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， 

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

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)

协方差分析

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

拟合线的简单图解

plot(x   = Data$Temp, y   = Data$Pulse, col = Data$Species, pch = 16,xlab = "Temperature",ylab = "Pulse")

模型的p值和R平方

Multiple R-squared:  0.9896,  Adjusted R-squared:  0.9888F-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。 

### additional model checking plots with: plot(model.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。 

### --------------------------------------------------------------
### Analysis of covariance, hypothetical data
### --------------------------------------------------------------Data = read.table(textConnection(Input),header=TRUE)

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)

协方差分析

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

拟合线的简单图解

组合模型的p值和R平方

Multiple R-squared:  0.9919,  Adjusted R-squared:  0.9913F-statistic:  1791 on 3 and 44 DF,  p-value: < 2.2e-16

检查模型的假设

hist(residuals(model.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。

plot(fitted(model.2), residuals(model.2))

残差与预测值的关系图。残差应无偏且均等。 

 ### additional model checking plots with: plot(model.2)
### alternative: library(FSA); residPlot(model.2)