R-GAM回归（mgcv）响应曲线在添加新变量时会更改形状/方向

Question

我正在使用GAM（使用mgcv软件包）来查看一种生物相对于几种环境变量的丰度变化。

我的数据如下：

library(tidyverse)

Station abd Temperature Oxygen  Salinity
crossing_01_st02    343.199 10.880389   222.62732   33.24007
crossing_01_st03    3427.2116   9.896878    170.52723   33.60561
crossing_01_st04    2091.7223   10.325418   146.88088   33.71725
crossing_01_st05    3365.6303   10.447803   152.83051   33.71425
crossing_01_st06    4895.5442   10.858568   168.23048   33.68162
crossing_01_st07    4785.7697   10.221149   142.10408   33.75456
crossing_01_st08    4739.7415   10.307083   139.84557   33.78507
crossing_01_st10    3930.383    9.624018    123.82912   33.81374
crossing_01_st11    5710.4398   9.513673    124.79245   33.80772
crossing_01_st12    8213.8983   9.314383    122.80188   33.83794
crossing_01_st13    6175.7285   9.268011    135.29098   33.83685
crossing_02_st01    5952.9914   9.055155    95.48518    33.9358
crossing_02_st03    2696.3755   9.335852    116.52235   33.85236
crossing_02_st04    4072.1314   9.754846    138.25631   33.77391
crossing_02_st05    2394.5551   9.597139    128.31808   33.77155
crossing_02_st06    1744.0551   9.774439    149.00231   33.65033
crossing_02_st07    1427.5309   9.535947    176.11583   33.54753
crossing_02_st08    541.8052    10.005704   197.96463   33.40531
crossing_02_st09    173.3703    10.205607   206.16945   33.36126
crossing_02_st10    456.3426    10.622767   221.5186    33.26646
cycle_01_cast01 6823.9262   9.786862    116.12442   33.85257
cycle_01_cast02 7400.7068   9.785606    120.85602   33.83325
cycle_01_cast03 5343.2857   10.158589   139.62563   33.77581
cycle_01_cast04 5561.953    9.689744    139.47995   33.76726
cycle_01_cast05 6855.6716   9.267254    138.03602   33.79975
cycle_01_cast06 6859.4645   9.791765    134.7162    33.76183
cycle_02_cast01 330.9797    10.746551   208.04335   33.33226
cycle_02_cast03 231.1604    10.616365   209.49808   33.31173
cycle_02_cast04 544.3918    10.565562   205.8037    33.34717
cycle_02_cast05 235.6214    10.38223    197.70585   33.39902
cycle_02_cast07 182.0388    10.540305   208.21308   33.33308
cycle_02_cast08_2   1187.5021   10.414415   201.71851   33.37685
cycle_02_cast09 1656.9597   9.978496    186.95632   33.48471
cycle_03_cast01 4816.7298   9.416381    100.71815   33.90358
cycle_03_cast02 5514.5958   9.427468    101.28535   33.90143
cycle_03_cast03 4436.9845   9.528815    107.20829   33.88003
cycle_03_cast04 5334.6542   9.40963 117.85671   33.82466
cycle_03_cast05 8826.6174   9.410874    116.09786   33.82881
cycle_03_cast06 8792.56 9.257086    111.92037   33.84714
cycle_03_cast08 8110.7264   9.372722    123.3256    33.82041
cycle_04_cast01 211.0595    11.554293   230.22028   33.20413
cycle_04_cast04 179.7914    11.197575   225.20708   33.23228
cycle_04_cast05 166.5575    11.393151   226.56168   33.21736
cycle_04_cast06 147.1021    11.379475   228.57757   33.20565
cycle_04_cast07 138.6963    11.339498   226.59277   33.21873
cycle_05_cast01 617.0933    10.538117   195.79625   33.49209
cycle_05_cast02 763.2103    9.854859    181.83223   33.50503
cycle_05_cast03 1454.6652   10.719085   208.2208    33.40604
cycle_05_cast04 940.1714    10.695348   211.12725   33.35623
cycle_05_cast05 984.9135    11.114098   214.13466   33.42644
p1408_008   429.6539    9.955556    117.60191   33.79807
p1408_009   551.5781    10.109037   129.78458   33.71664
p1408_010   1090.7607   10.096017   139.46102   33.64799
p1408_011   1008.6421   9.773443    121.056 33.7683
p1408_012   1018.451    10.009549   127.55012   33.72919
p1408_013   1478.1  9.837543    132.82643   33.71031
p1408_014   634.3147    9.171992    143.98665   33.69484
p1408_019   1261.4535   9.925149    144.02358   33.66018
p1408_020   895.1759    10.281067   157.89194   33.57496
p1408_021   894.1513    9.941134    137.3812    33.70525
p1408_022   1013.2815   10.012316   133.53466   33.71364
p1408_023   1465.2027   9.998437    132.7186    33.72103
p1408_024   1387.3383   10.023705   133.01306   33.70337
p1408_025   1131.3854   9.798109    126.38143   33.77076
p1408_026   1920.4206   9.796771    124.29865   33.78191
p1408_027   1518.2211   9.706037    115.40608   33.83985
p1408_028   1351.4425   9.71432 115.06117   33.83702
p1408_029   1776.763    9.819473    123.35006   33.7771
p1408_032   169.5453    9.601247    182.55748   33.46663
p1408_033   185.7481    9.459888    188.18871   33.44482
p1408_034   533.2673    9.805629    167.51825   33.50092
p1408_035   918.7359    9.430061    180.51512   33.49057
p1408_036   257.1976    9.674115    171.3   33.51555
p1408_037   905.7629    9.676409    171.52495   33.49375
p1408_038   867.7851    9.408992    161.45491   33.59505
p1408_039   597.6163    9.68413 188.2719    33.4009
p1408_040   1785.0849   9.474682    170.19411   33.54021
p1408_041   668.1221    9.448858    177.52229   33.506
p1408_051   166.1487    10.980822   216.65745   33.16259
p1408_056   106.383 11.867383   228.92551   33.0945
p1408_058   226.3468    12.124444   228.97567   33.08706
p1604_02    2527.2334   12.074301   199.61586   33.28931
p1604_03    3380.0072   11.922921   195.74938   33.30905
p1604_05    3675.7893   11.671741   188.88949   33.33841
p1604_09    3453.929    11.735068   190.83477   33.34591
p1604_10    1189.6463   12.264773   218.65712   33.18436
p1604_11    1196.9789   12.450878   220.982 33.1585
p1604_12    2027.3274   11.793328   210.32928   33.21888
p1604_13    1441.1081   12.653082   222.26812   33.17408
p1604_14    963.5869    12.326745   219.86165   33.17834
p1604_15    1613.0636   12.393148   219.8886    33.14464
p1604_16    658.4892    12.750862   223.2642    33.14848
p1604_17    1309.0813   12.471335   221.47351   33.15247
p1604_18    1354.5372   12.216455   218.88083   33.12412
p1604_19    1434.5431   12.657842   221.77662   33.1185
p1604_20    1062.6206   12.322844   220.29652   33.14848
p1604_21    1941.8302   12.782927   224.20348   33.089
p1604_23    3401.0905   10.280862   182.66022   33.51492
p1604_24    3502.4929   9.71893 163.12155   33.5462
p1604_25    4742.5206   9.772787    158.93855   33.55103
p1604_26    5364.7968   9.767572    151.34155   33.62338
p1604_27    3940.3145   9.472281    165.1516    33.6148
p1604_29    5670.4874   9.677677    169.85598   33.54579
p1604_30    4986.9538   9.987309    180.425 33.50413
p1604_33    5215.7347   9.530931    170.52985   33.57246
p1604_36    3154.6535   9.472636    110.74072   33.86774
p1604_37    3598.488    9.155606    101.19137   33.93614
p1604_38    3733.3041   9.238361    109.37808   33.87358
p1604_39    3777.4703   9.34017 112.88268   33.84185
p1604_40    4474.8835   9.165892    108.03168   33.88497
p1604_42    4838.1334   8.980138    109.30434   33.89938
p1604_43    4931.4312   8.925082    107.71142   33.91524
p1604_45    6332.5305   8.927316    111.68705   33.88828

在运行GAM之前，我进行了简单的图形检查，以查看我的丰度如何随变量而变化。使用ggplot，代码如下所示：

df %>%
  gather(variable, value, -Station, -abd) %>%
  ggplot(aes(x = value, y = abd)) +
  geom_point() +
  stat_smooth(aes(color = "lm"), method = "lm", geom = 'line') +
  stat_smooth(aes(color = "gam"), method = "gam",  formula = y ~ s(x),geom = 'line') +
  scale_y_log10() +
  facet_wrap(~variable, scales = "free_x") +
  theme_bw()

并提供以下图表：

在这里我可以看到每个变量的趋势。例如，我可以看到我的丰度似乎随着温度的升高而降低，或者随着氧气的增加而出现单调的丰度降低。

- 现在，在运行GAM时，我遇到了一些奇怪的反应。 乍一看，我将像这样运行GAM：

library(mgcv)

df.gam <- gam(log10(abd) ~ s(Oxygen) + s(Temperature) + s(Salinity), data = df, method = "REML")

输出告诉我，所有三个变量均具有显着影响，并且总共可以解释74％的偏差。 但是，当我绘制响应曲线（使用图或此处使用visreg）时，它会出现“问题”

library(visreg)

visreg(df.gam, scale = "response", rug = F, line = list(lwd = 1))

现在，曲线的行为与ggplot和stat_smooth输出完全不同（即使没有stat_smooth，我也可以说预测的曲线不适合数据？？

为了增加复杂性，如果我逐个对每个变量运行单变量GAM并查看它们的响应曲线，则它们实际上与ggplot输出一致。

这种差异是否是由于GAM的累加性质造成的，例如，如果我加上氧气或盐度的影响，我的丰度对温度的响应会有所不同（基本上是从减少到增加...）？

这是GAM函数的某种奇怪响应吗？

Answer 1

撤消了我的密切投票。在显示变量和氧气之间令人费解的关系的两个变量上使用te()函数，并在结果上调用plot.gam，这样相互作用就可以不是线性的。

df.gam <- gam(log10(abd) ~ te(Oxygen, Temperature) + s(Salinity), data = df,
                method = "REML")

#-----
> ?plot.gam
> plot(df.gam)
Hit <Return> to see next plot: 

Hit <Return> to see next plot:

O ₂ 和温度都可以促进生长或丰度，但是氧气在液态水中的溶解度与温度成反比，因此这种关系似乎是合理的。