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如何作 " 协方差分析 (ANCOVA)" 之 R (或 RStudio)应用篇
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简单应用来说，协方差分析 (ANCOVA) 就是在R语言中表达为y~x+/*y0，其中因变量y，协变量y0，自变量x。然后，开始写代码咯
> data.of.Wada2013.practice <- read.csv("~data of Wada2013 practice.csv")
> View(data.of.Wada2013.practice)
> eco<-data.of.Wada2013.practice
> eco
site d13C d15N
1 1 -28.40 4.05
2 1 -26.90 6.70
3 1 -25.90 7.30
4 1 -25.85 7.85
5 1 -25.60 9.90
6 1 -26.35 10.30
7 1 -26.25 10.70
8 1 -26.55 12.20
9 1 -26.60 12.65
10 1 -26.50 13.25
11 1 -26.40 13.70
12 1 -24.90 14.10
13 2 -24.00 9.02
14 2 -23.50 11.80
15 2 -22.71 15.78
16 2 -22.10 15.10
17 2 -20.50 14.00
18 2 -19.75 17.30
19 2 -20.35 17.95
20 3 -23.80 3.95
21 3 -23.50 4.80
22 3 -23.80 5.20
23 3 -23.70 6.10
24 3 -22.80 6.95
25 3 -21.95 7.10
> attach(eco)
>sitef<-factor(eco$site)
> #Step1: ANCOVA with InterAction
> mod.IA<-aov(d15N~d13C*sitef,data=eco, contrasts=list(sitef=contr.sum))
#aov() function, "contr.sum" for factor "sitef"(not numerical "site")
> summary(mod.IA) ??? # this summary is wroooong, it's for type I , not type III, don't do this!
> library(car)
> Anova(mod.IA,type=3) # this is riiiiight. Anova() function, not anova
>Anova Table (Type III tests)
Response: d15N
Sum Sq Df F value Pr(>F)
(Intercept) 70.098 1 13.0456 0.001858 **
d13C 43.563 1 8.1073 0.010302 *
sitef 3.341 2 0.3109 0.736451
d13C:sitef 1.771 2 0.1648 0.849262
Residuals 102.093 19
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# covariate d13C is significantly differ with d15N ( p = 0.001858),
and interation of d13C:sitef is not significantly differ ( p = 0.849262 ),
------->
then we can proceed ANCOVA next.
> # Step2: then ANCOVA NonInterAction, for equal slope, type III
> mod.NIA<-aov(d15N~d13C+sitef,data=eco,contrasts = list(sitef=contr.sum))
> Anova(mod.NIA, type=3)
Anova Table (Type III tests)
Response: d15N
Sum Sq Df F value Pr(>F)
(Intercept) 117.10 1 23.677 8.232e-05 ***
d13C 74.32 1 15.027 0.0008727 ***
sitef 258.75 2 26.158 1.989e-06 ***
Residuals 103.86 21
---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> # p value of 8.232e-05 *** means intercept is significantly not equal to 0.
> summary.lm(mod.NIA)
Call:
aov(formula = d15N ~ d13C + sitef, data = eco, contrasts = list(sitef = contr.sum))
Residuals:
Min 1Q Median 3Q Max
-3.6695 -1.5658 0.1179 1.1474 3.5577
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 49.51511 0.1760 4.866 8.23e-05 ***
d13C 1.6545 0.4268 3.876 0.000873 ***
sitef1 4.3049 1.2335 3.490 0.002183 **
sitef2 1.0468 1.0774 0.972 0.342273
---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.224 on 21 degrees of freedom
Multiple R-squared: 0.7556, Adjusted R-squared: 0.7207
F-statistic: 21.65 on 3 and 21 DF, p-value: 1.252e-06
#Based on above, we could get the equation with equal slope and common intercept of 3 sites which suitable with Wada_2013 as: d15N=1.6545[±0.4268]*d13C+49.51511[±0.1760 ]+[ecosystem specific sites constant] ( p = 0.000873).
> # Step3: then ANCOVA NonInterAction with treatment contrasts, or type I.
> mod.NIA.tc<-aov(d15N~d13C+sitef,data=eco,contrasts = list(sitef=contr.treatment))
> summary.lm(mod.NIA.tc) #this step is riiiight,for graphics with type I is what we need.
Call:
aov(formula = d15N ~ d13C + sitef, data = eco, contrasts = list(sitef = contr.treatment))
Residuals:
Min 1Q Median 3Q Max
-3.6695 -1.5658 0.1179 1.1474 3.5577
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 53.8200 11.2645 4.778 0.000101 ***
d13C 1.6545 0.4268 3.876 0.000873 ***
sitef2 -3.2581 2.1947 -1.485 0.152529
sitef3 -9.6567 1.7256 -5.596 1.49e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.224 on 21 degrees of freedom
Multiple R-squared: 0.7556, Adjusted R-squared: 0.7207
F-statistic: 21.65 on 3 and 21 DF, p-value: 1.252e-06
#Based on above, we could get the equation for 3 sites respectively with equal slope and specific intercepts which suitable with Wada_2013 as:
site1: d15N=1.6545*d13C+53.8200 ;
site2: d15N=1.6545*d13C+53.8200-3.2581 ;
site1: d15N=1.6545*d13C+53.8200-9.6567 .
> # Step4: Graphics
> dat1<-subset(eco,sitef == "1")
> dat2<-subset(eco,sitef == "2")
> dat3<-subset(eco,sitef=="3")
> reg1<-lm(d15N~d13C,data=dat1)
> reg2<-lm(d15N~d13C,data=dat2)
> reg3<-lm(d15N~d13C,data=dat3)
> plot(d15N~d13C,type="n") # type="n" means plot with axes,without any plots.
> points(dat1$d13C,dat1$d15N,pch=1)
> points(dat2$d13C,dat2$d15N,pch=2)
> points(dat3$d13C,dat3$d15N,pch=3)
> abline(reg1,lty=1)
> abline(reg2,lty=2)
> abline(reg3,lty=3)
> legend("topleft",c("L.Baikal","L.Biwa","Mongolian grassland"),lty=c(1,2,3),pch=c(1,2,3))
> #Above procedures output a graph with unequal slopes which we also need.
> summod.NIA.tc<-summary.lm(mod.NIA.tc) #type I
> coeffs.NIA.tc<-coef(summod.NIA.tc)
> coeffs.NIA.tc
Estimate Std. Error t value Pr(>|t|)
(Intercept) 53.820034 11.2645326 4.777831 1.014464e-04
d13C 1.654461 0.4268016 3.876416 8.726695e-04
sitef2 -3.258098 2.1947260 -1.484512 1.525294e-01
sitef3 -9.656707 1.7255811 -5.596206 1.488283e-05
> I1<-coeffs.NIA.tc[1,1]
> I2<-coeffs.NIA.tc[3,1]+I1
> I3<-coeffs.NIA.tc[4,1]+I1
> solpeAll<-coeffs.NIA.tc[2,1]
> plot(d15N~d13C,type="n")
> points(dat1$d13C,dat1$d15N,pch=1)
> points(dat2$d13C,dat2$d15N,pch=2)
> points(dat3$d13C,dat3$d15N,pch=3)
> abline(I1,slopeAll,lty=1)
> abline(I2,slopeAll,lty=2)
> abline(I3,slopeAll,lty=3)
#From above,we could clearly understand why we can not use summary.lm(mod.NIA) for graphics.
> legend("topleft",c("L.Baikal","L.Biwa","Mongolian grassland"),lty=c(1,2,3),pch=c(1,2,3))
OMG, so long so tired. Anyway, we correctly get what we need, that's enough ^_^
https://blog.sciencenet.cn/blog-651374-975758.html
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