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r - R中具有空间自相关的GAMM

问题描述

据我了解，GAMM 具有随机误差或空间自相关误差结构。

我正在尝试运行具有空间自相关错误结构的 GAMM 模型，例如 corExp（请参阅https://stat.ethz.ch/R-manual/R-devel/library/nlme/html/corClasses.html）。

但是我对从 GAM 建模 GAMM 感到困惑。

下面是我的 GAM（广义加法模型）代码。

library(mgcv)
mod.gam <- gam(Chave~s(Band_3) + s(Band_7) + s(Band_8) + s(BaCo_3_2) + s(BaCo_5_2) + 
  s(BaCo_5_3) + s(BaCo_5_4) + s(BaCo_8_2) + s(BaCo_8A_2),data = data)
summary(mod.gam)
fits = predict(mod.gam, newdata=data, type='response')
plot(data$Chave, fits, col='blue', ylab = "Predicted AGB KNN", xlab = "Estimated AGB")
plot(mod.gam)

如何将其更改为 GAMM？当我尝试使用 GAMM（如下所述）时，我没有看到太大的变化：

model <- gamm(Chave~s(Band_3) + s(Band_7) + s(Band_8) + s(BaCo_3_2) +
 s(BaCo_5_2) + s(BaCo_5_3) + s(BaCo_5_4) + s(BaCo_8_2) + s(BaCo_8A_2),
 data = data, correlation=corExp(1,form = ~ Latitude + Longitude)))
summary(model$gam)
plot(model$gam,pages=1)

据我了解，空间自相关函数应该以纬度和经度作为输入。我做得对吗？GAMM 的输出与 GAM 的输出有何不同？

不同型号的输出：

model.gamm <- gamm(Chave~s(Band_3) + s(Band_7) + s(Band_8) + s(BaCo_3_2) + s(BaCo_5_2) + 
       s(BaCo_5_3) + s(BaCo_5_4) + s(BaCo_8_2) + s(BaCo_8A_2), data = data, 
       correlation=corSpher(form = ~ Latitude + Longitude))
summary(model.gam$lme)

[Output]:
Linear mixed-effects model fit by maximum likelihood
 Data: strip.offset(mf) 
       AIC      BIC    logLik
  1176.797 1232.729 -567.3985
Correlation Structure: Spherical spatial correlation
 Formula: ~Latitude + Longitude | g/g.0/g.1/g.2/g.3/g.4/g.5/g.6/g.7 
 Parameter estimate(s):
      range 
0.003845795 
Fixed effects: y ~ X - 1 
                      Value Std.Error DF   t-value p-value
X(Intercept)      125.44208   5.23505 96 23.961953  0.0000
Xs(Band_3)Fx1      95.48991  38.42171 96  2.485311  0.0147
Xs(Band_7)Fx1     -17.69103  40.27462 96 -0.439260  0.6615
Xs(Band_8)Fx1     -84.45737  60.83131 96 -1.388386  0.1682
Xs(BaCo_3_2)Fx1  -183.67952 179.22609 96 -1.024848  0.3080
Xs(BaCo_5_2)Fx1   111.84971 266.21261 96  0.420152  0.6753
Xs(BaCo_5_3)Fx1   -46.55365 131.32239 96 -0.354499  0.7237
Xs(BaCo_5_4)Fx1   -10.57644   9.59420 96 -1.102378  0.2731
Xs(BaCo_8_2)Fx1    76.30654  52.36900 96  1.457094  0.1484
Xs(BaCo_8A_2)Fx1   35.37155  39.34172 96  0.899085  0.3709

#########################

model.gam <- gamm(Chave~s(Band_3) + s(Band_7) + s(Band_8) + s(BaCo_3_2) + 
s(BaCo_5_2) + s(BaCo_5_3) + s(BaCo_5_4) + s(BaCo_8_2) + s(BaCo_8A_2), data = data)
summary(model.gamm$lme)

[Output]:
Linear mixed-effects model fit by maximum likelihood
 Data: strip.offset(mf) 
       AIC      BIC   logLik
  1177.106 1230.375 -568.553
Fixed effects: y ~ X - 1 
                      Value Std.Error DF   t-value p-value
X(Intercept)      123.71814   4.94795 96 25.003936  0.0000
Xs(Band_3)Fx1     102.63429  38.76940 96  2.647301  0.0095
Xs(Band_7)Fx1     -26.65351  42.00784 96 -0.634489  0.5273
Xs(Band_8)Fx1     -81.96547  61.57940 96 -1.331053  0.1863
Xs(BaCo_3_2)Fx1  -312.47086 191.52784 96 -1.631464  0.1061
Xs(BaCo_5_2)Fx1   283.77313 280.17983 96  1.012825  0.3137
Xs(BaCo_5_3)Fx1  -126.82534 139.08953 96 -0.911825  0.3641
Xs(BaCo_5_4)Fx1   -11.82504   9.69256 96 -1.220012  0.2254
Xs(BaCo_8_2)Fx1    78.95786  52.86484 96  1.493580  0.1386
Xs(BaCo_8A_2)Fx1   38.03149  40.01424 96  0.950449  0.3443

##############################

mod.gam.gam <- gam(Chave~s(Band_3) + s(Band_7) + s(Band_8) + s(BaCo_3_2) + s(BaCo_5_2) + 
+   s(BaCo_5_3) + s(BaCo_5_4) + s(BaCo_8_2) + s(BaCo_8A_2),data = data)
summary(mod.gam.gam)

[Output]:
Family: gaussian 
Link function: identity 

Formula:
Chave ~ s(Band_3) + s(Band_7) + s(Band_8) + s(BaCo_3_2) + s(BaCo_5_2) + 
    s(BaCo_5_3) + s(BaCo_5_4) + s(BaCo_8_2) + s(BaCo_8A_2)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  123.718      4.155   29.78   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
               edf Ref.df     F p-value  
s(Band_3)    1.000  1.000 1.125  0.2922  
s(Band_7)    5.854  6.945 2.419  0.0268 *
s(Band_8)    4.130  5.210 2.989  0.0143 *
s(BaCo_3_2)  4.724  5.694 3.128  0.0113 *
s(BaCo_5_2)  2.628  3.431 1.449  0.2275  
s(BaCo_5_3)  2.614  3.262 2.713  0.0530 .
s(BaCo_5_4)  4.441  5.454 1.045  0.4176  
s(BaCo_8_2)  1.000  1.000 1.144  0.2881  
s(BaCo_8A_2) 3.373  4.250 1.077  0.3394  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.445   Deviance explained = 60.2%
GCV = 2578.1  Scale est. = 1829.9    n = 106

标签： rspatialgamautocorrelation

解决方案

你是，我想，叫corExp()错了。你用：

corExp(1, form = ~ Latitude + Longitude)

这是将指数相关函数中的相关参数的值固定为固定值，1而不是从数据中估计，这可以通过使用来实现

corExp(form = ~ Latitude + Longitude)

如果来自 GAM gam()（通过平均结构。

如果要查看包含相关函数效应的残差gamm()，则需要使用：

resid(model$lme, type = "normalized")

另外，如果你想比较一个有结构和没有结构的模型，你需要在模型anova()的$lme组件上使用，因此你需要使用 重新gam()拟合模型gamm()，只需留下correlation部分。然后anova(mod1$lme, mod2$lme)将为您提供指数相关函数中参数的广义似然比检验。

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