ANCOVA Can root-deformation affect biomass predictions of Genipa americana seedlings?
Andrea Phillips Valverde
6/9/2021
Universidad Nacional de Costa Rica, Heredia, Costa Rica, Facultad de Ciencias Exactas y Naturales, Escuela de Ciencias Biologicas.
Se asumen la totalidad de supuestos estadisticos
Universidad Nacional de Costa Rica, Heredia, Costa Rica, Facultad de Ciencias Exactas y Naturales, Escuela de Ciencias Biologicas.
Se asumen la totalidad de supuestos estadisticos
library(readxl)
FASE_6_ANCOVA_2 <- read_excel("FASE-6-ANCOVA_2.xlsx")
View(FASE_6_ANCOVA_2)DF <- data.frame(FASE_6_ANCOVA_2)
set.seed(2021)
n <- nrow(DF)
muestra <- sample(n,n* 0.80)# se toma una muestra aleatoria de 80%
df.train <- DF[muestra, ]
df.test <- DF[-muestra, ]
LDM <- df.test$LDM
SDM <- df.test$SDM
RDM <- df.test$RDM
TDM <- df.test$TDM
D2 <- df.test$D2
Deformation <- df.test$Deformation
#MODELO ANCOVA 1
lm.1<-lm(LDM~D2*Deformation,data=df.train)
lm.1 ##
## Call:
## lm(formula = LDM ~ D2 * Deformation, data = df.train)
##
## Coefficients:
## (Intercept) D2 DeformationYes D2:DeformationYes
## 0.2602733 0.0679758 -0.0010296 -0.0005135summary(lm.1)##
## Call:
## lm(formula = LDM ~ D2 * Deformation, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.53083 -0.46717 -0.08022 0.30631 2.87361
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2602733 0.3042009 0.856 0.395
## D2 0.0679758 0.0045465 14.951 <2e-16 ***
## DeformationYes -0.0010296 0.4222119 -0.002 0.998
## D2:DeformationYes -0.0005135 0.0068672 -0.075 0.941
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9995 on 76 degrees of freedom
## Multiple R-squared: 0.8417, Adjusted R-squared: 0.8354
## F-statistic: 134.7 on 3 and 76 DF, p-value: < 2.2e-16#FULL MODEL
pv1 <- predict(lm.1, newdata = data.frame(LDM,D2,Deformation), interval = "prediction")
meanRPE <- mean(((pv1[,1]-LDM)/LDM)*100)
meanRPE## [1] 16.78263sd2RPE <- sd(((pv1[,1]-LDM)/LDM)*100)
sd2RPE## [1] 41.79803#REDUCED MODEL (No consideramos Deformation)
lmr.1<-lm(LDM~D2,data=df.train)
lmr.1 ##
## Call:
## lm(formula = LDM ~ D2, data = df.train)
##
## Coefficients:
## (Intercept) D2
## 0.25621 0.06781summary(lmr.1)##
## Call:
## lm(formula = LDM ~ D2, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.51021 -0.46795 -0.07718 0.29440 2.88742
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.256207 0.206841 1.239 0.219
## D2 0.067809 0.003331 20.359 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9867 on 78 degrees of freedom
## Multiple R-squared: 0.8416, Adjusted R-squared: 0.8396
## F-statistic: 414.5 on 1 and 78 DF, p-value: < 2.2e-16pv1.2 <- predict(lmr.1, newdata = data.frame(LDM,D2), interval = "prediction")
meanRPER <- mean(((pv1.2[,1]-LDM)/LDM)*100)
meanRPER## [1] 16.77367sd2RPER <- sd(((pv1.2[,1]-LDM)/LDM)*100)
sd2RPER## [1] 41.80823##########################################################
#MODELO 2 ANCOVA
lm.2<-lm(SDM~D2*Deformation,data=df.train)
lm.2 ##
## Call:
## lm(formula = SDM ~ D2 * Deformation, data = df.train)
##
## Coefficients:
## (Intercept) D2 DeformationYes D2:DeformationYes
## -0.586328 0.039846 0.293565 -0.008372summary(lm.2)##
## Call:
## lm(formula = SDM ~ D2 * Deformation, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.13881 -0.21032 -0.03857 0.18749 1.95663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.586328 0.159041 -3.687 0.000424 ***
## D2 0.039846 0.002377 16.763 < 2e-16 ***
## DeformationYes 0.293565 0.220740 1.330 0.187524
## D2:DeformationYes -0.008372 0.003590 -2.332 0.022355 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5225 on 76 degrees of freedom
## Multiple R-squared: 0.8511, Adjusted R-squared: 0.8452
## F-statistic: 144.8 on 3 and 76 DF, p-value: < 2.2e-16pv2 <- predict(lm.2, newdata = data.frame(SDM,D2,Deformation), interval = "prediction")
meanRPE2 <- mean(((pv2[,1]-SDM)/SDM)*100)
meanRPE2## [1] -2.304031sd2RPE2 <- sd(((pv2[,1]-SDM)/SDM)*100)
sd2RPE2## [1] 171.1967#REDUCED MODEL (No consideramos Deformation)
lmr.2<-lm(SDM~D2,data=df.train)
lmr.2 ##
## Call:
## lm(formula = SDM ~ D2, data = df.train)
##
## Coefficients:
## (Intercept) D2
## -0.46296 0.03648summary(lmr.2)##
## Call:
## lm(formula = SDM ~ D2, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.03262 -0.29316 -0.04105 0.23185 2.16830
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.462962 0.112910 -4.10 1e-04 ***
## D2 0.036475 0.001818 20.06 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5386 on 78 degrees of freedom
## Multiple R-squared: 0.8377, Adjusted R-squared: 0.8356
## F-statistic: 402.5 on 1 and 78 DF, p-value: < 2.2e-16pv2.2 <- predict(lmr.2, newdata = data.frame(SDM,D2), interval = "prediction")
meanRPER2 <- mean(((pv2.2[,1]-SDM)/SDM)*100)
meanRPER2## [1] -22.24571sd2RPER2 <- sd(((pv2.2[,1]-SDM)/SDM)*100)
sd2RPER2## [1] 215.8252##########################################################
#MODELO 3 ANCOVA
lm.3<-lm(RDM~D2*Deformation,data=df.train)
lm.3 ##
## Call:
## lm(formula = RDM ~ D2 * Deformation, data = df.train)
##
## Coefficients:
## (Intercept) D2 DeformationYes D2:DeformationYes
## -1.111639 0.103382 0.398477 0.009583summary(lm.3)##
## Call:
## lm(formula = RDM ~ D2 * Deformation, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6190 -0.8771 -0.0611 0.6187 3.8996
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.111639 0.402978 -2.759 0.00727 **
## D2 0.103382 0.006023 17.165 < 2e-16 ***
## DeformationYes 0.398477 0.559309 0.712 0.47837
## D2:DeformationYes 0.009583 0.009097 1.053 0.29548
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.324 on 76 degrees of freedom
## Multiple R-squared: 0.8822, Adjusted R-squared: 0.8776
## F-statistic: 189.8 on 3 and 76 DF, p-value: < 2.2e-16pv3 <- predict(lm.3, newdata = data.frame(RDM,D2,Deformation), interval = "prediction")
meanRPE3 <- mean(((pv3[,1]-RDM)/RDM)*100)
meanRPE3## [1] -0.7072322sd2RPE3 <- sd(((pv3[,1]-RDM)/RDM)*100)
sd2RPE3## [1] 70.07905#REDUCED MODEL (No consideramos Deformation)
lmr.3<-lm(RDM~D2,data=df.train)
lmr.3 ##
## Call:
## lm(formula = RDM ~ D2, data = df.train)
##
## Coefficients:
## (Intercept) D2
## -0.8040 0.1057summary(lmr.3)##
## Call:
## lm(formula = RDM ~ D2, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9712 -0.9829 -0.0301 0.7542 4.6328
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.803990 0.291599 -2.757 0.00726 **
## D2 0.105687 0.004696 22.508 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.391 on 78 degrees of freedom
## Multiple R-squared: 0.8666, Adjusted R-squared: 0.8649
## F-statistic: 506.6 on 1 and 78 DF, p-value: < 2.2e-16pv3.2 <- predict(lmr.3, newdata = data.frame(RDM,D2), interval = "prediction")
meanRPER3 <- mean(((pv3.2[,1]-RDM)/RDM)*100)
meanRPER3## [1] -2.310501sd2RPER3 <- sd(((pv3.2[,1]-RDM)/RDM)*100)
sd2RPER3## [1] 82.22218##########################################################
#MODELO 4 ANCOVA
lm.4<-lm(TDM~D2*Deformation,data=df.train)
lm.4 ##
## Call:
## lm(formula = TDM ~ D2 * Deformation, data = df.train)
##
## Coefficients:
## (Intercept) D2 DeformationYes D2:DeformationYes
## -1.4376934 0.2112037 0.6910122 0.0006972summary(lm.4)##
## Call:
## lm(formula = TDM ~ D2 * Deformation, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9773 -1.5883 -0.2934 1.1806 6.5094
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.4376934 0.6995822 -2.055 0.0433 *
## D2 0.2112037 0.0104558 20.200 <2e-16 ***
## DeformationYes 0.6910122 0.9709766 0.712 0.4788
## D2:DeformationYes 0.0006972 0.0157928 0.044 0.9649
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.299 on 76 degrees of freedom
## Multiple R-squared: 0.9062, Adjusted R-squared: 0.9025
## F-statistic: 244.8 on 3 and 76 DF, p-value: < 2.2e-16pv4 <- predict(lm.4, newdata = data.frame(TDM,D2,Deformation), interval = "prediction")
meanRPE4 <- mean(((pv4[,1]-TDM)/TDM)*100)
meanRPE4## [1] 6.319529sd2RPE4 <- sd(((pv4[,1]-TDM)/TDM)*100)
sd2RPE4## [1] 38.14781#REDUCED MODEL (No consideramos Deformation)
lmr.4<-lm(TDM~D2,data=df.train)
lmr.4 ##
## Call:
## lm(formula = TDM ~ D2, data = df.train)
##
## Coefficients:
## (Intercept) D2
## -1.011 0.210summary(lmr.4)##
## Call:
## lm(formula = TDM ~ D2, data = df.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5169 -1.5956 -0.1005 1.1195 6.9438
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.010746 0.481723 -2.098 0.0391 *
## D2 0.209971 0.007757 27.068 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.298 on 78 degrees of freedom
## Multiple R-squared: 0.9038, Adjusted R-squared: 0.9026
## F-statistic: 732.7 on 1 and 78 DF, p-value: < 2.2e-16pv4.2 <- predict(lmr.4, newdata = data.frame(TDM,D2), interval = "prediction")
meanRPER4 <- mean(((pv4.2[,1]-TDM)/TDM)*100)
meanRPER4## [1] 3.06318sd2RPER4 <- sd(((pv4.2[,1]-TDM)/TDM)*100)
sd2RPER4## [1] 41.51472Figuras
library(ggplot2)
p <- ggplot(DF, (aes(x=`D2`, y=`TDM`, color=Deformation, shape=Deformation))) + theme_classic()
p + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)
p1 <- ggplot(DF, (aes(x=`D2`, y=`LDM`, color=Deformation, shape=Deformation))) + theme_classic()
p1 + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)
p2 <- ggplot(DF, (aes(x=`D2`, y=`RDM`, color=Deformation, shape=Deformation))) + theme_classic()
p2 + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)
p <- ggplot(DF, (aes(x=`D2`, y=`SDM`, color=Deformation, shape=Deformation))) + theme_classic()
p + geom_point() + geom_smooth(method=lm, se=FALSE, fullrange=TRUE)