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R語言對(duì)回歸模型進(jìn)行協(xié)方差分析

2021-03-02 22:31 作者:拓端tecdat  | 我要投稿

原文鏈接：http://tecdat.cn/?p=9529

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目錄

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怎么做測(cè)試

協(xié)方差分析

擬合線的簡(jiǎn)單圖解

模型的p值和R平方

檢查模型的假設(shè)

具有三類和II型平方和的協(xié)方差示例分析

協(xié)方差分析

擬合線的簡(jiǎn)單圖解

組合模型的p值和R平方

檢查模型的假設(shè)

怎么做測(cè)試

具有兩個(gè)類別和II型平方和的協(xié)方差示例的分析

本示例使用II型平方和 。參數(shù)估計(jì)值在R中的計(jì)算方式不同，?

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

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  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)

?

?

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協(xié)方差分析

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  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

?

?

擬合線的簡(jiǎn)單圖解

?


  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

?

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  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

?

?

檢查模型的假設(shè)

?

?

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線性模型中殘差的直方圖。這些殘差的分布應(yīng)近似正態(tài)。

?

?

?

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殘差與預(yù)測(cè)值的關(guān)系圖。殘差應(yīng)無偏且均等。?

?

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

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

?

具有三類和II型平方和的協(xié)方差示例分析

本示例使用II型平方和，并考慮具有三個(gè)組的情況。?

  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)

?

?

?

協(xié)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

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擬合線的簡(jiǎn)單圖解

?

?

?

組合模型的p值和R平方

?

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  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

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?

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檢查模型的假設(shè)

  1. hist(residuals(model.2),

  2. col="darkgray")

?

?

線性模型中殘差的直方圖。這些殘差的分布應(yīng)近似正態(tài)。

?

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  1. plot(fitted(model.2),

  2. residuals(model.2))

?

?

殘差與預(yù)測(cè)值的關(guān)系圖。殘差應(yīng)無偏且均等。?

?

?



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

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



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拓端研究室?拓端數(shù)據(jù)?編輯

拓端(http://tecdat.cn )創(chuàng)立于2016年，自成立以來，就定位為提供專業(yè)的統(tǒng)計(jì)分析與數(shù)據(jù)挖掘服務(wù)的提供商，致力于充分挖掘數(shù)據(jù)的價(jià)值，為客戶定制個(gè)性化的數(shù)據(jù)方案與報(bào)告等。
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