8 Interação
O gráfico de interações é usado quando temos ao menos dois fatores. Tem como função identificar visualmente se os fatores apresentam efeito conjunto ou se são independentes
8.0.1 Conjunto de dados
Um experimento foi realizado com o intuito de avaliar 5 manejos na entrelinha do pomar de laranja Natal e sua influência em relação a linha de plantio. O experimento foi instalado em Delineamento em blocos casualizados com 12 repetições por tratamento em esquema de parcelas subdividida (2 [linha e entrelinha] x 5[ U. brizantha (T1),U. decumbens (T2), U. ruziziensis (T3), Glifosato (T4), Pousio (T5). Foi analisado o carbono da biomassa microbiana (CBM).
RESP=c(224.92, 180.32, 130.19, 110.31, 163.74,193.03, 211.49, 137.65, 127.15, 203.39,182.36, 124.75, 177.70, 231.01, 202.14,214.89, 198.42, 267.85, 207.67, 176.74,162.18, 124.59, 158.99, 209.12, 128.14,113.95, 215.53, 190.51, 174.58, 148.70,150.90, 209.03, 210.40, 199.03, 237.05,196.97, 176.06, 263.27, 240.19, 160.72,239.90, 188.07, 251.35, 215.45, 198.50,271.42, 226.56, 217.65, 213.69, 101.26,115.41, 140.10, 117.67, 106.45, 139.34,104.22, 206.13, 195.89, 147.11, 122.93,176.55, 173.63, 112.83, 184.82, 178.18,115.85, 183.89, 134.92, 086.49, 103.96,096.33, 091.64, 157.76, 107.45, 106.61,095.28, 152.37, 066.02, 125.75, 075.34,088.64, 104.00, 066.38, 084.74, 101.76,173.70, 101.24, 143.71, 119.88, 157.79,070.42, 152.75, 111.65, 153.08, 146.64,142.57, 098.96, 065.92, 065.62, 063.26,095.72, 084.14, 054.92, 090.49, 112.11,102.68, 144.77, 122.58, 125.14, 127.61,117.14, 147.87, 156.18, 154.82, 183.91,159.11, 155.41, 184.55, 121.39, 155.77)
FATOR1=rep(rep(c("L","EL"), e=12),5); FATOR1=factor(FATOR1)
FATOR2=rep(c(paste("T",1:5)),e=24); FATOR2=factor(FATOR2)
repe=rep(c(paste("R",1:12)),10); repe=factor(repe)
dados = data.frame(FATOR1,FATOR2,repe,RESP)8.0.2 Fator1 x Fator 2
with(dados, interaction.plot(FATOR1, FATOR2, RESP))
8.0.3 Editando o gráfico
with(dados, interaction.plot(FATOR1, FATOR2, RESP, las=1, col=1:6, bty='l',
ylab='CBM', trace.label="FATOR2"))
8.0.4 Fator2 x Fator 1
with(dados, interaction.plot(FATOR2, FATOR1, RESP))
8.0.5 Editando o gráfico
with(dados, interaction.plot(FATOR2,FATOR1, RESP, las=1, col=c("blue","red"), bty='l',xlab='', ylab='CBM', trace.label="repe"))
8.1 Usando o interaction(s)
8.1.1 Conjunto de dados
Este conjunto de dados pertence ao pacote ExpDes.pt (data6). Ao qual é composto de três fatores (fatorA, fatorB e fatorC), cuja resposta é nomeada como resp.
x=scan(dec=",",text="
1 1 1 1 1 10,0
2 1 1 1 2 10,8
3 1 1 1 3 9,8
4 1 1 2 1 10,3
5 1 1 2 2 11,3
6 1 1 2 3 10,3
7 1 2 1 1 9,7
8 1 2 1 2 10,1
9 1 2 1 3 10,2
10 1 2 2 1 9,4
11 1 2 2 2 11,6
12 1 2 2 3 9,1
13 2 1 1 1 9,2
14 2 1 1 2 8,6
15 2 1 1 3 10,1
16 2 1 2 1 9,3
17 2 1 2 2 10,3
18 2 1 2 3 9,1
19 2 2 1 1 11,5
20 2 2 1 2 9,5
21 2 2 1 3 10,8
22 2 2 2 1 10,7
23 2 2 2 2 10,4
24 2 2 2 3 9,6
")
data=data.frame(t(matrix(x,6,24)))
colnames(data)=c("N","fatorA", "fatorB", "fatorC","rep","resp")
data## N fatorA fatorB fatorC rep resp
## 1 1 1 1 1 1 10,0
## 2 2 1 1 1 2 10,8
## 3 3 1 1 1 3 9,8
## 4 4 1 1 2 1 10,3
## 5 5 1 1 2 2 11,3
## 6 6 1 1 2 3 10,3
## 7 7 1 2 1 1 9,7
## 8 8 1 2 1 2 10,1
## 9 9 1 2 1 3 10,2
## 10 10 1 2 2 1 9,4
## 11 11 1 2 2 2 11,6
## 12 12 1 2 2 3 9,1
## 13 13 2 1 1 1 9,2
## 14 14 2 1 1 2 8,6
## 15 15 2 1 1 3 10,1
## 16 16 2 1 2 1 9,3
## 17 17 2 1 2 2 10,3
## 18 18 2 1 2 3 9,1
## 19 19 2 2 1 1 11,5
## 20 20 2 2 1 2 9,5
## 21 21 2 2 1 3 10,8
## 22 22 2 2 2 1 10,7
## 23 23 2 2 2 2 10,4
## 24 24 2 2 2 3 9,68.1.2 Separado por Fator A
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"])
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"])
8.1.3 Alterando escala do eixo Y
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1)
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1)
8.1.4 Título do eixo x e y
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1,
xlab="Fator B",
ylab="Resposta")
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B",
ylab="Resposta")
8.1.5 Removendo linhas da caixa
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l")
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l")
8.1.6 Cor da linhas
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"))
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"))
8.1.7 Título dos gráficos
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 1")
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 2")
8.1.8 Título da legenda
par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 1",
trace.label = "Fator C")
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 2",
trace.label = "Fator C")
8.1.9 Pontos da média
Calculando as médias
# Média para nível 1 do fator A
media=with(data,
tapply(resp[fatorA=="1"],
list(fatorB[fatorA=="1"],
fatorC[fatorA=="1"]),
mean))
# Média e desvio-padrão para nível 2 do fator A
media1=with(data,
tapply(resp[fatorA=="2"],
list(fatorB[fatorA=="2"],
fatorC[fatorA=="2"]),
mean)) par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 1",
trace.label = "Fator C")
points(c(1,2,1,2),media, col="red", pch=16)
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B",
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 2",
trace.label = "Fator C")
points(c(1,2,1,2),media1, col="red", pch=16)
8.1.10 Barras de desvio-padrão
Calculando os desvios-padrões
# Desvio-padrão para nível 1 do fator A
desvio=with(data,
tapply(resp[fatorA=="1"],
list(fatorB[fatorA=="1"],
fatorC[fatorA=="1"]),
sd))
# Desvio-padrão para nível 2 do fator A
desvio1=with(data,
tapply(resp[fatorA=="2"],
list(fatorB[fatorA=="2"],
fatorC[fatorA=="2"]),
sd))par(mfrow=c(1,2))
interaction.plot(data$fatorB[data$fatorA=="1"],
data$fatorC[data$fatorA=="1"],
data$resp[data$fatorA=="1"],
las=1, args.legend=list(x="topleft"),
xlab="Fator B", ylim=c(8,13),
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 1",
trace.label = "Fator C")
points(c(1,2,1,2),media, col="red", pch=16)
arrows(c(1,2,1,2), media+desvio,c(1,2,1,2),media-desvio, code=3,angle=90,length = 0.1, col=c("red","red","blue","blue"))
interaction.plot(data$fatorB[data$fatorA=="2"],
data$fatorC[data$fatorA=="2"],
data$resp[data$fatorA=="2"],
las=1,
xlab="Fator B", ylim=c(8,13),
ylab="Resposta",
bty="l",
col = c("red","blue"),
main="Fator A = 2",
trace.label = "Fator C")
points(c(1,2,1,2),media1, col="red", pch=16)
arrows(c(1,2,1,2), media1+desvio1,c(1,2,1,2),media1-desvio1, code=3,angle=90,length = 0.1, col=c("red","red","blue","blue"))
8.2 Pacote dae
8.2.1 Conjunto de dados
resp=c(4599.55,6203.50,4566.02,5616.38,4978.35,5126.15,4816.23,4251.00,4106.79,
4600.58,4012.14,4623.41,4274.16,4683.50,4433.33,4326.16,4932.66,5066.67,
4697.29,5011.38,5156.72,4744.21,4826.80,4663.26,4807.19,4377.19,4442.07,
4685.58,5066.90,5317.66,5144.19,4580.18,4860.37,5204.21,5146.19,5015.67,
5801.99,4668.05,5393.16,5282.27,5369.41,5494.43,4980.32,5715.76,4754.54,
5000.83,4664.11,4969.41,5315.43,4872.29,5546.79,4765.79,4649.63,4899.31,
4890.89,5117.10,4942.97,4548.97,4916.97,4225.38,4820.21,4150.44,4648.46,
4271.57,5143.54,4808.97,5459.66,4928.35,5224.70,4900.90,4770.88,4977.68,
5816.80,5107.11,5555.80,5767.65,5117.10,5573.08,5673.87,4859.00,4687.26,
5055.22,5235.22,4961.72,4984.93,5425.67,4978.33,5172.60,5328.07,4973.87,
5296.55,4928.01,4528.12,5337.93,5809.20,4914.70,5191.89,5261.24,5287.53,
5680.55,5080.06,5425.53,4949.13,5300.57,4481.23,5039.54,5223.75,4581.65)
FATOR1=rep(rep(c("A1","A2","A3"), e=12),3)
FATOR2=rep(c("B1","B2","B3"), e=36)
FATOR3=rep(rep(c("C1","c2","c3"),e=4),9)
dados=data.frame(FATOR1,FATOR2,FATOR3,resp)8.2.2 Gráfico com a média
Para se construir esse gráfico é necessário instalar o pacote dae
library(dae)
interaction.ABC.plot(resp,FATOR1,FATOR2,FATOR3,data=dados)
interaction.ABC.plot(resp,FATOR1,FATOR3,FATOR2,data=dados)
interaction.ABC.plot(resp,FATOR2,FATOR3,FATOR1,data=dados)
interaction.ABC.plot(resp,FATOR2,FATOR1,FATOR3,data=dados)
interaction.ABC.plot(resp,FATOR3,FATOR2,FATOR1,data=dados)
interaction.ABC.plot(resp,FATOR3,FATOR1,FATOR2,data=dados)
8.2.3 Média e desvio-padrão
media=tapply(resp, paste(FATOR1,FATOR2,FATOR3),mean)
desvio=tapply(resp, paste(FATOR1,FATOR2,FATOR3),sd)(F1=rep(c("A1","A2","A3"), e=9))## [1] "A1" "A1" "A1" "A1" "A1" "A1" "A1" "A1" "A1" "A2" "A2" "A2" "A2" "A2" "A2"
## [16] "A2" "A2" "A2" "A3" "A3" "A3" "A3" "A3" "A3" "A3" "A3" "A3"(F2=rep(rep(c("B1","B2","B3"), e=3),3)) ## [1] "B1" "B1" "B1" "B2" "B2" "B2" "B3" "B3" "B3" "B1" "B1" "B1" "B2" "B2" "B2"
## [16] "B3" "B3" "B3" "B1" "B1" "B1" "B2" "B2" "B2" "B3" "B3" "B3"(F3=rep(c("C1","c2","c3"),9))## [1] "C1" "c2" "c3" "C1" "c2" "c3" "C1" "c2" "c3" "C1" "c2" "c3" "C1" "c2" "c3"
## [16] "C1" "c2" "c3" "C1" "c2" "c3" "C1" "c2" "c3" "C1" "c2" "c3"paste(F1,F2,F3) # tratamentos## [1] "A1 B1 C1" "A1 B1 c2" "A1 B1 c3" "A1 B2 C1" "A1 B2 c2" "A1 B2 c3"
## [7] "A1 B3 C1" "A1 B3 c2" "A1 B3 c3" "A2 B1 C1" "A2 B1 c2" "A2 B1 c3"
## [13] "A2 B2 C1" "A2 B2 c2" "A2 B2 c3" "A2 B3 C1" "A2 B3 c2" "A2 B3 c3"
## [19] "A3 B1 C1" "A3 B1 c2" "A3 B1 c3" "A3 B2 C1" "A3 B2 c2" "A3 B2 c3"
## [25] "A3 B3 C1" "A3 B3 c2" "A3 B3 c3"8.2.4 Criando uma data.frame
data=data.frame(F1,F2,F3,media,desvio)8.2.5 Construindo o gráfico
interaction.ABC.plot(media,F1,F2,F3,data=data,
ggplotFunc=
list(geom_errorbar(data=data,
aes(ymax=media+desvio,
ymin=media-desvio),
width=0.2)))