5, 1932.82, 1912.08, 1903.99, 1914.09, 
1902.17, 1915.08, 1916.14, 1932.75, 1922.91, 1914.29, 1915.2, 
1934.44, 1904.43, 1936.41, 1903.17, 1938.07, 1902.5, 1938.02, 
1902.48, 1723.01, 2225.15, 1940.32, 1938.35, 1901.94, 1901.92, 
1903.22, 1901.91, 1901.93, 2219.35, 2218.75, 1901.91, 1944.29, 
2216.48, 1901.94, 1946.04, 1901.96, 1947.24, 2207.48, 1901.91, 
2204.64, 1948.74, 1901.99, 2193.47, 1901.04, 1950.25, 1725.13, 
2192.55, 1899.9, 1950.86, 2192.36, 1951.09, 1893.62, 2025.57, 
2188.52, 2011.76, 2023.53, 2018.23, 2033.62, 2022.24, 2010.83, 
2009.79, 1954.57, 2101.77, 2007.61, 2034.71, 2109.56, 2173.75, 
1959.35, 2010.4, 2098.15, 1976.98, 1961.81, 1890.4, 2115.34, 
1976.8, 1963.54, 2038.5, 1963.56, 2001.21, 1889.72, 1890.61, 
2120.13, 1996.95, 2168.35, 2098.63, 1963.51, 1974.27, 2120.01, 
1973.45, 1963.76, 1971.47, 1965.09, 2040.76, 2120.84, 2086.92, 
2124.03, 2132.81, 1889.83, 2043.69, 2052.11, 2158.47, 2047.67,2133.93, 2069.27, 2137.94, 2142.95, 1889.71, 2156.19, 2145.34, 
2077.96, 2149.46, 2146.56, 1889.56, 2077.97, 1727.14, 1889.97, 
1889.52, 1889.55, 1889.66, 1889.66, 1889.43, 1889.82, 1890.37, 
1889.78, 1889.33, 1888.81, 1889.27, 1887.77, 1729.92, 1889.4, 
1888.38, 1889.46, 1888.1, 1889.02, 1730.97, 1889.62, 1886.39, 
1882.77, 1878.25, 1878.55, 1732.12, 1881.32, 1886.54, 1877.46, 
1878.27, 1737.56, 1877.55, 1877.68, 1877.73, 1877.45, 1877.43, 
1877.42, 1878.29, 1876.89, 1876, 1876.75, 1876.25, 1870.85, 1867.05, 
1869.89, 1866.53, 1866.94, 1746.48, 1864.61, 1864.07, 1748.33, 
1863.07, 1864.13, 1750.49, 1862.93, 1863.03, 1863.16, 1751.31, 
1863.19, 1862.92, 1862.95, 1753.05, 1862.93, 1863.03, 1864.12, 
1862.93, 1862.8, 1856.28, 1754.17, 1854.11, 1755.62, 1757.18, 
1853.99, 1853.98, 1759.96, 1853.13, 1740.91, 1852.56, 1852.44, 
1762.71, 1853.72, 1852.82, 1764.36, 1851.1, 1741.95, 1764.45, 
1850.01, 1849.63, 1766.6, 1850.63, 1743.01, 1850.85, 1842.18, 
1768.84, 1840.46, 1840.76, 1842.49, 1744.39, 1839.77, 1772.73, 
1837.41, 1841.33, 1834.92, 1745.12, 1776.63, 1829.04, 1827.93, 
1779.97, 1829.79, 1782.22, 1828.53, 1830.62, 1783.97, 1827.74, 
1786.68, 1831.09, 1825.75, 1788.19, 1746.17, 1825.5, 1790.37, 
1818.35, 1818.19, 1792.41, 1817.08, 1793.87, 1819.06, 1794.25, 
1797.18, 1818.26, 1815.02, 1814.11, 1815.84, 1799.14, 1813.09, 
1812.92, 1813.89, 1812.33, 1812.04, 1800.49, 1802.19, 1811.64, 
1804.87, 1811.4, 1813.42, 1752.03, 1809.08, 1808.67, 1807.37, 
1805.93, 1805.48, 1807.77, 1803.93, 1802.22, 1802.78, 1801.65, 
1802.62, 1802.5, 1752.67, 1800.97, 1813.63, 1800.5, 1815.28, 
1799.48, 1797.99, 1755.6, 1797.71, 1798.05, 1796.27, 1796.9, 
1794.06, 1792.36, 1792.99, 1790.65, 1791.16, 1789.92, 1789.94, 
1789.01, 1757.84, 1788.33, 1788.58, 1788.27, 1786.5, 1786.16, 
1785.88, 1785.58, 1784.27, 1763.94, 1784.82, 1768.21, 1768.01, 
1764.2, 1783.01, 1771.94, 1763.11, 1763.51, 1770.36, 1769.7, 
1765.57, 1777.21, 1776.14, 1776.69, 1770.34, 1775.5, 1775.05, 
1775.91, 1778.65, 1780.19, 1779.96, 1779.18, 1776.59, 1779.63, 
1778.05, 1777.26, 1761.97, 1762.44, 1764.13, 1766.15, 1767.69, 
1767.26, 1768.75, 1770.93, 1772.52, 1777.11, 1779.86, 1779.64, 
1779.34, 1917.73, 1917.71, 1923.29, 1912.43, 1922.86, 1923.71, 
1903.65, 1780.31, 1925.46, 1929, 1932.02, 1934.43, 1777.95, 1804.96, 
1807.93, 1938.6, 1902.78, 1802.99, 1810.59, 1939.48, 1801.73, 
1798.44, 1901, 1796.54, 1782.16, 1781.21, 1814.04, 1941.99, 1815.55, 
1794.75, 1818, 1897.76, 1792.72, 1944.83, 1791.25, 1896.75, 1819.75, 
1945.57, 1853.68, 1890.88, 1894.6, 1888.73, 1851.72, 1822.29, 
1890.96, 1886.88, 1849.91, 1784.11, 1945.47, 1856.43, 1848.56, 
1885.92, 1825.24, 1783.09, 1846.9, 1947.9, 1881.56, 1827.85, 
1832.55, 1880.35, 1830.48, 1844.54, 1843.07, 1859.73, 1835.88, 
1878.36, 1861.92, 1788.58, 1953.35, 1786.04, 1842.89, 1839.23, 
1875.58, 1788.51, 1864.77, 1957.86, 1786.62, 1872.43, 1869.94, 
1867.4, 1961.32, 1788.87, 1961.8, 1962.85, 1790.93, 1964.52, 
1975.17, 1977.23, 1973.22, 1972.71, 1978.95, 1791.88, 1791.47, 
1983.11, 1790.61, 1985.42, 1785.62, 1790.9, 1791.18, 1791.64, 
1987.16, 1792, 1990.31, 1788.24, 1791.68, 1791.59, 1793.23, 1993.54, 
1792.6, 1999.36, 1999.11, 1789.57, 1791.92, 1793.61, 2001.08, 
2010.03, 1790.75, 1794.05, 2011.14, 2014.25, 1791.73, 1794.82,2017.13, 1794.22, 2022.89, 2023.66, 1795.95, 1793.59, 1795.52, 
2027.24, 1799.63, 1797.86, 1798.08, 2033.89, 1795.03, 2034.61, 
2035.44, 1797.2, 1796.28, 2035.16, 1811.38, 1815.54, 2041.69, 
1796.7, 1815.21, 1812.67, 1796.2, 1814.42, 2044.94, 1816.37, 
1815.83, 2045.72, 1816.91, 1811.4, 1815.11, 1796.26, 1809.74, 
2049.19, 1797.83, 1808.23, 1818.27, 2057.36, 2072.06, 1801.35, 
2060.49, 2061.48, 1802.16, 2243.49, 1806.6, 1804, 2168.52, 2154.35, 
2158.78, 2234.3, 2168.46, 2173.64, 2146.41, 2230.64, 2075.03, 
2179.79, 2109.15, 2116.69, 2142.9, 2124.1, 2220.3, 2222.55, 1818.53, 
2216.72, 2196.56, 2179.52, 1824.68, 2192.8, 2098.23, 2129.92, 
2186.49, 2184.4, 2203.64, 2083.22, 2208.83, 2135.86, 2087.47, 
2131.31, 2205.24, 1821.12, 2083.4, 2131.92, 1821.53, 1821.77, 
1823.3, 1797.87, 1823.67, 1822.63, 1821.61, 2092.94, 1824.39, 
1824.59, 1828.08, 1829.39, 2096.16, 1828.28, 1828.44, 2100.71, 
1827.75, 1800.58, 2106.87, 1828.26, 2110.01, 2112.92, 1828.96, 
1801.75, 1831.11, 2119.06, 2119.9, 1831.43, 2120.19, 1802.65, 
1832.43, 1833.84, 1805.05, 2121.7, 1833.51, 1806.83, 2129.11, 
1809.04, 1810.34, 1833.15, 2132.54, 2135.95, 1810.58, 1834.28, 
2142.68, 1812.44, 2144.2, 1814.18, 1835.95, 2145.67, 1815.11, 
1818.33, 2149.61, 1837.32, 2153.75, 2157.44, 2169.83, 2174, 1838.69, 
1818.93, 2179.41, 1839.41, 1951.04, 1820.96, 2181.19, 1839.94, 
1941.84, 2196.77, 1821.99, 1940.25, 1840.09, 1932.06, 1938.69, 
1924.98, 1937.19, 1932.57, 1932.28, 1839.95, 1822.15, 1919.97, 
1840.47, 1919.86, 1841.51, 1823.52, 1917.86, 1843.54, 1825.24, 
1916.44, 1844.93, 1827.12, 1914.46, 1914.19, 1828.12, 1913.22, 
1827.88, 1846.16, 1829.38, 1832.26, 1848.55, 1907.12, 1906.78, 
1906.99, 1850.9, 1835.08, 1903.74, 1901.55, 1837.54, 1851.59, 
1898.61, 1840.15, 1897.77, 1851.68, 1852.35, 1852.33, 1896.24, 
1841.05, 1854.28, 1893.12, 1842.15, 1841.55, 1841.62, 1841.44, 
1856.49, 1891.74, 1843.09, 1890.18, 1845.1, 1888.84, 1870.77, 
1871.77, 1858.39, 1857, 1871.29, 1886.55, 1845.39, 1878.96, 1885.84, 
1845.45, 1880.05, 1879.16, 1857.02, 1850.36, 1867.19, 1862.37, 
1851.63, 1851.91, 1868.64, 1862.6, 1852.53, 1870.75, 1864.11, 
1852.46, 1864.66, 1853.31, 1852.88, 1871.04, 1853.86, 1865.5, 
1853.47, 1873.25, 1867.24, 1858.89, 1868.92, 1857.28, 1876.26, 
1870.66, 1858.34, 1877.39, 1871.34, 1859.81, 1878.99, 1871.35, 
1859.23, 1886.02, 1859.71, 1873.11, 1883.71, 1867.03, 1884.62, 
1877.96, 1863.53, 1888.45, 1876.56, 1863.37, 1888.76, 1881.78, 
1863.69, 1892.6, 1880.54, 1864.96, 1896.4, 1883.5, 1909.95, 1866.91
)

首先，我強制將 NDVI 限制在 0 和 1 之間，以便我可以使用 beta 分布

ndvi_corrected=(ndvi + 1)/2

然后我使用 mgcv 運行一個 gam

mod_el <- gam(ndvi_corrected ~ s(Elevation),
              family = betar(link='logit'), 
              data = ndvi)

我試圖繪制一個可解釋的圖，也就是說，y 軸具有 NDVI 值，這是我們根據模型預測“在地面上”所期望的值。 因此，y 軸應介於 -1 和 1 之間。這里我使用的是Plotting output of GAM model中的代碼。

preds <- predict(mod_el,se.fit=TRUE,data.frame(Elevation = Elevation))
summary((preds$fit+1)*2)
my_data <- data.frame(mu=preds$fit, low =(preds$fit - 1.96 * preds$se.fit), high = (preds$fit + 1.96 * preds$se.fit))

ggplot()+
  geom_point(data= my_data, aes(x= Elevation, y=ndvi_corrected), size = 1, alpha = 0.5)+
  geom_smooth(data=my_data,aes(ymin = low, ymax = high, x=Elevation, y = mu), stat = "identity", col="green")

所以我猜測（但很難說）上面的圖有 1. 從 logit 鏈接反向轉換 mu 和 2. 在預測中包括截距。

我需要的下一步是解除 mu 與 0,1 的綁定……也就是說，將其從 ndvi_corrected 狀態取回。 為此，我：

ggplot()+
  geom_point(data= my_data, aes(x= ndvi_noNA, y=ndvi), size = 1, alpha = 0.5)+
  geom_smooth(data=my_data,aes(ymin = ((low*2)-1), ymax = ((high*2)-1), x=ndvi_noNA, y = ((mu*2)-1)), stat = "identity", col="green")

但這似乎也說不通。

我的問題是：

1. 實際策划的第一個情節是什么？ 是包含截距的 mod_el 的反邏輯嗎？
2. 為什么第二個圖根據我在景觀上觀察到的初始 NDVI 值具有無意義的值？ 也就是說，我的整個數據集的 NDVI 值在 0.04 - 0.7 之間。 而 ((mu*2)-1)) 從-0.14到1.01，這沒有意義。
3. 與我的數據相比，為什么樣條曲線看起來很糟糕？ 好像膨脹了，應該多“壓扁”。

Answer 1

好的，我想我已經解決了所有問題，如果還有其他問題請告訴我。

我使用您提供的 1000 行數據創建了一個數據框（感謝您對其進行了更新），並將這兩個變量綁定到一個名為df的數據框中，然后為 Beta 回歸創建了介於 0 和 1 之間的更正變量。 然后我適合模型。

# Created data frame 
df <- data.frame(ndvi, Elevation)
# Transformed variable
df$ndvi_corrected <- (df$ndvi + 1)/2
# Fit model
mod_el <- gam(ndvi_corrected ~ s(Elevation),
              family = betar(link='logit'), 
              data = df)

然后你得到你的預測值，這些值在 logit 尺度上（我相信問題 #1 的答案），然后你調用預測值的 summary 我認為這是試圖撤銷你之前為創建ndvi_corrected所做的轉換，但它產生的價值遠高於它們應有的價值。

preds <- predict(mod_el,se.fit=TRUE,data.frame(Elevation = Elevation))
summary((preds$fit+1)*2)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.468   3.607   3.760   3.771   3.922   4.320 

原來的transformation是先加1再除以2，也就是說要撤銷，我們需要先乘以2，再減1。 但首先，我們需要將它們從 logit 尺度返回到 0 和 1 之間的有界變量，這意味着應用逆 logit。 下面這個函數是這樣做的：

backtransform <- function(x) {
  x = ((exp(x)/(1+exp(x)))*2)-1
  return(x)
}

summary(backtransform(preds$fit))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.3515  0.3815  0.4136  0.4152  0.4466  0.5226 

現在，如果我們使用原始未轉換的數據以及反向轉換的模型預測來創建您的圖，事情看起來非常合理。 我已經在此處修改了您的代碼，對預測值調用我的backtransform轉換函數以創建它們的第二個版本。

# Backtransforming predicted values
preds$fit2 <- backtransform(preds$fit)
preds$se.fit2 <- backtransform(preds$se.fit)

# Creating data frame of predicted values
my_data <- data.frame(mu=preds$fit2, low =(preds$fit2 - 1.96 * preds$se.fit2), high = (preds$fit2 + 1.96 * preds$se.fit2))

# Plotting the predicted values with original data
ggplot()+
  geom_point(data= df, aes(x= Elevation, y=ndvi), size = 1, alpha = 0.5)+
  geom_smooth(data=my_data,aes(ymin = low, ymax = high, x=Elevation, y = mu), stat = "identity", col="green")

所以我認為你的問題不是適當地反向轉換模型預測，這導致了所有其他的混亂。 我希望這個解決方案可以擴展並適用於完整的數據集。

順便說一句，我通常使用itsadug包繪制 GAMM。 函數plot_smooth有一個可選參數transform ，它允許您使用自定義函數轉換 y 軸，這樣您就可以使用我在繪圖調用中上面定義的函數。

# Define function that uses inverse logit and then back-transforms your original transformation

# Plot values back-transformed to original scale
plot_smooth(mod_el,
            view = "Elevation",
            transform = "backtransform")