Análise de desempenho
Maria Fernanda Burbarelli, Leonardo de Oliveira Seno & Walmes Marques Zeviani
Preparação e análise exploratória
library(nlme) # Modelos de efeitos mistos.
# Para não exibir o bloco de correlação entre estimativas dos efeitos
# fixos na saída do `summary()`. ATTENTION: tem que vir antes da
# `lmerTest`.
assignInNamespace("print.correlation",
function(x, title) return(),
ns = "nlme")
library(lmerTest) # Testes de hipótese para classe lme e similares.
library(emmeans) # Médias ajustadas.
library(tidyverse) # Manipulação e visualização de dados.
# Para apresentar letras ordenadas com o "a" vínculado a maior média.
numbers_to_letters <- function(.group) {
list_num <- trimws(.group) %>%
strsplit(split = "")
n <- max(as.integer(unlist(list_num)))
list_num %>%
lapply(FUN = function(x) sort(letters[n:1][as.integer(x)])) %>%
sapply(FUN = paste, collapse = "")
}# Leitura da tabela de dados.
url <- "Dados níveis de erva-mate - PARA ENVIAR ESTATISTICA.xlsx"
tb <- gdata::read.xls(xls = url,
sheet = 1,
na.strings = ".",
check.names = FALSE)
# Adequação dos nomes das variáveis.
names(tb) <- names(tb) %>%
str_to_lower() %>%
str_replace_all("[[:punct:]]", "")
str(tb)## 'data.frame': 120 obs. of 8 variables:
## $ mate : num 0 0 0 0 0 0 1.5 1.5 1.5 1.5 ...
## $ rep : int 1 2 3 4 5 6 1 2 3 4 ...
## $ per : int 1 1 1 1 1 1 1 1 1 1 ...
## $ consumo : num 98.8 98.3 104.1 97.5 97.5 ...
## $ postura : num 94 94 94 93.5 NA ...
## $ massaovos: num 55.6 50.2 53.7 55.6 43.5 ...
## $ caduzia : num 7.5 7.46 7.91 7.45 9.52 ...
## $ camovos : num 1.78 1.96 1.94 1.75 2.24 ...# Faz ordenação dos registros.
tb <- tb %>%
arrange(mate, rep, per)
# Versão empilhada ou verticalizada das respostas.
tb_long <- tb %>%
gather(key = "variable", value = "value", consumo:camovos)
str(tb_long)## 'data.frame': 600 obs. of 5 variables:
## $ mate : num 0 0 0 0 0 0 0 0 0 0 ...
## $ rep : int 1 1 1 1 2 2 2 2 3 3 ...
## $ per : int 1 2 3 4 1 2 3 4 1 2 ...
## $ variable: chr "consumo" "consumo" "consumo" "consumo" ...
## $ value : num 98.8 81.8 83.7 83.3 98.3 ...ggplot(data = tb_long,
mapping = aes(x = mate, y = value)) +
facet_grid(facets = variable ~ per, scale = "free_y") +
# geom_point() +
geom_jitter(width = 0.1, height = 0) +
stat_summary(mapping = aes(group = 1),
fun.y = "mean",
geom = "line") +
labs(x = "Concentração de mate",
y = "Valor de cada resposta")## Warning: Removed 4 rows containing non-finite values (stat_summary).## Warning: Removed 4 rows containing missing values (geom_point).
ggplot(data = tb_long,
mapping = aes(x = per, y = value)) +
facet_grid(facets = variable ~ mate, scale = "free_y") +
# geom_point() +
geom_jitter(width = 0.1, height = 0) +
stat_summary(mapping = aes(group = 1),
fun.y = "mean",
geom = "line") +
labs(x = "Período de postura",
y = "Valor de cada resposta")## Warning: Removed 4 rows containing non-finite values (stat_summary).
## Warning: Removed 4 rows containing missing values (geom_point).
# ATTENTION: `massaovos` deve ser o valor total ou médio porque está
# repetindo no período.
# Conta os valores presentes (tamanho de amostra).
tb %>%
group_by(mate, per) %>%
summarise_at(vars(consumo:camovos),
function(x) sum(is.finite(x)))## # A tibble: 20 x 7
## # Groups: mate [5]
## mate per consumo postura massaovos caduzia camovos
## <dbl> <int> <int> <int> <int> <int> <int>
## 1 0 1 6 5 6 6 6
## 2 0 2 6 5 6 6 6
## 3 0 3 6 5 6 6 6
## 4 0 4 6 5 6 6 6
## 5 1.5 1 6 6 6 6 6
## 6 1.5 2 6 6 6 6 6
## 7 1.5 3 6 6 6 6 6
## 8 1.5 4 6 6 6 6 6
## 9 3 1 6 6 6 6 6
## 10 3 2 6 6 6 6 6
## 11 3 3 6 6 6 6 6
## 12 3 4 6 6 6 6 6
## 13 4.5 1 6 6 6 6 6
## 14 4.5 2 6 6 6 6 6
## 15 4.5 3 6 6 6 6 6
## 16 4.5 4 6 6 6 6 6
## 17 6 1 6 6 6 6 6
## 18 6 2 6 6 6 6 6
## 19 6 3 6 6 6 6 6
## 20 6 4 6 6 6 6 6# Conta os valores ausentes.
tb %>%
group_by(mate, per) %>%
summarise_at(vars(consumo:camovos),
function(x) sum(is.na(x)))## # A tibble: 20 x 7
## # Groups: mate [5]
## mate per consumo postura massaovos caduzia camovos
## <dbl> <int> <int> <int> <int> <int> <int>
## 1 0 1 0 1 0 0 0
## 2 0 2 0 1 0 0 0
## 3 0 3 0 1 0 0 0
## 4 0 4 0 1 0 0 0
## 5 1.5 1 0 0 0 0 0
## 6 1.5 2 0 0 0 0 0
## 7 1.5 3 0 0 0 0 0
## 8 1.5 4 0 0 0 0 0
## 9 3 1 0 0 0 0 0
## 10 3 2 0 0 0 0 0
## 11 3 3 0 0 0 0 0
## 12 3 4 0 0 0 0 0
## 13 4.5 1 0 0 0 0 0
## 14 4.5 2 0 0 0 0 0
## 15 4.5 3 0 0 0 0 0
## 16 4.5 4 0 0 0 0 0
## 17 6 1 0 0 0 0 0
## 18 6 2 0 0 0 0 0
## 19 6 3 0 0 0 0 0
## 20 6 4 0 0 0 0 0# Cria variável para representar a parcela e cria cópias como fator.
tb <- tb %>%
mutate(parcela = interaction(mate, rep, drop = TRUE),
Mate = factor(mate),
Per = factor(per))
#Especificação do modelo
O modelo para análise das variáveis medidas ao nível de animais, ou seja, nas unidades experimentais que são as gaiolas é \[ \begin{aligned} y_{ijk}| ijk &\sim \text{Normal}(\mu_{ij}, \sigma^2) \\ \mu_{ij} &= \mu + \alpha_i + e_{ik} + \beta_j + \gamma_{ij} \\ e_{ik} &\sim \text{Normal}(0, \sigma_{e}^2) \end{aligned} \]
Colocado de outra forma, esse modelo pode ser escrito como soma da parte determinística e aleatória que terá dois estratos: o de parcela e subparcela. Na parcela foram casualizados os níveis de mate. E na subparcela assume-se que foram casualizados os níveis de tempo. Todavia, de fato não foi feita essa casualização porque trata-se de um experimento longitudinal ou de medidas repetidas, também chamado de parcelas subdivididas no tempo.
O modelo escrito como soma de termos determinístico e de erro é \[ \begin{aligned} y_{ijk} &= \mu + \tau_i + \theta_j + \gamma_{ij} + \varepsilon_{ij} + \epsilon_{ijk}\\ \varepsilon_{ij} &\sim \text{Normal}(0, \sigma_\varepsilon^2) \\ \epsilon_{ijk} &\sim \text{Normal}(0, \sigma_\epsilon^2), \\ \end{aligned} \] em que \(\varepsilon_{ij}\) e \(\epsilon_{ijk}\) são os erros ao nível de parcela e subparcela (residual), respectivamente. Estes erros são independentes entre si.
Nas seções a seguir será feito a análise para uma das variáveis resposta. Essa análise será feita usando o método ANOVA, o modelo misto (REML) e por último o modelo misto com estrutura de dependência entre observações ao longo do tempo.
Análise da variável consumo
Método ANOVA
O método ANOVA é muito utilizado. Todavia, para experimentos desbalanceados ocorrem complicações para a obtenção das somas de quadrados. Por isso o método REML é preferível. A título de ilustração, o código abaixo ajusta o modelo e exibe o quadro de análise de variância de dois estratos: com erro ao nível de parcela e erro ao nível de subparcela.
# Modelo de um estrato apenas para conferir pressupostos.
m0 <- lm(terms(consumo ~ Mate + parcela + Per + Mate:Per,
keep.order = TRUE),
data = tb)
# Inspeção dos pressupostos.
par(mfrow = c(2, 2))
plot(m0)
layout(1)
# Algumas estatísticas F estão erradas.
anova(m0)## Analysis of Variance Table
##
## Response: consumo
## Df Sum Sq Mean Sq F value Pr(>F)
## Mate 4 215.76 53.94 2.2021 0.07679 .
## parcela 25 805.14 32.21 1.3148 0.18241
## Per 3 2790.02 930.01 37.9682 4.935e-15 ***
## Mate:Per 12 1831.95 152.66 6.2326 1.743e-07 ***
## Residuals 75 1837.08 24.49
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Modelo de 2 estratos.
m0 <- aov(consumo ~ Mate + Error(parcela) + Per + Mate:Per,
data = tb)
# Quadro de análise de variância de 2 estratos.
summary(m0)##
## Error: parcela
## Df Sum Sq Mean Sq F value Pr(>F)
## Mate 4 215.8 53.94 1.675 0.187
## Residuals 25 805.1 32.21
##
## Error: Within
## Df Sum Sq Mean Sq F value Pr(>F)
## Per 3 2790 930.0 37.968 4.94e-15 ***
## Mate:Per 12 1832 152.7 6.233 1.74e-07 ***
## Residuals 75 1837 24.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Modelos de efeitos aleatórios REML
O modelo ajustado com as instruções a seguir corresponde ao mesmo modelo usado no método ANOVA. Para dados balanceados, os resultados serão os mesmo, exceto somente que o método REML só produz estimativas dentro do espaço paramétrico, ou seja, as estimativa para os componentes serão positivas.
mm0 <- lme(consumo ~ Mate + Per + Mate:Per,
random = ~1 | parcela,
method = "ML",
data = tb)
anova(mm0)## numDF denDF F-value p-value
## (Intercept) 1 75 26473.649 <.0001
## Mate 4 25 1.675 0.1872
## Per 3 75 37.968 <.0001
## Mate:Per 12 75 6.233 <.0001#Para verificar se os resídos apresentam algum padrão de correlação serial, será obtida a correlação entre resíduos de observações vizinhas de primeira e segunda ordem dentro de cada parcela.
# Extrai dados envolvidos no ajuste e adiciona resíduos e ajustados.
tb_fit <- mm0$data
tb_fit <- tb_fit %>%
mutate(res = residuals(mm0),
fit = fitted(mm0))
tb_cor <- tb_fit %>%
select(parcela, per, res) %>%
spread(key = "per", value = "res") %>%
select(-1)
lattice::splom(tb_cor, type = c("p", "r"))
tb_cor %>%
cor()## 1 2 3 4
## 1 1.00000000 -0.09830009 -0.08129783 -0.24978273
## 2 -0.09830009 1.00000000 -0.18133727 -0.01598283
## 3 -0.08129783 -0.18133727 1.00000000 0.35518427
## 4 -0.24978273 -0.01598283 0.35518427 1.00000000# Calcula correlação média entre vizinhos dentro de cada parcela.
tb_cor <- tb_fit %>%
mutate(res_1 = lead(res, n = 1),
res_2 = lead(res, n = 2)) %>%
group_by(parcela) %>%
summarise(viz1 = cor(res, res_1, method = "pearson"),
viz2 = cor(res, res_2, method = "pearson"))
tb_cor %>%
summarise_if(is.numeric, mean, na.rm = TRUE)## # A tibble: 1 x 2
## viz1 viz2
## <dbl> <dbl>
## 1 -0.103 -0.245tb_cor %>%
gather(key = "vizinho", value = "pearson", viz1:viz2) %>%
ggplot(mapping = aes(x = pearson, color = vizinho)) +
stat_ecdf() +
geom_vline(xintercept = 0, col = "orange")## Warning: Removed 2 rows containing non-finite values (stat_ecdf).
#Pela análise exploratória, parece não haver evidências, pelo menos não gráficas, para contra a hipótese nula de que os erros são independentes entre observações da mesma parcela.
Modelos de efeitos aleatórios com estrutura AR1 nos erros
O modelo a seguir considera uma estrutura de erro autoregressivo de primeira ordem. Ou seja, os erros dentro da mesma parcela apresentam correção decrescente em função do grau de vizinhança. A correlação entre vizinhos de ordem \(k\) é \(\rho^k\). A matriz para 4 medidas no tempo é, \[ \begin{bmatrix} 1 & \rho & \rho^2 & \rho^3 \\ & 1 & \rho & \rho^2 \\ & & 1 & \rho \\ & & & 1 \end{bmatrix}. \]
# Modelo com correlação AR(1) entre observações.
mm1 <- lme(consumo ~ Mate + Per + Mate:Per,
random = ~1 | parcela,
correlation = corAR1(value = 0.1, form = ~per | parcela),
method = "ML",
data = tb)
anova(mm1)## numDF denDF F-value p-value
## (Intercept) 1 75 26339.562 <.0001
## Mate 4 25 1.852 0.1505
## Per 3 75 39.215 <.0001
## Mate:Per 12 75 6.030 <.0001summary(mm1)## Linear mixed-effects model fit by maximum likelihood
## Data: tb
## AIC BIC logLik
## 756.3027 820.415 -355.1513
##
## Random effects:
## Formula: ~1 | parcela
## (Intercept) Residual
## StdDev: 0.763366 4.63111
##
## Correlation Structure: AR(1)
## Formula: ~per | parcela
## Parameter estimate(s):
## Phi
## 0.09537041
## Fixed effects: consumo ~ Mate + Per + Mate:Per
## Value Std.Error DF t-value p-value
## (Intercept) 100.08135 2.099043 75 47.67951 0.0000
## Mate1.5 -6.56053 2.968495 25 -2.21005 0.0365
## Mate3 -3.09327 2.968495 25 -1.04203 0.3074
## Mate4.5 -12.49008 2.968495 25 -4.20755 0.0003
## Mate6 -21.41568 2.968495 25 -7.21432 0.0000
## Per2 -22.03768 2.785804 75 -7.91071 0.0000
## Per3 -17.80853 2.915621 75 -6.10797 0.0000
## Per4 -21.70833 2.927701 75 -7.41481 0.0000
## Mate1.5:Per2 11.18255 3.939721 75 2.83841 0.0058
## Mate3:Per2 8.07540 3.939721 75 2.04974 0.0439
## Mate4.5:Per2 14.36210 3.939721 75 3.64546 0.0005
## Mate6:Per2 25.38590 3.939721 75 6.44358 0.0000
## Mate1.5:Per3 8.32155 4.123310 75 2.01817 0.0471
## Mate3:Per3 8.29067 4.123310 75 2.01068 0.0480
## Mate4.5:Per3 18.12798 4.123310 75 4.39646 0.0000
## Mate6:Per3 26.87700 4.123310 75 6.51831 0.0000
## Mate1.5:Per4 5.56850 4.140394 75 1.34492 0.1827
## Mate3:Per4 3.09328 4.140394 75 0.74710 0.4573
## Mate4.5:Per4 12.49012 4.140394 75 3.01665 0.0035
## Mate6:Per4 24.43652 4.140394 75 5.90198 0.0000
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.94167994 -0.65613082 -0.09842584 0.59321265 3.70606830
##
## Number of Observations: 120
## Number of Groups: 30# Estimativa de \rho.
intervals(mm1)$corStruct## lower est. upper
## Phi -0.1564151 0.09537041 0.3355168
## attr(,"label")
## [1] "Correlation structure:"# LRT entre modelos aninhados.
anova(mm1, mm0)## Model df AIC BIC logLik Test L.Ratio p-value
## mm1 1 23 756.3027 820.4150 -355.1513
## mm0 2 22 754.6911 816.0159 -355.3455 1 vs 2 0.3883899 0.5331#Pelo teste de razão de verossimilhanças entre modelos encaixados, não rejeitou-se a hipótese nula de que \(\rho = 0\).
Médias ajustadas e comparações múltiplas
# Médias ajustadas para todas as combinações entre níveis.
emm <- emmeans(mm0, specs = ~Per + Mate)
emm## Per Mate emmean SE df lower.CL upper.CL
## 1 0 100.1 2.1 29 95.8 104.4
## 2 0 78.0 2.1 29 73.8 82.3
## 3 0 82.3 2.1 29 78.0 86.6
## 4 0 78.4 2.1 29 74.1 82.7
## 1 1.5 93.5 2.1 25 89.2 97.8
## 2 1.5 82.7 2.1 25 78.3 87.0
## 3 1.5 84.0 2.1 25 79.7 88.4
## 4 1.5 77.4 2.1 25 73.1 81.7
## 1 3 97.0 2.1 25 92.7 101.3
## 2 3 83.0 2.1 25 78.7 87.3
## 3 3 87.5 2.1 25 83.1 91.8
## 4 3 78.4 2.1 25 74.1 82.7
## 1 4.5 87.6 2.1 25 83.3 91.9
## 2 4.5 79.9 2.1 25 75.6 84.2
## 3 4.5 87.9 2.1 25 83.6 92.2
## 4 4.5 78.4 2.1 25 74.1 82.7
## 1 6 78.7 2.1 25 74.3 83.0
## 2 6 82.0 2.1 25 77.7 86.3
## 3 6 87.7 2.1 25 83.4 92.1
## 4 6 81.4 2.1 25 77.1 85.7
##
## d.f. method: containment
## Confidence level used: 0.95# Gráfico com intervalos de confiança.
gg1 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Per,
y = emmean)) +
facet_wrap(facets = ~Mate,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Período de postura",
y = "Consumo") +
ggtitle(label = NULL,
subtitle = "Níveis de mate")
# Gráfico com intervalos de confiança.
gg2 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Níveis de mate",
y = "Consumo") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
gridExtra::grid.arrange(gg1, gg2, ncol = 1)
# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Per | Mate)
emm## Mate = 0:
## Per emmean SE df lower.CL upper.CL
## 1 100.1 2.1 29 95.8 104.4
## 2 78.0 2.1 29 73.8 82.3
## 3 82.3 2.1 29 78.0 86.6
## 4 78.4 2.1 29 74.1 82.7
##
## Mate = 1.5:
## Per emmean SE df lower.CL upper.CL
## 1 93.5 2.1 25 89.2 97.8
## 2 82.7 2.1 25 78.3 87.0
## 3 84.0 2.1 25 79.7 88.4
## 4 77.4 2.1 25 73.1 81.7
##
## Mate = 3:
## Per emmean SE df lower.CL upper.CL
## 1 97.0 2.1 25 92.7 101.3
## 2 83.0 2.1 25 78.7 87.3
## 3 87.5 2.1 25 83.1 91.8
## 4 78.4 2.1 25 74.1 82.7
##
## Mate = 4.5:
## Per emmean SE df lower.CL upper.CL
## 1 87.6 2.1 25 83.3 91.9
## 2 79.9 2.1 25 75.6 84.2
## 3 87.9 2.1 25 83.6 92.2
## 4 78.4 2.1 25 74.1 82.7
##
## Mate = 6:
## Per emmean SE df lower.CL upper.CL
## 1 78.7 2.1 25 74.3 83.0
## 2 82.0 2.1 25 77.7 86.3
## 3 87.7 2.1 25 83.4 92.1
## 4 81.4 2.1 25 77.1 85.7
##
## d.f. method: containment
## Confidence level used: 0.95# Comparações múltiplas.
contrast(emm, method = "pairwise")## Mate = 0:
## contrast estimate SE df t.ratio p.value
## 1 - 2 22.038 2.86 75 7.712 <.0001
## 1 - 3 17.809 2.86 75 6.232 <.0001
## 1 - 4 21.708 2.86 75 7.597 <.0001
## 2 - 3 -4.229 2.86 75 -1.480 0.4545
## 2 - 4 -0.329 2.86 75 -0.115 0.9994
## 3 - 4 3.900 2.86 75 1.365 0.5252
##
## Mate = 1.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 10.855 2.86 75 3.799 0.0016
## 1 - 3 9.487 2.86 75 3.320 0.0074
## 1 - 4 16.140 2.86 75 5.648 <.0001
## 2 - 3 -1.368 2.86 75 -0.479 0.9636
## 2 - 4 5.285 2.86 75 1.849 0.2588
## 3 - 4 6.653 2.86 75 2.328 0.1007
##
## Mate = 3:
## contrast estimate SE df t.ratio p.value
## 1 - 2 13.962 2.86 75 4.886 <.0001
## 1 - 3 9.518 2.86 75 3.331 0.0072
## 1 - 4 18.615 2.86 75 6.515 <.0001
## 2 - 3 -4.444 2.86 75 -1.555 0.4102
## 2 - 4 4.653 2.86 75 1.628 0.3692
## 3 - 4 9.097 2.86 75 3.184 0.0111
##
## Mate = 4.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 7.676 2.86 75 2.686 0.0432
## 1 - 3 -0.319 2.86 75 -0.112 0.9995
## 1 - 4 9.218 2.86 75 3.226 0.0099
## 2 - 3 -7.995 2.86 75 -2.798 0.0324
## 2 - 4 1.543 2.86 75 0.540 0.9490
## 3 - 4 9.538 2.86 75 3.338 0.0071
##
## Mate = 6:
## contrast estimate SE df t.ratio p.value
## 1 - 2 -3.348 2.86 75 -1.172 0.6464
## 1 - 3 -9.068 2.86 75 -3.174 0.0115
## 1 - 4 -2.728 2.86 75 -0.955 0.7753
## 2 - 3 -5.720 2.86 75 -2.002 0.1965
## 2 - 4 0.620 2.86 75 0.217 0.9964
## 3 - 4 6.340 2.86 75 2.219 0.1275
##
## P value adjustment: tukey method for comparing a family of 4 estimatesmultcomp::cld(emm)## Mate = 0:
## Per emmean SE df lower.CL upper.CL .group
## 2 78.0 2.1 29 73.8 82.3 1
## 4 78.4 2.1 29 74.1 82.7 1
## 3 82.3 2.1 29 78.0 86.6 1
## 1 100.1 2.1 29 95.8 104.4 2
##
## Mate = 1.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 77.4 2.1 25 73.1 81.7 1
## 2 82.7 2.1 25 78.3 87.0 1
## 3 84.0 2.1 25 79.7 88.4 1
## 1 93.5 2.1 25 89.2 97.8 2
##
## Mate = 3:
## Per emmean SE df lower.CL upper.CL .group
## 4 78.4 2.1 25 74.1 82.7 1
## 2 83.0 2.1 25 78.7 87.3 12
## 3 87.5 2.1 25 83.1 91.8 2
## 1 97.0 2.1 25 92.7 101.3 3
##
## Mate = 4.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 78.4 2.1 25 74.1 82.7 1
## 2 79.9 2.1 25 75.6 84.2 1
## 1 87.6 2.1 25 83.3 91.9 2
## 3 87.9 2.1 25 83.6 92.2 2
##
## Mate = 6:
## Per emmean SE df lower.CL upper.CL .group
## 1 78.7 2.1 25 74.3 83.0 1
## 4 81.4 2.1 25 77.1 85.7 12
## 2 82.0 2.1 25 77.7 86.3 12
## 3 87.7 2.1 25 83.4 92.1 2
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 4 estimates
## significance level used: alpha = 0.05# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Mate | Per)
emm## Per = 1:
## Mate emmean SE df lower.CL upper.CL
## 0 100.1 2.1 29 95.8 104.4
## 1.5 93.5 2.1 25 89.2 97.8
## 3 97.0 2.1 25 92.7 101.3
## 4.5 87.6 2.1 25 83.3 91.9
## 6 78.7 2.1 25 74.3 83.0
##
## Per = 2:
## Mate emmean SE df lower.CL upper.CL
## 0 78.0 2.1 29 73.8 82.3
## 1.5 82.7 2.1 25 78.3 87.0
## 3 83.0 2.1 25 78.7 87.3
## 4.5 79.9 2.1 25 75.6 84.2
## 6 82.0 2.1 25 77.7 86.3
##
## Per = 3:
## Mate emmean SE df lower.CL upper.CL
## 0 82.3 2.1 29 78.0 86.6
## 1.5 84.0 2.1 25 79.7 88.4
## 3 87.5 2.1 25 83.1 91.8
## 4.5 87.9 2.1 25 83.6 92.2
## 6 87.7 2.1 25 83.4 92.1
##
## Per = 4:
## Mate emmean SE df lower.CL upper.CL
## 0 78.4 2.1 29 74.1 82.7
## 1.5 77.4 2.1 25 73.1 81.7
## 3 78.4 2.1 25 74.1 82.7
## 4.5 78.4 2.1 25 74.1 82.7
## 6 81.4 2.1 25 77.1 85.7
##
## d.f. method: containment
## Confidence level used: 0.95# Comparações múltiplas.
contrast(emm, method = "pairwise")## Per = 1:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 6.560533 2.97 25 2.211 0.2086
## 0 - 3 3.093267 2.97 25 1.042 0.8333
## 0 - 4.5 12.490083 2.97 25 4.209 0.0025
## 0 - 6 21.415683 2.97 25 7.216 <.0001
## 1.5 - 3 -3.467267 2.97 25 -1.168 0.7688
## 1.5 - 4.5 5.929550 2.97 25 1.998 0.2959
## 1.5 - 6 14.855150 2.97 25 5.006 0.0003
## 3 - 4.5 9.396817 2.97 25 3.166 0.0301
## 3 - 6 18.322417 2.97 25 6.174 <.0001
## 4.5 - 6 8.925600 2.97 25 3.008 0.0429
##
## Per = 2:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 -4.622017 2.97 25 -1.557 0.5368
## 0 - 3 -4.982133 2.97 25 -1.679 0.4643
## 0 - 4.5 -1.872017 2.97 25 -0.631 0.9686
## 0 - 6 -3.970217 2.97 25 -1.338 0.6710
## 1.5 - 3 -0.360117 2.97 25 -0.121 0.9999
## 1.5 - 4.5 2.750000 2.97 25 0.927 0.8839
## 1.5 - 6 0.651800 2.97 25 0.220 0.9994
## 3 - 4.5 3.110117 2.97 25 1.048 0.8306
## 3 - 6 1.011917 2.97 25 0.341 0.9969
## 4.5 - 6 -2.098200 2.97 25 -0.707 0.9530
##
## Per = 3:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 -1.761017 2.97 25 -0.593 0.9748
## 0 - 3 -5.197400 2.97 25 -1.751 0.4227
## 0 - 4.5 -5.637900 2.97 25 -1.900 0.3434
## 0 - 6 -5.461317 2.97 25 -1.840 0.3741
## 1.5 - 3 -3.436383 2.97 25 -1.158 0.7745
## 1.5 - 4.5 -3.876883 2.97 25 -1.306 0.6899
## 1.5 - 6 -3.700300 2.97 25 -1.247 0.7247
## 3 - 4.5 -0.440500 2.97 25 -0.148 0.9999
## 3 - 6 -0.263917 2.97 25 -0.089 1.0000
## 4.5 - 6 0.176583 2.97 25 0.060 1.0000
##
## Per = 4:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 0.992033 2.97 25 0.334 0.9971
## 0 - 3 -0.000017 2.97 25 0.000 1.0000
## 0 - 4.5 -0.000033 2.97 25 0.000 1.0000
## 0 - 6 -3.020833 2.97 25 -1.018 0.8447
## 1.5 - 3 -0.992050 2.97 25 -0.334 0.9971
## 1.5 - 4.5 -0.992067 2.97 25 -0.334 0.9971
## 1.5 - 6 -4.012867 2.97 25 -1.352 0.6624
## 3 - 4.5 -0.000017 2.97 25 0.000 1.0000
## 3 - 6 -3.020817 2.97 25 -1.018 0.8447
## 4.5 - 6 -3.020800 2.97 25 -1.018 0.8447
##
## P value adjustment: tukey method for comparing a family of 5 estimatesmultcomp::cld(emm)## Per = 1:
## Mate emmean SE df lower.CL upper.CL .group
## 6 78.7 2.1 25 74.3 83.0 1
## 4.5 87.6 2.1 25 83.3 91.9 2
## 1.5 93.5 2.1 25 89.2 97.8 23
## 3 97.0 2.1 25 92.7 101.3 3
## 0 100.1 2.1 29 95.8 104.4 3
##
## Per = 2:
## Mate emmean SE df lower.CL upper.CL .group
## 0 78.0 2.1 29 73.8 82.3 1
## 4.5 79.9 2.1 25 75.6 84.2 1
## 6 82.0 2.1 25 77.7 86.3 1
## 1.5 82.7 2.1 25 78.3 87.0 1
## 3 83.0 2.1 25 78.7 87.3 1
##
## Per = 3:
## Mate emmean SE df lower.CL upper.CL .group
## 0 82.3 2.1 29 78.0 86.6 1
## 1.5 84.0 2.1 25 79.7 88.4 1
## 3 87.5 2.1 25 83.1 91.8 1
## 6 87.7 2.1 25 83.4 92.1 1
## 4.5 87.9 2.1 25 83.6 92.2 1
##
## Per = 4:
## Mate emmean SE df lower.CL upper.CL .group
## 1.5 77.4 2.1 25 73.1 81.7 1
## 0 78.4 2.1 29 74.1 82.7 1
## 3 78.4 2.1 25 74.1 82.7 1
## 4.5 78.4 2.1 25 74.1 82.7 1
## 6 81.4 2.1 25 77.1 85.7 1
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 5 estimates
## significance level used: alpha = 0.05grid <- multcomp::cld(emm)
grid <- grid %>%
group_by(Per) %>%
mutate(cld = numbers_to_letters(.group)) %>%
ungroup()
ggplot(data = grid,
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
geom_text(mapping = aes(label = sprintf("%0.2f %s", emmean, cld)),
angle = 90,
vjust = 0,
nudge_x = -0.05) +
labs(x = "Níveis de mate",
y = "Consumo") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
#Na seções a seguir serão apenas considerados os modelos de efeito aleatório, o teste para o para o parâmetro de autocorrelação de primeira ordem, as médias ajustadas e constrastes entre elas.
Análise da variável postura
# ATTENTION: a variável `postura` contém valores ausentes.
# Modelo de efeitos aleatórios.
mm0 <- lme(postura ~ Mate + Per + Mate:Per,
random = ~1 | parcela,
method = "ML",
na.action = na.omit,
data = tb)
# Modelo com correlação AR(1) entre observações.
mm1 <- update(mm0,
correlation = corAR1(value = 0.1, form = ~per | parcela))
# Estimativa de \rho.
intervals(mm1)$corStruct## lower est. upper
## Phi -0.3688275 -0.06999067 0.2419598
## attr(,"label")
## [1] "Correlation structure:"# LRT entre modelos aninhados.
anova(mm1, mm0)## Model df AIC BIC logLik Test L.Ratio p-value
## mm1 1 23 366.9966 430.3291 -160.4983
## mm0 2 22 365.1943 425.7733 -160.5971 1 vs 2 0.1977131 0.6566# Estimativas dos parâmetros do modelo escolhido.
summary(mm0)## Linear mixed-effects model fit by maximum likelihood
## Data: tb
## AIC BIC logLik
## 365.1943 425.7733 -160.5971
##
## Random effects:
## Formula: ~1 | parcela
## (Intercept) Residual
## StdDev: 0.8321831 0.7796921
##
## Fixed effects: postura ~ Mate + Per + Mate:Per
## Value Std.Error DF t-value p-value
## (Intercept) 93.92856 0.5606024 72 167.54934 0.0000
## Mate1.5 -1.36906 0.7590592 24 -1.80363 0.0839
## Mate3 -1.17063 0.7590592 24 -1.54221 0.1361
## Mate4.5 -1.07144 0.7590592 24 -1.41154 0.1709
## Mate6 -1.66666 0.7590592 24 -2.19569 0.0380
## Per2 -0.83332 0.5420589 72 -1.53732 0.1286
## Per3 0.00000 0.5420589 72 0.00000 1.0000
## Per4 0.00000 0.5420589 72 0.00000 1.0000
## Mate1.5:Per2 0.33732 0.7339512 72 0.45959 0.6472
## Mate3:Per2 1.82539 0.7339512 72 2.48707 0.0152
## Mate4.5:Per2 1.23017 0.7339512 72 1.67609 0.0981
## Mate6:Per2 1.03172 0.7339512 72 1.40571 0.1641
## Mate1.5:Per3 0.59523 0.7339512 72 0.81100 0.4200
## Mate3:Per3 0.79363 0.7339512 72 1.08132 0.2832
## Mate4.5:Per3 0.00003 0.7339512 72 0.00005 1.0000
## Mate6:Per3 0.09920 0.7339512 72 0.13516 0.8929
## Mate1.5:Per4 0.59525 0.7339512 72 0.81102 0.4200
## Mate3:Per4 0.29762 0.7339512 72 0.40550 0.6863
## Mate4.5:Per4 -0.09920 0.7339512 72 -0.13516 0.8929
## Mate6:Per4 0.29760 0.7339512 72 0.40548 0.6863
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.69310930 -0.38900664 -0.01593018 0.58917028 2.58239450
##
## Number of Observations: 116
## Number of Groups: 29# Quadro de testes para os termos de efeito fixo.
anova(mm0)## numDF denDF F-value p-value
## (Intercept) 1 72 245745.03 <.0001
## Mate 4 24 1.37 0.2735
## Per 3 72 0.76 0.5205
## Mate:Per 12 72 1.23 0.2827# Médias ajustadas para todas as combinações entre níveis.
emm <- emmeans(mm0, specs = ~Per + Mate)
emm## Per Mate emmean SE df lower.CL upper.CL
## 1 0 93.9 0.561 28 92.8 95.1
## 2 0 93.1 0.561 28 91.9 94.2
## 3 0 93.9 0.561 28 92.8 95.1
## 4 0 93.9 0.561 28 92.8 95.1
## 1 1.5 92.6 0.512 24 91.5 93.6
## 2 1.5 92.1 0.512 24 91.0 93.1
## 3 1.5 93.2 0.512 24 92.1 94.2
## 4 1.5 93.2 0.512 24 92.1 94.2
## 1 3 92.8 0.512 24 91.7 93.8
## 2 3 93.8 0.512 24 92.7 94.8
## 3 3 93.6 0.512 24 92.5 94.6
## 4 3 93.1 0.512 24 92.0 94.1
## 1 4.5 92.9 0.512 24 91.8 93.9
## 2 4.5 93.3 0.512 24 92.2 94.3
## 3 4.5 92.9 0.512 24 91.8 93.9
## 4 4.5 92.8 0.512 24 91.7 93.8
## 1 6 92.3 0.512 24 91.2 93.3
## 2 6 92.5 0.512 24 91.4 93.5
## 3 6 92.4 0.512 24 91.3 93.4
## 4 6 92.6 0.512 24 91.5 93.6
##
## d.f. method: containment
## Confidence level used: 0.95# Gráfico com intervalos de confiança.
gg1 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Per,
y = emmean)) +
facet_wrap(facets = ~Mate,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Período de postura",
y = "Postura") +
ggtitle(label = NULL,
subtitle = "Níveis de mate")
# Gráfico com intervalos de confiança.
gg2 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Níveis de mate",
y = "Postura") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
gridExtra::grid.arrange(gg1, gg2, ncol = 1)
# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Per | Mate)
multcomp::cld(emm)## Mate = 0:
## Per emmean SE df lower.CL upper.CL .group
## 2 93.1 0.561 28 91.9 94.2 1
## 1 93.9 0.561 28 92.8 95.1 1
## 3 93.9 0.561 28 92.8 95.1 1
## 4 93.9 0.561 28 92.8 95.1 1
##
## Mate = 1.5:
## Per emmean SE df lower.CL upper.CL .group
## 2 92.1 0.512 24 91.0 93.1 1
## 1 92.6 0.512 24 91.5 93.6 1
## 3 93.2 0.512 24 92.1 94.2 1
## 4 93.2 0.512 24 92.1 94.2 1
##
## Mate = 3:
## Per emmean SE df lower.CL upper.CL .group
## 1 92.8 0.512 24 91.7 93.8 1
## 4 93.1 0.512 24 92.0 94.1 1
## 3 93.6 0.512 24 92.5 94.6 1
## 2 93.8 0.512 24 92.7 94.8 1
##
## Mate = 4.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 92.8 0.512 24 91.7 93.8 1
## 1 92.9 0.512 24 91.8 93.9 1
## 3 92.9 0.512 24 91.8 93.9 1
## 2 93.3 0.512 24 92.2 94.3 1
##
## Mate = 6:
## Per emmean SE df lower.CL upper.CL .group
## 1 92.3 0.512 24 91.2 93.3 1
## 3 92.4 0.512 24 91.3 93.4 1
## 2 92.5 0.512 24 91.4 93.5 1
## 4 92.6 0.512 24 91.5 93.6 1
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 4 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## Mate = 0:
## contrast estimate SE df t.ratio p.value
## 1 - 2 8.33e-01 0.542 72 1.537 0.4209
## 1 - 3 0.00e+00 0.542 72 0.000 1.0000
## 1 - 4 0.00e+00 0.542 72 0.000 1.0000
## 2 - 3 -8.33e-01 0.542 72 -1.537 0.4209
## 2 - 4 -8.33e-01 0.542 72 -1.537 0.4209
## 3 - 4 0.00e+00 0.542 72 0.000 1.0000
##
## Mate = 1.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 4.96e-01 0.495 72 1.002 0.7485
## 1 - 3 -5.95e-01 0.495 72 -1.203 0.6270
## 1 - 4 -5.95e-01 0.495 72 -1.203 0.6270
## 2 - 3 -1.09e+00 0.495 72 -2.205 0.1316
## 2 - 4 -1.09e+00 0.495 72 -2.205 0.1316
## 3 - 4 -1.67e-05 0.495 72 0.000 1.0000
##
## Mate = 3:
## contrast estimate SE df t.ratio p.value
## 1 - 2 -9.92e-01 0.495 72 -2.005 0.1958
## 1 - 3 -7.94e-01 0.495 72 -1.604 0.3830
## 1 - 4 -2.98e-01 0.495 72 -0.601 0.9313
## 2 - 3 1.98e-01 0.495 72 0.401 0.9780
## 2 - 4 6.94e-01 0.495 72 1.403 0.5014
## 3 - 4 4.96e-01 0.495 72 1.002 0.7485
##
## Mate = 4.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 -3.97e-01 0.495 72 -0.802 0.8533
## 1 - 3 -3.33e-05 0.495 72 0.000 1.0000
## 1 - 4 9.92e-02 0.495 72 0.200 0.9971
## 2 - 3 3.97e-01 0.495 72 0.802 0.8533
## 2 - 4 4.96e-01 0.495 72 1.002 0.7484
## 3 - 4 9.92e-02 0.495 72 0.201 0.9971
##
## Mate = 6:
## contrast estimate SE df t.ratio p.value
## 1 - 2 -1.98e-01 0.495 72 -0.401 0.9780
## 1 - 3 -9.92e-02 0.495 72 -0.200 0.9971
## 1 - 4 -2.98e-01 0.495 72 -0.601 0.9313
## 2 - 3 9.92e-02 0.495 72 0.200 0.9971
## 2 - 4 -9.92e-02 0.495 72 -0.200 0.9971
## 3 - 4 -1.98e-01 0.495 72 -0.401 0.9780
##
## P value adjustment: tukey method for comparing a family of 4 estimates# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Mate | Per)
multcomp::cld(emm)## Per = 1:
## Mate emmean SE df lower.CL upper.CL .group
## 6 92.3 0.512 24 91.2 93.3 1
## 1.5 92.6 0.512 24 91.5 93.6 1
## 3 92.8 0.512 24 91.7 93.8 1
## 4.5 92.9 0.512 24 91.8 93.9 1
## 0 93.9 0.561 28 92.8 95.1 1
##
## Per = 2:
## Mate emmean SE df lower.CL upper.CL .group
## 1.5 92.1 0.512 24 91.0 93.1 1
## 6 92.5 0.512 24 91.4 93.5 1
## 0 93.1 0.561 28 91.9 94.2 1
## 4.5 93.3 0.512 24 92.2 94.3 1
## 3 93.8 0.512 24 92.7 94.8 1
##
## Per = 3:
## Mate emmean SE df lower.CL upper.CL .group
## 6 92.4 0.512 24 91.3 93.4 1
## 4.5 92.9 0.512 24 91.8 93.9 1
## 1.5 93.2 0.512 24 92.1 94.2 1
## 3 93.6 0.512 24 92.5 94.6 1
## 0 93.9 0.561 28 92.8 95.1 1
##
## Per = 4:
## Mate emmean SE df lower.CL upper.CL .group
## 6 92.6 0.512 24 91.5 93.6 1
## 4.5 92.8 0.512 24 91.7 93.8 1
## 3 93.1 0.512 24 92.0 94.1 1
## 1.5 93.2 0.512 24 92.1 94.2 1
## 0 93.9 0.561 28 92.8 95.1 1
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 5 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## Per = 1:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 1.3691 0.759 24 1.804 0.3946
## 0 - 3 1.1706 0.759 24 1.542 0.5466
## 0 - 4.5 1.0714 0.759 24 1.412 0.6265
## 0 - 6 1.6667 0.759 24 2.196 0.2153
## 1.5 - 3 -0.1984 0.724 24 -0.274 0.9987
## 1.5 - 4.5 -0.2976 0.724 24 -0.411 0.9936
## 1.5 - 6 0.2976 0.724 24 0.411 0.9936
## 3 - 4.5 -0.0992 0.724 24 -0.137 0.9999
## 3 - 6 0.4960 0.724 24 0.685 0.9577
## 4.5 - 6 0.5952 0.724 24 0.822 0.9211
##
## Per = 2:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 1.0317 0.759 24 1.359 0.6583
## 0 - 3 -0.6548 0.759 24 -0.863 0.9077
## 0 - 4.5 -0.1587 0.759 24 -0.209 0.9995
## 0 - 6 0.6349 0.759 24 0.836 0.9165
## 1.5 - 3 -1.6865 0.724 24 -2.330 0.1700
## 1.5 - 4.5 -1.1905 0.724 24 -1.645 0.4849
## 1.5 - 6 -0.3968 0.724 24 -0.548 0.9811
## 3 - 4.5 0.4960 0.724 24 0.685 0.9577
## 3 - 6 1.2897 0.724 24 1.782 0.4064
## 4.5 - 6 0.7937 0.724 24 1.097 0.8065
##
## Per = 3:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 0.7738 0.759 24 1.019 0.8439
## 0 - 3 0.3770 0.759 24 0.497 0.9869
## 0 - 4.5 1.0714 0.759 24 1.411 0.6265
## 0 - 6 1.5675 0.759 24 2.065 0.2673
## 1.5 - 3 -0.3968 0.724 24 -0.548 0.9811
## 1.5 - 4.5 0.2976 0.724 24 0.411 0.9936
## 1.5 - 6 0.7936 0.724 24 1.097 0.8065
## 3 - 4.5 0.6944 0.724 24 0.959 0.8703
## 3 - 6 1.1905 0.724 24 1.645 0.4849
## 4.5 - 6 0.4960 0.724 24 0.685 0.9577
##
## Per = 4:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 0.7738 0.759 24 1.019 0.8439
## 0 - 3 0.8730 0.759 24 1.150 0.7786
## 0 - 4.5 1.1706 0.759 24 1.542 0.5465
## 0 - 6 1.3691 0.759 24 1.804 0.3946
## 1.5 - 3 0.0992 0.724 24 0.137 0.9999
## 1.5 - 4.5 0.3968 0.724 24 0.548 0.9811
## 1.5 - 6 0.5952 0.724 24 0.822 0.9211
## 3 - 4.5 0.2976 0.724 24 0.411 0.9936
## 3 - 6 0.4960 0.724 24 0.685 0.9577
## 4.5 - 6 0.1984 0.724 24 0.274 0.9987
##
## P value adjustment: tukey method for comparing a family of 5 estimatesgrid <- multcomp::cld(emm)
grid <- grid %>%
group_by(Per) %>%
mutate(cld = numbers_to_letters(.group)) %>%
ungroup()
ggplot(data = grid,
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
geom_text(mapping = aes(label = sprintf("%0.2f %s", emmean, cld)),
angle = 90,
vjust = 0,
nudge_x = -0.05) +
labs(x = "Níveis de mate",
y = "Postura") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
#Análise da variável caduzia
# Modelo de efeitos aleatórios.
mm0 <- lme(caduzia ~ Mate + Per + Mate:Per,
random = ~1 | parcela,
method = "ML",
na.action = na.omit,
data = tb)
# Modelo com correlação AR(1) entre observações.
mm1 <- update(mm0,
correlation = corAR1(value = 0.1, form = ~per | parcela))
# Estimativa de \rho.
intervals(mm1)$corStruct## lower est. upper
## Phi -0.2205656 0.08816632 0.3808404
## attr(,"label")
## [1] "Correlation structure:"# LRT entre modelos aninhados.
anova(mm1, mm0)## Model df AIC BIC logLik Test L.Ratio p-value
## mm1 1 23 172.7175 236.8298 -63.35876
## mm0 2 22 171.0476 232.3724 -63.52381 1 vs 2 0.3301042 0.5656# Estimativas dos parâmetros do modelo escolhido.
summary(mm0)## Linear mixed-effects model fit by maximum likelihood
## Data: tb
## AIC BIC logLik
## 171.0476 232.3724 -63.52381
##
## Random effects:
## Formula: ~1 | parcela
## (Intercept) Residual
## StdDev: 0.3057077 0.3437366
##
## Fixed effects: caduzia ~ Mate + Per + Mate:Per
## Value Std.Error DF t-value p-value
## (Intercept) 7.960317 0.2057241 75 38.69414 0.0000
## Mate1.5 -0.741700 0.2909378 25 -2.54934 0.0173
## Mate3 -0.491400 0.2909378 25 -1.68902 0.1037
## Mate4.5 -1.222217 0.2909378 25 -4.20095 0.0003
## Mate6 -1.868567 0.2909378 25 -6.42256 0.0000
## Per2 -1.730050 0.2173981 75 -7.95798 0.0000
## Per3 -1.412483 0.2173981 75 -6.49722 0.0000
## Per4 -1.723167 0.2173981 75 -7.92632 0.0000
## Mate1.5:Per2 0.933267 0.3074474 75 3.03553 0.0033
## Mate3:Per2 0.588650 0.3074474 75 1.91464 0.0594
## Mate4.5:Per2 1.111217 0.3074474 75 3.61433 0.0005
## Mate6:Per2 1.973517 0.3074474 75 6.41904 0.0000
## Mate1.5:Per3 0.637850 0.3074474 75 2.07466 0.0414
## Mate3:Per3 0.623067 0.3074474 75 2.02658 0.0463
## Mate4.5:Per3 1.444167 0.3074474 75 4.69728 0.0000
## Mate6:Per3 2.105933 0.3074474 75 6.84974 0.0000
## Mate1.5:Per4 0.444083 0.3074474 75 1.44442 0.1528
## Mate3:Per4 0.271617 0.3074474 75 0.88346 0.3798
## Mate4.5:Per4 1.021150 0.3074474 75 3.32138 0.0014
## Mate6:Per4 1.912717 0.3074474 75 6.22128 0.0000
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.576517355 -0.596609987 -0.004727694 0.488033630 2.861621803
##
## Number of Observations: 120
## Number of Groups: 30# Quadro de testes para os termos de efeito fixo.
anova(mm0)## numDF denDF F-value p-value
## (Intercept) 1 75 8673.713 <.0001
## Mate 4 25 0.941 0.4567
## Per 3 75 40.566 <.0001
## Mate:Per 12 75 6.684 <.0001# Médias ajustadas para todas as combinações entre níveis.
emm <- emmeans(mm0, specs = ~Per + Mate)
emm## Per Mate emmean SE df lower.CL upper.CL
## 1 0 7.96 0.206 29 7.54 8.38
## 2 0 6.23 0.206 29 5.81 6.65
## 3 0 6.55 0.206 29 6.13 6.97
## 4 0 6.24 0.206 29 5.82 6.66
## 1 1.5 7.22 0.206 25 6.79 7.64
## 2 1.5 6.42 0.206 25 6.00 6.85
## 3 1.5 6.44 0.206 25 6.02 6.87
## 4 1.5 5.94 0.206 25 5.52 6.36
## 1 3 7.47 0.206 25 7.05 7.89
## 2 3 6.33 0.206 25 5.90 6.75
## 3 3 6.68 0.206 25 6.26 7.10
## 4 3 6.02 0.206 25 5.59 6.44
## 1 4.5 6.74 0.206 25 6.31 7.16
## 2 4.5 6.12 0.206 25 5.70 6.54
## 3 4.5 6.77 0.206 25 6.35 7.19
## 4 4.5 6.04 0.206 25 5.61 6.46
## 1 6 6.09 0.206 25 5.67 6.52
## 2 6 6.34 0.206 25 5.91 6.76
## 3 6 6.79 0.206 25 6.36 7.21
## 4 6 6.28 0.206 25 5.86 6.70
##
## d.f. method: containment
## Confidence level used: 0.95# Gráfico com intervalos de confiança.
gg1 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Per,
y = emmean)) +
facet_wrap(facets = ~Mate,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Período de postura",
y = "???") +
ggtitle(label = NULL,
subtitle = "Níveis de mate")
# Gráfico com intervalos de confiança.
gg2 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Níveis de mate",
y = "???") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
gridExtra::grid.arrange(gg1, gg2, ncol = 1)
# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Per | Mate)
multcomp::cld(emm)## Mate = 0:
## Per emmean SE df lower.CL upper.CL .group
## 2 6.23 0.206 29 5.81 6.65 1
## 4 6.24 0.206 29 5.82 6.66 1
## 3 6.55 0.206 29 6.13 6.97 1
## 1 7.96 0.206 29 7.54 8.38 2
##
## Mate = 1.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 5.94 0.206 25 5.52 6.36 1
## 2 6.42 0.206 25 6.00 6.85 1
## 3 6.44 0.206 25 6.02 6.87 1
## 1 7.22 0.206 25 6.79 7.64 2
##
## Mate = 3:
## Per emmean SE df lower.CL upper.CL .group
## 4 6.02 0.206 25 5.59 6.44 1
## 2 6.33 0.206 25 5.90 6.75 12
## 3 6.68 0.206 25 6.26 7.10 2
## 1 7.47 0.206 25 7.05 7.89 3
##
## Mate = 4.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 6.04 0.206 25 5.61 6.46 1
## 2 6.12 0.206 25 5.70 6.54 1
## 1 6.74 0.206 25 6.31 7.16 2
## 3 6.77 0.206 25 6.35 7.19 2
##
## Mate = 6:
## Per emmean SE df lower.CL upper.CL .group
## 1 6.09 0.206 25 5.67 6.52 1
## 4 6.28 0.206 25 5.86 6.70 12
## 2 6.34 0.206 25 5.91 6.76 12
## 3 6.79 0.206 25 6.36 7.21 2
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 4 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## Mate = 0:
## contrast estimate SE df t.ratio p.value
## 1 - 2 1.73005 0.217 75 7.958 <.0001
## 1 - 3 1.41248 0.217 75 6.497 <.0001
## 1 - 4 1.72317 0.217 75 7.926 <.0001
## 2 - 3 -0.31757 0.217 75 -1.461 0.4662
## 2 - 4 -0.00688 0.217 75 -0.032 1.0000
## 3 - 4 0.31068 0.217 75 1.429 0.4854
##
## Mate = 1.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 0.79678 0.217 75 3.665 0.0025
## 1 - 3 0.77463 0.217 75 3.563 0.0035
## 1 - 4 1.27908 0.217 75 5.884 <.0001
## 2 - 3 -0.02215 0.217 75 -0.102 0.9996
## 2 - 4 0.48230 0.217 75 2.219 0.1276
## 3 - 4 0.50445 0.217 75 2.320 0.1025
##
## Mate = 3:
## contrast estimate SE df t.ratio p.value
## 1 - 2 1.14140 0.217 75 5.250 <.0001
## 1 - 3 0.78942 0.217 75 3.631 0.0028
## 1 - 4 1.45155 0.217 75 6.677 <.0001
## 2 - 3 -0.35198 0.217 75 -1.619 0.3743
## 2 - 4 0.31015 0.217 75 1.427 0.4869
## 3 - 4 0.66213 0.217 75 3.046 0.0165
##
## Mate = 4.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 0.61883 0.217 75 2.847 0.0285
## 1 - 3 -0.03168 0.217 75 -0.146 0.9989
## 1 - 4 0.70202 0.217 75 3.229 0.0098
## 2 - 3 -0.65052 0.217 75 -2.992 0.0192
## 2 - 4 0.08318 0.217 75 0.383 0.9808
## 3 - 4 0.73370 0.217 75 3.375 0.0063
##
## Mate = 6:
## contrast estimate SE df t.ratio p.value
## 1 - 2 -0.24347 0.217 75 -1.120 0.6785
## 1 - 3 -0.69345 0.217 75 -3.190 0.0110
## 1 - 4 -0.18955 0.217 75 -0.872 0.8193
## 2 - 3 -0.44998 0.217 75 -2.070 0.1725
## 2 - 4 0.05392 0.217 75 0.248 0.9946
## 3 - 4 0.50390 0.217 75 2.318 0.1031
##
## P value adjustment: tukey method for comparing a family of 4 estimates# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Mate | Per)
multcomp::cld(emm)## Per = 1:
## Mate emmean SE df lower.CL upper.CL .group
## 6 6.09 0.206 25 5.67 6.52 1
## 4.5 6.74 0.206 25 6.31 7.16 12
## 1.5 7.22 0.206 25 6.79 7.64 23
## 3 7.47 0.206 25 7.05 7.89 23
## 0 7.96 0.206 29 7.54 8.38 3
##
## Per = 2:
## Mate emmean SE df lower.CL upper.CL .group
## 4.5 6.12 0.206 25 5.70 6.54 1
## 0 6.23 0.206 29 5.81 6.65 1
## 3 6.33 0.206 25 5.90 6.75 1
## 6 6.34 0.206 25 5.91 6.76 1
## 1.5 6.42 0.206 25 6.00 6.85 1
##
## Per = 3:
## Mate emmean SE df lower.CL upper.CL .group
## 1.5 6.44 0.206 25 6.02 6.87 1
## 0 6.55 0.206 29 6.13 6.97 1
## 3 6.68 0.206 25 6.26 7.10 1
## 4.5 6.77 0.206 25 6.35 7.19 1
## 6 6.79 0.206 25 6.36 7.21 1
##
## Per = 4:
## Mate emmean SE df lower.CL upper.CL .group
## 1.5 5.94 0.206 25 5.52 6.36 1
## 3 6.02 0.206 25 5.59 6.44 1
## 4.5 6.04 0.206 25 5.61 6.46 1
## 0 6.24 0.206 29 5.82 6.66 1
## 6 6.28 0.206 25 5.86 6.70 1
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 5 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## Per = 1:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 0.7417 0.291 25 2.549 0.1115
## 0 - 3 0.4914 0.291 25 1.689 0.4583
## 0 - 4.5 1.2222 0.291 25 4.201 0.0025
## 0 - 6 1.8686 0.291 25 6.423 <.0001
## 1.5 - 3 -0.2503 0.291 25 -0.860 0.9086
## 1.5 - 4.5 0.4805 0.291 25 1.652 0.4803
## 1.5 - 6 1.1269 0.291 25 3.873 0.0056
## 3 - 4.5 0.7308 0.291 25 2.512 0.1199
## 3 - 6 1.3772 0.291 25 4.734 0.0007
## 4.5 - 6 0.6463 0.291 25 2.222 0.2046
##
## Per = 2:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 -0.1916 0.291 25 -0.658 0.9634
## 0 - 3 -0.0973 0.291 25 -0.334 0.9971
## 0 - 4.5 0.1110 0.291 25 0.382 0.9952
## 0 - 6 -0.1050 0.291 25 -0.361 0.9961
## 1.5 - 3 0.0943 0.291 25 0.324 0.9974
## 1.5 - 4.5 0.3026 0.291 25 1.040 0.8344
## 1.5 - 6 0.0866 0.291 25 0.298 0.9982
## 3 - 4.5 0.2082 0.291 25 0.716 0.9509
## 3 - 6 -0.0077 0.291 25 -0.026 1.0000
## 4.5 - 6 -0.2160 0.291 25 -0.742 0.9443
##
## Per = 3:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 0.1038 0.291 25 0.357 0.9963
## 0 - 3 -0.1317 0.291 25 -0.453 0.9908
## 0 - 4.5 -0.2220 0.291 25 -0.763 0.9388
## 0 - 6 -0.2374 0.291 25 -0.816 0.9233
## 1.5 - 3 -0.2355 0.291 25 -0.810 0.9252
## 1.5 - 4.5 -0.3258 0.291 25 -1.120 0.7947
## 1.5 - 6 -0.3412 0.291 25 -1.173 0.7664
## 3 - 4.5 -0.0903 0.291 25 -0.310 0.9978
## 3 - 6 -0.1057 0.291 25 -0.363 0.9960
## 4.5 - 6 -0.0154 0.291 25 -0.053 1.0000
##
## Per = 4:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 0.2976 0.291 25 1.023 0.8424
## 0 - 3 0.2198 0.291 25 0.755 0.9408
## 0 - 4.5 0.2011 0.291 25 0.691 0.9566
## 0 - 6 -0.0442 0.291 25 -0.152 0.9999
## 1.5 - 3 -0.0778 0.291 25 -0.268 0.9988
## 1.5 - 4.5 -0.0965 0.291 25 -0.332 0.9972
## 1.5 - 6 -0.3418 0.291 25 -1.175 0.7653
## 3 - 4.5 -0.0187 0.291 25 -0.064 1.0000
## 3 - 6 -0.2639 0.291 25 -0.907 0.8914
## 4.5 - 6 -0.2452 0.291 25 -0.843 0.9145
##
## P value adjustment: tukey method for comparing a family of 5 estimatesgrid <- multcomp::cld(emm)
grid <- grid %>%
group_by(Per) %>%
mutate(cld = numbers_to_letters(.group)) %>%
ungroup()
ggplot(data = grid,
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
geom_text(mapping = aes(label = sprintf("%0.2f %s", emmean, cld)),
angle = 90,
vjust = 0,
nudge_x = -0.05) +
labs(x = "Níveis de mate",
y = "???") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
#Análise da variável camovos
# Modelo de efeitos aleatórios.
mm0 <- lme(camovos ~ Mate + Per + Mate:Per,
random = ~1 | parcela,
method = "ML",
na.action = na.omit,
data = tb)
# Modelo com correlação AR(1) entre observações.
mm1 <- update(mm0,
correlation = corAR1(value = 0.1, form = ~per | parcela))
# Estimativa de \rho.
intervals(mm1)$corStruct## lower est. upper
## Phi -0.2425798 0.05163788 0.3371567
## attr(,"label")
## [1] "Correlation structure:"# LRT entre modelos aninhados.
anova(mm1, mm0)## Model df AIC BIC logLik Test L.Ratio p-value
## mm1 1 23 -154.340 -90.22766 100.170
## mm0 2 22 -156.228 -94.90321 100.114 1 vs 2 0.1119421 0.7379# Estimativas dos parâmetros do modelo escolhido.
summary(mm0)## Linear mixed-effects model fit by maximum likelihood
## Data: tb
## AIC BIC logLik
## -156.228 -94.90321 100.114
##
## Random effects:
## Formula: ~1 | parcela
## (Intercept) Residual
## StdDev: 0.08285527 0.08668787
##
## Fixed effects: camovos ~ Mate + Per + Mate:Per
## Value Std.Error DF t-value p-value
## (Intercept) 1.9228500 0.05362795 75 35.85537 0.0000
## Mate1.5 -0.1640167 0.07584137 25 -2.16263 0.0403
## Mate3 -0.0544167 0.07584137 25 -0.71751 0.4797
## Mate4.5 -0.2110500 0.07584137 25 -2.78278 0.0101
## Mate6 -0.3778833 0.07584137 25 -4.98255 0.0000
## Per2 -0.4231667 0.05482623 75 -7.71833 0.0000
## Per3 -0.3430667 0.05482623 75 -6.25735 0.0000
## Per4 -0.4148500 0.05482623 75 -7.56663 0.0000
## Mate1.5:Per2 0.2211333 0.07753599 75 2.85201 0.0056
## Mate3:Per2 0.1549333 0.07753599 75 1.99821 0.0493
## Mate4.5:Per2 0.2691000 0.07753599 75 3.47065 0.0009
## Mate6:Per2 0.4851833 0.07753599 75 6.25752 0.0000
## Mate1.5:Per3 0.1639500 0.07753599 75 2.11450 0.0378
## Mate3:Per3 0.1614667 0.07753599 75 2.08247 0.0407
## Mate4.5:Per3 0.3481500 0.07753599 75 4.49017 0.0000
## Mate6:Per3 0.5168500 0.07753599 75 6.66594 0.0000
## Mate1.5:Per4 0.1130833 0.07753599 75 1.45846 0.1489
## Mate3:Per4 0.0579500 0.07753599 75 0.74739 0.4572
## Mate4.5:Per4 0.2339333 0.07753599 75 3.01709 0.0035
## Mate6:Per4 0.4651167 0.07753599 75 5.99872 0.0000
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.56143798 -0.60470629 0.03188733 0.58494602 3.38945169
##
## Number of Observations: 120
## Number of Groups: 30# Quadro de testes para os termos de efeito fixo.
anova(mm0)## numDF denDF F-value p-value
## (Intercept) 1 75 7556.111 <.0001
## Mate 4 25 0.457 0.7661
## Per 3 75 37.904 <.0001
## Mate:Per 12 75 6.187 <.0001# Médias ajustadas para todas as combinações entre níveis.
emm <- emmeans(mm0, specs = ~Per + Mate)
emm## Per Mate emmean SE df lower.CL upper.CL
## 1 0 1.92 0.0536 29 1.81 2.03
## 2 0 1.50 0.0536 29 1.39 1.61
## 3 0 1.58 0.0536 29 1.47 1.69
## 4 0 1.51 0.0536 29 1.40 1.62
## 1 1.5 1.76 0.0536 25 1.65 1.87
## 2 1.5 1.56 0.0536 25 1.45 1.67
## 3 1.5 1.58 0.0536 25 1.47 1.69
## 4 1.5 1.46 0.0536 25 1.35 1.57
## 1 3 1.87 0.0536 25 1.76 1.98
## 2 3 1.60 0.0536 25 1.49 1.71
## 3 3 1.69 0.0536 25 1.58 1.80
## 4 3 1.51 0.0536 25 1.40 1.62
## 1 4.5 1.71 0.0536 25 1.60 1.82
## 2 4.5 1.56 0.0536 25 1.45 1.67
## 3 4.5 1.72 0.0536 25 1.61 1.83
## 4 4.5 1.53 0.0536 25 1.42 1.64
## 1 6 1.54 0.0536 25 1.43 1.66
## 2 6 1.61 0.0536 25 1.50 1.72
## 3 6 1.72 0.0536 25 1.61 1.83
## 4 6 1.60 0.0536 25 1.48 1.71
##
## d.f. method: containment
## Confidence level used: 0.95# Gráfico com intervalos de confiança.
gg1 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Per,
y = emmean)) +
facet_wrap(facets = ~Mate,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Período de postura",
y = "???") +
ggtitle(label = NULL,
subtitle = "Níveis de mate")
# Gráfico com intervalos de confiança.
gg2 <-
ggplot(data = as.data.frame(emm),
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
labs(x = "Níveis de mate",
y = "???") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
gridExtra::grid.arrange(gg1, gg2, ncol = 1)
# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Per | Mate)
multcomp::cld(emm)## Mate = 0:
## Per emmean SE df lower.CL upper.CL .group
## 2 1.50 0.0536 29 1.39 1.61 1
## 4 1.51 0.0536 29 1.40 1.62 1
## 3 1.58 0.0536 29 1.47 1.69 1
## 1 1.92 0.0536 29 1.81 2.03 2
##
## Mate = 1.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 1.46 0.0536 25 1.35 1.57 1
## 2 1.56 0.0536 25 1.45 1.67 1
## 3 1.58 0.0536 25 1.47 1.69 1
## 1 1.76 0.0536 25 1.65 1.87 2
##
## Mate = 3:
## Per emmean SE df lower.CL upper.CL .group
## 4 1.51 0.0536 25 1.40 1.62 1
## 2 1.60 0.0536 25 1.49 1.71 12
## 3 1.69 0.0536 25 1.58 1.80 2
## 1 1.87 0.0536 25 1.76 1.98 3
##
## Mate = 4.5:
## Per emmean SE df lower.CL upper.CL .group
## 4 1.53 0.0536 25 1.42 1.64 1
## 2 1.56 0.0536 25 1.45 1.67 1
## 1 1.71 0.0536 25 1.60 1.82 2
## 3 1.72 0.0536 25 1.61 1.83 2
##
## Mate = 6:
## Per emmean SE df lower.CL upper.CL .group
## 1 1.54 0.0536 25 1.43 1.66 1
## 4 1.60 0.0536 25 1.48 1.71 12
## 2 1.61 0.0536 25 1.50 1.72 12
## 3 1.72 0.0536 25 1.61 1.83 2
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 4 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## Mate = 0:
## contrast estimate SE df t.ratio p.value
## 1 - 2 0.42317 0.0548 75 7.718 <.0001
## 1 - 3 0.34307 0.0548 75 6.257 <.0001
## 1 - 4 0.41485 0.0548 75 7.567 <.0001
## 2 - 3 -0.08010 0.0548 75 -1.461 0.4660
## 2 - 4 -0.00832 0.0548 75 -0.152 0.9987
## 3 - 4 0.07178 0.0548 75 1.309 0.5600
##
## Mate = 1.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 0.20203 0.0548 75 3.685 0.0024
## 1 - 3 0.17912 0.0548 75 3.267 0.0087
## 1 - 4 0.30177 0.0548 75 5.504 <.0001
## 2 - 3 -0.02292 0.0548 75 -0.418 0.9752
## 2 - 4 0.09973 0.0548 75 1.819 0.2726
## 3 - 4 0.12265 0.0548 75 2.237 0.1227
##
## Mate = 3:
## contrast estimate SE df t.ratio p.value
## 1 - 2 0.26823 0.0548 75 4.892 <.0001
## 1 - 3 0.18160 0.0548 75 3.312 0.0076
## 1 - 4 0.35690 0.0548 75 6.510 <.0001
## 2 - 3 -0.08663 0.0548 75 -1.580 0.3961
## 2 - 4 0.08867 0.0548 75 1.617 0.3753
## 3 - 4 0.17530 0.0548 75 3.197 0.0107
##
## Mate = 4.5:
## contrast estimate SE df t.ratio p.value
## 1 - 2 0.15407 0.0548 75 2.810 0.0314
## 1 - 3 -0.00508 0.0548 75 -0.093 0.9997
## 1 - 4 0.18092 0.0548 75 3.300 0.0079
## 2 - 3 -0.15915 0.0548 75 -2.903 0.0245
## 2 - 4 0.02685 0.0548 75 0.490 0.9612
## 3 - 4 0.18600 0.0548 75 3.393 0.0060
##
## Mate = 6:
## contrast estimate SE df t.ratio p.value
## 1 - 2 -0.06202 0.0548 75 -1.131 0.6716
## 1 - 3 -0.17378 0.0548 75 -3.170 0.0116
## 1 - 4 -0.05027 0.0548 75 -0.917 0.7959
## 2 - 3 -0.11177 0.0548 75 -2.039 0.1833
## 2 - 4 0.01175 0.0548 75 0.214 0.9965
## 3 - 4 0.12352 0.0548 75 2.253 0.1186
##
## P value adjustment: tukey method for comparing a family of 4 estimates# Médias ajustadas para níveis de um fator fixando níveis dos demais.
emm <- emmeans(mm0, specs = ~Mate | Per)
multcomp::cld(emm)## Per = 1:
## Mate emmean SE df lower.CL upper.CL .group
## 6 1.54 0.0536 25 1.43 1.66 1
## 4.5 1.71 0.0536 25 1.60 1.82 12
## 1.5 1.76 0.0536 25 1.65 1.87 12
## 3 1.87 0.0536 25 1.76 1.98 2
## 0 1.92 0.0536 29 1.81 2.03 2
##
## Per = 2:
## Mate emmean SE df lower.CL upper.CL .group
## 0 1.50 0.0536 29 1.39 1.61 1
## 1.5 1.56 0.0536 25 1.45 1.67 1
## 4.5 1.56 0.0536 25 1.45 1.67 1
## 3 1.60 0.0536 25 1.49 1.71 1
## 6 1.61 0.0536 25 1.50 1.72 1
##
## Per = 3:
## Mate emmean SE df lower.CL upper.CL .group
## 1.5 1.58 0.0536 25 1.47 1.69 1
## 0 1.58 0.0536 29 1.47 1.69 1
## 3 1.69 0.0536 25 1.58 1.80 1
## 4.5 1.72 0.0536 25 1.61 1.83 1
## 6 1.72 0.0536 25 1.61 1.83 1
##
## Per = 4:
## Mate emmean SE df lower.CL upper.CL .group
## 1.5 1.46 0.0536 25 1.35 1.57 1
## 0 1.51 0.0536 29 1.40 1.62 1
## 3 1.51 0.0536 25 1.40 1.62 1
## 4.5 1.53 0.0536 25 1.42 1.64 1
## 6 1.60 0.0536 25 1.48 1.71 1
##
## d.f. method: containment
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 5 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## Per = 1:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 1.64e-01 0.0758 25 2.163 0.2264
## 0 - 3 5.44e-02 0.0758 25 0.718 0.9505
## 0 - 4.5 2.11e-01 0.0758 25 2.783 0.0694
## 0 - 6 3.78e-01 0.0758 25 4.983 0.0003
## 1.5 - 3 -1.10e-01 0.0758 25 -1.445 0.6057
## 1.5 - 4.5 4.70e-02 0.0758 25 0.620 0.9705
## 1.5 - 6 2.14e-01 0.0758 25 2.820 0.0642
## 3 - 4.5 1.57e-01 0.0758 25 2.065 0.2660
## 3 - 6 3.23e-01 0.0758 25 4.265 0.0021
## 4.5 - 6 1.67e-01 0.0758 25 2.200 0.2125
##
## Per = 2:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 -5.71e-02 0.0758 25 -0.753 0.9415
## 0 - 3 -1.01e-01 0.0758 25 -1.325 0.6785
## 0 - 4.5 -5.80e-02 0.0758 25 -0.765 0.9381
## 0 - 6 -1.07e-01 0.0758 25 -1.415 0.6243
## 1.5 - 3 -4.34e-02 0.0758 25 -0.572 0.9779
## 1.5 - 4.5 -9.33e-04 0.0758 25 -0.012 1.0000
## 1.5 - 6 -5.02e-02 0.0758 25 -0.662 0.9628
## 3 - 4.5 4.25e-02 0.0758 25 0.560 0.9796
## 3 - 6 -6.78e-03 0.0758 25 -0.089 1.0000
## 4.5 - 6 -4.93e-02 0.0758 25 -0.649 0.9652
##
## Per = 3:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 6.67e-05 0.0758 25 0.001 1.0000
## 0 - 3 -1.07e-01 0.0758 25 -1.411 0.6263
## 0 - 4.5 -1.37e-01 0.0758 25 -1.808 0.3915
## 0 - 6 -1.39e-01 0.0758 25 -1.832 0.3783
## 1.5 - 3 -1.07e-01 0.0758 25 -1.412 0.6257
## 1.5 - 4.5 -1.37e-01 0.0758 25 -1.809 0.3911
## 1.5 - 6 -1.39e-01 0.0758 25 -1.833 0.3779
## 3 - 4.5 -3.01e-02 0.0758 25 -0.396 0.9945
## 3 - 6 -3.19e-02 0.0758 25 -0.421 0.9930
## 4.5 - 6 -1.87e-03 0.0758 25 -0.025 1.0000
##
## Per = 4:
## contrast estimate SE df t.ratio p.value
## 0 - 1.5 5.09e-02 0.0758 25 0.672 0.9607
## 0 - 3 -3.53e-03 0.0758 25 -0.047 1.0000
## 0 - 4.5 -2.29e-02 0.0758 25 -0.302 0.9981
## 0 - 6 -8.72e-02 0.0758 25 -1.150 0.7786
## 1.5 - 3 -5.45e-02 0.0758 25 -0.718 0.9503
## 1.5 - 4.5 -7.38e-02 0.0758 25 -0.973 0.8646
## 1.5 - 6 -1.38e-01 0.0758 25 -1.822 0.3840
## 3 - 4.5 -1.93e-02 0.0758 25 -0.255 0.9990
## 3 - 6 -8.37e-02 0.0758 25 -1.104 0.8030
## 4.5 - 6 -6.44e-02 0.0758 25 -0.848 0.9126
##
## P value adjustment: tukey method for comparing a family of 5 estimatesgrid <- multcomp::cld(emm)
grid <- grid %>%
group_by(Per) %>%
mutate(cld = numbers_to_letters(.group)) %>%
ungroup()
ggplot(data = grid,
mapping = aes(x = Mate,
y = emmean)) +
facet_wrap(facets = ~Per,
nrow = 1) +
geom_point() +
geom_errorbar(mapping = aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.1) +
geom_text(mapping = aes(label = sprintf("%0.2f %s", emmean, cld)),
angle = 90,
vjust = 0,
nudge_x = -0.05) +
labs(x = "Níveis de mate",
y = "???") +
ggtitle(label = NULL,
subtitle = "Perído de postura")
#Análise da variável massaovos
# Modelo para um fator.
m0 <- lm(massaovos ~ Mate,
data = subset(tb, per == 1))
# par(mfrow = c(2, 2))
# plot(m0)
# layout(1)
anova(m0)## Analysis of Variance Table
##
## Response: massaovos
## Df Sum Sq Mean Sq F value Pr(>F)
## Mate 4 19.748 4.9371 0.6605 0.6252
## Residuals 25 186.882 7.4753# Médias ajustadas.
emm <- emmeans(m0, specs = ~Mate)
multcomp::cld(emm)## Mate emmean SE df lower.CL upper.CL .group
## 6 51.0 1.12 25 48.7 53.3 1
## 4.5 51.3 1.12 25 49.0 53.6 1
## 3 51.9 1.12 25 49.6 54.2 1
## 0 52.4 1.12 25 50.1 54.7 1
## 1.5 53.3 1.12 25 51.0 55.6 1
##
## Confidence level used: 0.95
## P value adjustment: tukey method for comparing a family of 5 estimates
## significance level used: alpha = 0.05# Comparações múltiplas.
contrast(emm, method = "pairwise")## contrast estimate SE df t.ratio p.value
## 0 - 1.5 -0.882 1.58 25 -0.559 0.9798
## 0 - 3 0.492 1.58 25 0.311 0.9978
## 0 - 4.5 1.138 1.58 25 0.721 0.9496
## 0 - 6 1.368 1.58 25 0.867 0.9064
## 1.5 - 3 1.374 1.58 25 0.870 0.9051
## 1.5 - 4.5 2.020 1.58 25 1.280 0.7055
## 1.5 - 6 2.250 1.58 25 1.425 0.6177
## 3 - 4.5 0.647 1.58 25 0.410 0.9937
## 3 - 6 0.876 1.58 25 0.555 0.9803
## 4.5 - 6 0.230 1.58 25 0.146 0.9999
##
## P value adjustment: tukey method for comparing a family of 5 estimates