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R语言对回归模型进行协方差分析

2021-03-02 22:31 作者:拓端tecdat  | 我要投稿

原文链接：http://tecdat.cn/?p=9529

 

目录

 

怎么做测试

协方差分析

拟合线的简单图解

模型的p值和R平方

检查模型的假设

具有三类和II型平方和的协方差示例分析

协方差分析

拟合线的简单图解

组合模型的p值和R平方

检查模型的假设

怎么做测试

具有两个类别和II型平方和的协方差示例的分析

本示例使用II型平方和 。参数估计值在R中的计算方式不同， 

 



  3. Data = read.table(textConnection(Input),header=TRUE)

 

 

 

  1. plot(x   = Data$Temp,

  2. y   = Data$Pulse,

  3. col = Data$Species,

  4. pch = 16,

  5. xlab = "Temperature",

  6. ylab = "Pulse")


  8. legend('bottomright',

  9. legend = levels(Data$Species),

  10. col = 1:2,

  11. cex = 1,

  12. pch = 16)

 

 

 

协方差分析

 





  5. Anova Table (Type II tests)




  9. Sum Sq Df  F value    Pr(>F)


  11. Temp         4376.1  1 1388.839 < 2.2e-16 ***


  13. Species       598.0  1  189.789 9.907e-14 ***


  15. Temp:Species    4.3  1    1.357    0.2542




  19. ### Interaction is not significant, so the slope across groups


  21. ### is not different.






  27. model.2 = lm (Pulse ~ Temp + Species,

  28. data = Data)


  30. library(car)


  32. Anova(model.2, type="II")




  36. Anova Table (Type II tests)




  40. Sum Sq Df F value    Pr(>F)


  42. Temp      4376.1  1  1371.4 < 2.2e-16 ***


  44. Species    598.0  1   187.4 6.272e-14 ***




  48. ### The category variable (Species) is significant,


  50. ### so the intercepts among groups are different






  56. Coefficients:


  58. Estimate Std. Error t value Pr(>|t|)


  60. (Intercept)  -7.21091    2.55094  -2.827  0.00858 **


  62. Temp          3.60275    0.09729  37.032  < 2e-16 ***


  64. Speciesniv  -10.06529    0.73526 -13.689 6.27e-14 ***





  69. ###   but the calculated results will be identical.


  71. ### The slope estimate is the same.


  73. ### The intercept for species 1 (ex) is (intercept).


  75. ### The intercept for species 2 (niv) is (intercept) + Speciesniv.


  77. ### This is determined from the contrast coding of the Species


  79. ### variable shown below, and the fact that Speciesniv is shown in


  81. ### coefficient table above.






  87. niv


  89. ex    0


  91. niv   1

 

 

拟合线的简单图解

 


  2. plot(x   = Data$Temp,

  3. y   = Data$Pulse,

  4. col = Data$Species,

  5. pch = 16,

  6. xlab = "Temperature",

  7. ylab = "Pulse")

 

模型的p值和R平方

 

 



  3. Multiple R-squared:  0.9896,  Adjusted R-squared:  0.9888


  5. F-statistic:  1331 on 2 and 28 DF,  p-value: < 2.2e-16

 

 

检查模型的假设

 

 

 

线性模型中残差的直方图。这些残差的分布应近似正态。

 

 

 

 

残差与预测值的关系图。残差应无偏且均等。 

 

 

  1. ### additional model checking plots with: plot(model.2)

  2. ### alternative: library(FSA); residPlot(model.2)

 

具有三类和II型平方和的协方差示例分析

本示例使用II型平方和，并考虑具有三个组的情况。 

  1. ### --------------------------------------------------------------

  2. ### Analysis of covariance, hypothetical data

  3. ### --------------------------------------------------------------



  6. Data = read.table(textConnection(Input),header=TRUE)

 

 

 

 

  1. plot(x   = Data$Temp,

  2. y   = Data$Pulse,

  3. col = Data$Species,

  4. pch = 16,

  5. xlab = "Temperature",

  6. ylab = "Pulse")


  8. legend('bottomright',

  9. legend = levels(Data$Species),

  10. col = 1:3,

  11. cex = 1,

  12. pch = 16)

 

 

 

协方差分析

 

  1. options(contrasts = c("contr.treatment", "contr.poly"))


  3. ### These are the default contrasts in R



  6. Anova(model.1, type="II")




  10. Sum Sq Df   F value Pr(>F)


  12. Temp         7026.0  1 2452.4187 <2e-16 ***


  14. Species      7835.7  2 1367.5377 <2e-16 ***


  16. Temp:Species    5.2  2    0.9126 0.4093




  20. ### Interaction is not significant, so the slope among groups


  22. ### is not different.








  30. Anova(model.2, type="II")




  34. Sum Sq Df F value    Pr(>F)


  36. Temp      7026.0  1  2462.2 < 2.2e-16 ***


  38. Species   7835.7  2  1373.0 < 2.2e-16 ***


  40. Residuals  125.6 44




  44. ### The category variable (Species) is significant,


  46. ### so the intercepts among groups are different






  52. summary(model.2)




  56. Coefficients:


  58. Estimate Std. Error t value Pr(>|t|)


  60. (Intercept)  -6.35729    1.90713  -3.333  0.00175 **


  62. Temp          3.56961    0.07194  49.621  < 2e-16 ***


  64. Speciesfake  19.81429    0.66333  29.871  < 2e-16 ***


  66. Speciesniv  -10.18571    0.66333 -15.355  < 2e-16 ***




  70. ### The slope estimate is the Temp coefficient.


  72. ### The intercept for species 1 (ex) is (intercept).


  74. ### The intercept for species 2 (fake) is (intercept) + Speciesfake.


  76. ### The intercept for species 3 (niv) is (intercept) + Speciesniv.


  78. ### This is determined from the contrast coding of the Species


  80. ### variable shown below.






  86. contrasts(Data$Species)




  90. fake niv


  92. ex      0   0


  94. fake    1   0


  96. niv     0   1

 

拟合线的简单图解

 

 

 

组合模型的p值和R平方

 

 




  4. Multiple R-squared:  0.9919,  Adjusted R-squared:  0.9913


  6. F-statistic:  1791 on 3 and 44 DF,  p-value: < 2.2e-16

 

 

 

检查模型的假设

  1. hist(residuals(model.2),

  2. col="darkgray")

 

 

线性模型中残差的直方图。这些残差的分布应近似正态。

 

 

  1. plot(fitted(model.2),

  2. residuals(model.2))

 

 

残差与预测值的关系图。残差应无偏且均等。 

 

 



  3. ### additional model checking plots with: plot(model.2)

  4. ### alternative: library(FSA); residPlot(model.2)



 

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