R語言對(duì)回歸模型進(jìn)行協(xié)方差分析
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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Data = read.table(textConnection(Input),header=TRUE)
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plot(x ? = Data$Temp,y ? = Data$Pulse,col = Data$Species,pch = 16,xlab = "Temperature",ylab = "Pulse")legend('bottomright',legend = levels(Data$Species),col = 1:2,cex = 1,pch = 16)
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協(xié)方差分析
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Anova Table (Type II tests)Sum Sq Df ?F value ? ?Pr(>F)Temp ? ? ? ? 4376.1 ?1 1388.839 < 2.2e-16 ***Species ? ? ? 598.0 ?1 ?189.789 9.907e-14 ***Temp:Species ? ?4.3 ?1 ? ?1.357 ? ?0.2542### Interaction is not significant, so the slope across groups### is not different.model.2 = lm (Pulse ~ Temp + Species,data = Data)library(car)Anova(model.2, type="II")Anova Table (Type II tests)Sum Sq Df F value ? ?Pr(>F)Temp ? ? ?4376.1 ?1 ?1371.4 < 2.2e-16 ***Species ? ?598.0 ?1 ? 187.4 6.272e-14 ***### The category variable (Species) is significant,### so the intercepts among groups are differentCoefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) ?-7.21091 ? ?2.55094 ?-2.827 ?0.00858 **Temp ? ? ? ? ?3.60275 ? ?0.09729 ?37.032 ?< 2e-16 ***Speciesniv ?-10.06529 ? ?0.73526 -13.689 6.27e-14 ***### ? but the calculated results will be identical.### The slope estimate is the same.### The intercept for species 1 (ex) is (intercept).### The intercept for species 2 (niv) is (intercept) + Speciesniv.### This is determined from the contrast coding of the Species### variable shown below, and the fact that Speciesniv is shown in### coefficient table above.nivex ? ?0niv ? 1
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擬合線的簡(jiǎn)單圖解
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plot(x ? = Data$Temp,y ? = Data$Pulse,col = Data$Species,pch = 16,xlab = "Temperature",ylab = "Pulse")
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模型的p值和R平方
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Multiple R-squared: ?0.9896, ?Adjusted R-squared: ?0.9888F-statistic: ?1331 on 2 and 28 DF, ?p-value: < 2.2e-16
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檢查模型的假設(shè)
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線性模型中殘差的直方圖。這些殘差的分布應(yīng)近似正態(tài)。
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殘差與預(yù)測(cè)值的關(guān)系圖。殘差應(yīng)無偏且均等。?
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### additional model checking plots with: plot(model.2)### alternative: library(FSA); residPlot(model.2)
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具有三類和II型平方和的協(xié)方差示例分析
本示例使用II型平方和，并考慮具有三個(gè)組的情況。?
### --------------------------------------------------------------### Analysis of covariance, hypothetical data### --------------------------------------------------------------Data = read.table(textConnection(Input),header=TRUE)
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plot(x ? = Data$Temp,y ? = Data$Pulse,col = Data$Species,pch = 16,xlab = "Temperature",ylab = "Pulse")legend('bottomright',legend = levels(Data$Species),col = 1:3,cex = 1,pch = 16)
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協(xié)方差分析
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options(contrasts = c("contr.treatment", "contr.poly"))### These are the default contrasts in RAnova(model.1, type="II")Sum Sq Df ? F value Pr(>F)Temp ? ? ? ? 7026.0 ?1 2452.4187 <2e-16 ***Species ? ? ?7835.7 ?2 1367.5377 <2e-16 ***Temp:Species ? ?5.2 ?2 ? ?0.9126 0.4093### Interaction is not significant, so the slope among groups### is not different.Anova(model.2, type="II")Sum Sq Df F value ? ?Pr(>F)Temp ? ? ?7026.0 ?1 ?2462.2 < 2.2e-16 ***Species ? 7835.7 ?2 ?1373.0 < 2.2e-16 ***Residuals ?125.6 44### The category variable (Species) is significant,### so the intercepts among groups are differentsummary(model.2)Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) ?-6.35729 ? ?1.90713 ?-3.333 ?0.00175 **Temp ? ? ? ? ?3.56961 ? ?0.07194 ?49.621 ?< 2e-16 ***Speciesfake ?19.81429 ? ?0.66333 ?29.871 ?< 2e-16 ***Speciesniv ?-10.18571 ? ?0.66333 -15.355 ?< 2e-16 ***### The slope estimate is the Temp coefficient.### The intercept for species 1 (ex) is (intercept).### The intercept for species 2 (fake) is (intercept) + Speciesfake.### The intercept for species 3 (niv) is (intercept) + Speciesniv.### This is determined from the contrast coding of the Species### variable shown below.contrasts(Data$Species)fake nivex ? ? ?0 ? 0fake ? ?1 ? 0niv ? ? 0 ? 1
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擬合線的簡(jiǎn)單圖解
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組合模型的p值和R平方
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Multiple R-squared: ?0.9919, ?Adjusted R-squared: ?0.9913F-statistic: ?1791 on 3 and 44 DF, ?p-value: < 2.2e-16
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檢查模型的假設(shè)
hist(residuals(model.2),col="darkgray")
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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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plot(fitted(model.2),residuals(model.2))
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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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### additional model checking plots with: plot(model.2)### alternative: library(FSA); residPlot(model.2)
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拓端研究室?拓端數(shù)據(jù)?編輯
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