风机参数对风速影响分析的可视化矛盾问题咨询

数据集与初始模型 #

数据集来自Dryad平台，DOI: 10.5061/dryad.vx0k6djxg。初始构建的线性模型如下：

mod4= lm(wind_speed~turbine_distance* rotor_size *tower_height+ 
           turbine_operation_bin+number_turbines, data = d2)

逐步简化后的模型汇总结果 #

逐步删除非显著项后，模型汇总输出如下：

Estimate Std. Error t value Pr(>|t|)
(Intercept)                8.089e+00  1.943e+00   4.164 3.16e-05 ***
rotor_size                -1.117e-01  1.780e-02  -6.274 3.67e-10 ***
tower_height              -1.565e-02  1.005e-02  -1.557     0.12    
turbine_operation_binTRUE  5.126e-01  1.264e-02  40.558  < 2e-16 ***
number_turbines            7.961e-02  5.357e-03  14.860  < 2e-16 ***
rotor_size:tower_height    3.962e-04  9.111e-05   4.348 1.39e-05 ***

对结果的解释：rotor_size每增加1米，地面以上10米处的wind_speed会降低0.1117±0.0178 m/s（p=3.67e-10）；且tower_height每增加1米，该降低幅度会减缓0.0003962±0.00009111 m/s（p=1.39e-05）。

塔筒高度分组后的矛盾问题 #

为进一步分析，将连续变量tower_height按样本前后50%分为“short（矮）”和“tall（高）”两组，处理代码与新模型如下：

d3 <- d2 %>% mutate(tower_height = 
    case_when(tower_height<-floor(0.5*(nrow(d2))) ~'short',
              tower_height<-ceiling(0.5*(nrow(d2)))~'tall')
d3$tower_height = as.factor(d3$tower_height)
mod5= lm(wind_speed~turbine_distance*rotor_size*tower_height+ 
           turbine_operation_bin+number_turbines, data = d3)
summary(mod5)

模型系数输出：

Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                   2.216e+00  2.985e-01   7.424 1.24e-13 ***
turbine_distance                              9.164e-04  1.113e-03   0.823  0.41042    
rotor_size                                   -7.813e-03  2.825e-03  -2.766  0.00568 ** 
tower_heighttall                              4.095e+00  4.660e-01   8.787  < 2e-16 ***
turbine_operation_binTRUE                     5.631e-01  1.282e-02  43.941  < 2e-16 ***
number_turbines                               6.409e-02  5.421e-03  11.822  < 2e-16 ***
turbine_distance:rotor_size                  -1.009e-05  1.045e-05  -0.966  0.33416    
turbine_distance:tower_heighttall            -2.294e-03  1.743e-03  -1.317  0.18804    
rotor_size:tower_heighttall                  -3.459e-02  4.095e-03  -8.445  < 2e-16 ***
turbine_distance:rotor_size:tower_heighttall  2.196e-05  1.533e-05   1.433  0.15185

随后绘制可视化图表：

ggplot(data=d3, aes(x=rotor_size, y=wind_speed)) + geom_point(aes(colour=tower_height)) + geom_smooth(method=lm, aes(colour=tower_height))

生成的图表显示：tower_height为“tall（高）”时，wind_speed随rotor_size的下降速率更快；但模型汇总结果却显示塔筒高度升高会减缓下降幅度，两者存在矛盾。目前不清楚问题出在哪里，也不确定该图表是否适合用于汇报。

内容的提问来源于stack exchange，提问作者user24217668