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COM-Poisson +ajustados aos dados apresentados na seção \ref{cap03:materiais-dados}. -<<capdesfo, fig.cap="Experimento sobre capulhos de algodão sob efeito de desfolha">>= -library(MRDCr) -library(lattice) +\section{Análise de dados de capulhos de algodão sob efeito de desfolha} + +<<ajuste-cottonBolls, include=FALSE, cache=TRUE>>= + +## Dados +library(tccPackage) +data(cottonBolls) + +## Preditores +f1 <- ncap ~ 1 +f2 <- ncap ~ des +f3 <- ncap ~ des + I(des^2) +f4 <- ncap ~ est:des + I(des^2) +f5 <- ncap ~ est:(des + I(des^2)) + +## Ajustando os modelos Poisson +m1P <- glm(f1, data = cottonBolls, family = poisson) +m2P <- glm(f2, data = cottonBolls, family = poisson) +m3P <- glm(f3, data = cottonBolls, family = poisson) +m4P <- glm(f4, data = cottonBolls, family = poisson) +m5P <- glm(f5, data = cottonBolls, family = poisson) + +## Ajustando os modelos quasiPoisson +m1Q <- glm(f1, data = cottonBolls, family = quasipoisson) +m2Q <- glm(f2, data = cottonBolls, family = quasipoisson) +m3Q <- glm(f3, data = cottonBolls, family = quasipoisson) +m4Q <- glm(f4, data = cottonBolls, family = quasipoisson) +m5Q <- glm(f5, data = cottonBolls, family = quasipoisson) + +## Ajustando os modelos COM-Poisson +m1C <- cmp(f1, data = cottonBolls, sumto = 30) +m2C <- cmp(f2, data = cottonBolls, sumto = 30) +m3C <- cmp(f3, data = cottonBolls, sumto = 30) +m4C <- cmp(f4, data = cottonBolls, sumto = 30) +m5C <- cmp(f5, data = cottonBolls, sumto = 30) + +##====================================================================== +## Perfil de log-verossimilhanca para o parametro phi +prof.cottonBolls <- profile(m5C, which = "phi") + +@ + +Diante da estrutura do experimento apresentada na seção +\ref{sec:cottonBolls} foram propostos, por \citeonline{Zeviani2014}, +cinco preditores crescentes em complexidade que testam aspectos +interesses sobre os fatores experimentais envolvidos no experimento. +Abaixo expressamos os cinco preditores considerados. + +\noindent +Preditor 1: $g(\mu) = \beta_0$ \\ +Preditor 2: $g(\mu) = \beta_0 + \beta_1 \textrm{def}$ \\ +Preditor 3: $g(\mu) = \beta_0 + \beta_{1j} \textrm{def} + \beta_2 +\textrm{def}^2$ \\ +Preditor 3: $g(\mu) = \beta_0 + \beta_{1j} \textrm{def} + \beta_{2j} +\textrm{def}^2$ \\ + +\noindent +onde $j$ varia nos nÃveis de estágio fenológico da planta +(\Sexpr{niveis.est}). A proposta desses preditores foi realizada de +forma aninhada a fim de facilitar a condução de testes de hipóteses. O +modelo 1 contêm apenas o intercepto, e é ajustado apenas como ponto de +partida para verificar como modelos mais estruturados melhoram o +ajuste. O modelo 2 apresenta apenas o efeito de desfolha de forma +linear, o modelo 3 é o modelo 2 somado um efeito de segunda ordem. O +modelo 4, apresenta o efeito de desfolha linear mudando de acordo com o +estágio de crescimento, e por fim o modelo 5 diz que não somente o +efeito de primeira ordem muda com o estágio de crescimento, mais também +o efeito de segunda ordem. + +A seguir ajustamos os modelos Poisson e COM-Poisson como alternativas +paramétricas à análise de dados e como alternativa semi-paramétrica a +estimação via quase-verossimilhança Poisson. Na tabela +\ref{tab:ajuste-cottonBolls} apresentamos os resultados dos três modelos +ajustados aos cinco preditores considerados. O modelo COM-Poisson +apresentou melhor desempenho dentre todos os preditores considerados +quando comparado ao Poisson, indicado pelas maiores log-verossimilhanças +e menores AIC's. + +<<loglik-cottonBolls, include=FALSE>>= + +## Análise de desvios dos modelos +anP <- myanova(m1P, m2P, m3P, m4P, m5P) +anC <- myanova(m1C, m2C, m3C, m4C, m5C) +anQ <- myanova(m1Q, m2Q, m3Q, m4Q, m5Q) + +## Parâmetros de dispersão +listQ <- list(m1Q, m2Q, m3Q, m4Q, m5Q) +sigma <- sapply(listQ, function(x) summary(x)$dispersion) +phi <- cmptest(m1C, m2C, m3C, m4C, m5C) + +## Tabelas com as medidas de ajuste +tabP <- cbind(anP, matrix(nrow = nrow(anP), ncol = 2)) +tabC <- cbind(anC, phi) +tabQ <- cbind(anQ, cbind(sigma, NA)) + +rownames(tabP) <- paste("Preditor", 1:5) +rownames(tabC) <- paste("Preditor", 1:5) +rownames(tabQ) <- paste("Preditor", 1:5) + +## Empilhando as tabelas de ANODEV +tab.ajuste <- rbind(tabP, tabC, tabQ) + +## ##---------------------------------------------------------------------- +## ## Copiar e colar o corpo do resultado na customização latex abaixo +## digits <- c(1, 0, 3, 3, 3, 0, -3, 3, -3) +## print(xtable(tabC, digits = digits), include.rownames = TRUE) + +@ + +\begin{table}[ht] +\centering +\small +\caption{Medidas de ajuste para avaliação e comparação entre preditores + e modelos ajustados} +\label{tab:ajuste-cottonBolls} +\begin{tabular}{lcccccrcr} + \toprule + Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & & \\ + \midrule + Preditor 1 & 1 & -279,933 & 561,866 & & & & & \\ + Preditor 2 & 2 & -272,001 & 548,001 & 15,864 & 1 & 6,805E-05 & & \\ + Preditor 3 & 3 & -271,354 & 548,709 & 1,293 & 1 & 2,556E-01 & & \\ + Preditor 4 & 7 & -258,674 & 531,348 & 25,360 & 4 & 4,258E-05 & & \\ + Preditor 5 & 11 & -255,803 & 533,606 & 5,742 & 4 & 2,193E-01 & & \\[0.3cm] + COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ & P($>\rchi^2$) \\ + \midrule +Preditor 1 & 2 & -272,479 & 548,959 & & & & 0,551 & 1,130E-04 \\ + Preditor 2 & 3 & -257,464 & 520,927 & 30,032 & 1 & 4,251E-08 & 0,794 & 6,966E-08 \\ + Preditor 3 & 4 & -256,089 & 520,179 & 2,749 & 1 & 9,734E-02 & 0,816 & 3,287E-08 \\ + Preditor 4 & 8 & -220,198 & 456,395 & 71,783 & 4 & 9,537E-15 & 1,392 & 1,751E-18 \\ + Preditor 5 & 12 & -208,250 & 440,500 & 23,896 & 4 & 8,382E-05 & 1,585 & 1,804E-22 \\[0.3cm] + Quase-Poisson & np & deviance & AIC & F & diff np & P(>F) & $\hat{\sigma}^2$ & P($>F$) \\ + \midrule + Preditor 1 & 1 & 75,514 & & & & & 0,567 & \\ + Preditor 2 & 2 & 59,650 & & 65,820 & 1 & 6,343E-13 & 0,464 & \\ + Preditor 3 & 3 & 58,357 & & 5,363 & 1 & 2,236E-02 & 0,460 & \\ + Preditor 4 & 7 & 32,997 & & 26,305 & 4 & 1,846E-15 & 0,278 & \\ + Preditor 5 & 11 & 27,255 & & 5,956 & 4 & 2,176E-04 & 0,241 & \\ + \bottomrule +\end{tabular} +\begin{tablenotes} + \footnotesize +\item np, número de parâmetros, diff $\ell$, diferença entre + log-verossimilhanças, F, estatÃstica F baseada nas quasi-deviances, + diff np, diferença entre o np. \\[0.1cm] +\item Fonte: Elaborado pelo autor. +\end{tablenotes} +\end{table} + +As estimativas dos parâmetros extras $phi$ e $sigma^2$ dos modelos +COM-Poisson e Quasi-Poisson respectivamente, também são apresentadas na +\ref{tab:ajuste-cottonBolls} e indicam subdispersão ($\phi>0$ e +$\sigma^2<1$). Note que mesmo quando não consideramos covariáveis, +preditor 1, a hipótese de equidispersão foi rejeitada pelo modelo +COM-Poisson. + +<<prof-cottonBolls, fig.height=4, fig.width=4, fig.show="hide", results="asis", fig.cap="Perfil de log-verossimilhança para o parâmetro extra da COM-Poisson">>= + +myprof(prof.cottonBolls, par.settings = ps.sub) +fonte.xy("Fonte: Elaborado pelo autor.") + +wrapfigure() + +@ + +\lipsum[1] + +<<corr-cottonBolls, fig.width=7, fig.height=7, fig.cap="Imagem da matriz de correlação entre os parâmetros do modelo COM-Poisson">>= + +Vcov <- vcov(m5C) +Corr <- cov2cor(Vcov) + +## Usando expression não funciona! Estudar a função posteriormente +pnames <- c("phi", "beta0", paste0("beta1", 1:5), + paste0("beta2", 1:5)) +dimnames(Corr) <- list(pnames, pnames) + +mycorrplot(Corr) +fonte("Fonte: Elaborado pelo autor.") + +@ + +\lipsum[1] + +<<pred-cottonBolls, fig.height=3.5, fig.width=7, fig.cap="Curva dos valores preditos com intervalo de confiança de (95\\%) como função do nÃvel de desfolha e do estágio fenológico da planta.">>= + +## Predição pontual/intervalar +pred <- with(cottonBolls, + expand.grid( + est = levels(est), + des = seq(min(des), max(des), l = 20) + )) +qn <- qnorm(0.975) * c(fit = 0, lwr = -1, upr = 1) + +##------------------------------------------- +## Considerando a Poisson +aux <- predict(m5P, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Poisson", aux) +predP <- cbind(pred, aux) + +##------------------------------------------- +## Considerando a COM-Poisson +aux <- predict(m5C, newdata = pred, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux) +predC <- cbind(pred, aux) + +##------------------------------------------- +## Considerando a Quasi-Poisson +aux <- predict(m5Q, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ <- cbind(pred, aux) + +da <- rbind(predP, predC, predQ) + +##------------------------------------------- +## Gráfico dos valores preditos e IC de 95% para média +cols <- trellis.par.get("superpose.line")$col[1:3] + +key <- list( + column = 3, + lines = list(lty = c(3, 1, 2), lwd = 1, col = cols), + text = list(c("Poisson", "COM-Poisson", "Quasi-Poisson"))) xyplot(ncap ~ des | est, - data = capdesfo, - layout = c(NA, 2), - type = c("p", "g", "smooth"), + data = cottonBolls, + layout = c(NA, 1), + as.table = TRUE, + alpha = 0.5, + type = c("p", "g"), xlab = "NÃveis de desfolha artificial", ylab = "Número de capulhos produzidos", xlim = extendrange(c(0:1), f = 0.15), - panel = panel.beeswarm, r = 0.05) + spread = 0.08, + panel = panel.beeswarm, + key = key, + par.settings = ps.sub) + + as.layer( + xyplot(fit + lwr + upr ~ des | est, data = predP, + type = "l", col = cols[1], lty = c(1, 3, 3), lwd = 1) + ) + + as.layer( + xyplot(fit + lwr + upr ~ des | est, data = predC, + type = "l", col = cols[2], lty = c(1, 1, 1), lwd = 1) + ) + + as.layer( + xyplot(fit + lwr + upr ~ des | est, data = predQ, + type = "l", col = cols[3], lty = c(1, 2, 2), lwd = 1) + ) @ -\lipsum[1-2] +\lipsum[1] -<<capmosca, fig.cap="Experimento sobre capulhos de algodão sob efeito de infestação de mosca-branca">>= +\section{Análise de dados de capulhos de algodão sob efeito de Mosca-Branca} -# Número de capulhos produzidos por planta -xyplot(ncap ~ dexp, groups = planta, - data = capmosca, - xlab = "Dias sob exposição a alta infestação de mosca-branca", - ylab = "Número de capulhos produzidos", - auto.key = list(column = 2), - panel = panel.beeswarm, r = 0.08, - type = c("p", "g", "smooth")) +<<ajuste-cottonBolls2, include=FALSE, cache=TRUE>>= + +## Dados +library(tccPackage) +data(cottonBolls2) + +## Preditores considerados +f1.ncapu <- ncapu ~ 1 +f2.ncapu <- ncapu ~ dexp +f3.ncapu <- ncapu ~ dexp + I(dexp^2) + +f1.nerep <- nerep ~ 1 +f2.nerep <- nerep ~ dexp +f3.nerep <- nerep ~ dexp + I(dexp^2) + +f1.nnos <- nnos ~ 1 +f2.nnos <- nnos ~ dexp +f3.nnos <- nnos ~ dexp + I(dexp^2) + +## Ajustando os modelos Poisson +m1P.ncapu <- glm(f1.ncapu, data = cottonBolls2, family = poisson) +m2P.ncapu <- glm(f2.ncapu, data = cottonBolls2, family = poisson) +m3P.ncapu <- glm(f3.ncapu, data = cottonBolls2, family = poisson) + +m1P.nerep <- glm(f1.nerep, data = cottonBolls2, family = poisson) +m2P.nerep <- glm(f2.nerep, data = cottonBolls2, family = poisson) +m3P.nerep <- glm(f3.nerep, data = cottonBolls2, family = poisson) + +m1P.nnos <- glm(f1.nnos, data = cottonBolls2, family = poisson) +m2P.nnos <- glm(f2.nnos, data = cottonBolls2, family = poisson) +m3P.nnos <- glm(f3.nnos, data = cottonBolls2, family = poisson) + +## Ajustando os modelos quasiPoisson +m1Q.ncapu <- glm(f1.ncapu, data = cottonBolls2, family = quasipoisson) +m2Q.ncapu <- glm(f2.ncapu, data = cottonBolls2, family = quasipoisson) +m3Q.ncapu <- glm(f3.ncapu, data = cottonBolls2, family = quasipoisson) + +m1Q.nerep <- glm(f1.nerep, data = cottonBolls2, family = quasipoisson) +m2Q.nerep <- glm(f2.nerep, data = cottonBolls2, family = quasipoisson) +m3Q.nerep <- glm(f3.nerep, data = cottonBolls2, family = quasipoisson) + +m1Q.nnos <- glm(f1.nnos, data = cottonBolls2, family = quasipoisson) +m2Q.nnos <- glm(f2.nnos, data = cottonBolls2, family = quasipoisson) +m3Q.nnos <- glm(f3.nnos, data = cottonBolls2, family = quasipoisson) + +## Ajustando os modelos COM-Poisson +m1C.ncapu <- cmp(f1.ncapu, data = cottonBolls2, sumto = 30) +m2C.ncapu <- cmp(f2.ncapu, data = cottonBolls2, sumto = 30) +m3C.ncapu <- cmp(f3.ncapu, data = cottonBolls2, sumto = 30) + +m1C.nerep <- cmp(f1.nerep, data = cottonBolls2, sumto = 30) +m2C.nerep <- cmp(f2.nerep, data = cottonBolls2, sumto = 30) +m3C.nerep <- cmp(f3.nerep, data = cottonBolls2, sumto = 30) + +m1C.nnos <- cmp(f1.nnos, data = cottonBolls2, sumto = 30) +m2C.nnos <- cmp(f2.nnos, data = cottonBolls2, sumto = 30) +m3C.nnos <- cmp(f3.nnos, data = cottonBolls2, sumto = 30) + +##====================================================================== +## Perfil de log-verossimilhanca para o parametro phi +prof.ncapu <- profile(m3C.ncapu, which = "phi") +prof.nerep <- profile(m2C.nerep, which = "phi") +prof.nnos <- profile(m3C.nnos, which = "phi") + +@ + +\lipsum[1] + +<<loglik-cottonBolls2, include=FALSE>>= + +## Análise de desvios dos modelos +anP.ncapu <- myanova(m1P.ncapu, m2P.ncapu, m3P.ncapu) +anC.ncapu <- myanova(m1C.ncapu, m2C.ncapu, m3C.ncapu) +anQ.ncapu <- myanova(m1Q.ncapu, m2Q.ncapu, m3Q.ncapu) + +anP.nerep <- myanova(m1P.nerep, m2P.nerep, m3P.nerep) +anC.nerep <- myanova(m1C.nerep, m2C.nerep, m3C.nerep) +anQ.nerep <- myanova(m1Q.nerep, m2Q.nerep, m3Q.nerep) + +anP.nnos <- myanova(m1P.nnos, m2P.nnos, m3P.nnos) +anC.nnos <- myanova(m1C.nnos, m2C.nnos, m3C.nnos) +anQ.nnos <- myanova(m1Q.nnos, m2Q.nnos, m3Q.nnos) + +## Tabela com medidas de ajuste +tab.ncapu <- data.frame( + modelos = paste("Preditor", 1:3), + anP.ncapu[, c("np", "ll", "AIC", "P(>Chisq)")], + anC.ncapu[, c("ll", "AIC", "P(>Chisq)")], + anQ.ncapu[, c("dev", "P(>F)")]) + +tab.nerep <- data.frame( + modelos = paste("Preditor", 1:3), + anP.nerep[, c("np", "ll", "AIC", "P(>Chisq)")], + anC.nerep[, c("ll", "AIC", "P(>Chisq)")], + anQ.nerep[, c("dev", "P(>F)")]) + +tab.nnos <- data.frame( + modelos = paste("Preditor", 1:3), + anP.nnos[, c("np", "ll", "AIC", "P(>Chisq)")], + anC.nnos[, c("ll", "AIC", "P(>Chisq)")], + anQ.nnos[, c("dev", "P(>F)")]) + +## Empilhando +tab.ajuste <- rbind(tab.ncapu, tab.nerep, tab.nnos) + +## ##---------------------------------------------------------------------- +## ## Copiar e colar o corpo do resultado na customização latex abaixo +## digits <- c(1, 1, 0, 2, 2, -2, 2, 2, -2, 2, -2) +## print(xtable(tab.ajuste, digits = digits)) + +@ + +\begin{table}[ht] +\centering +\small +\caption{Medidas de ajuste para avaliação e comparação entre preditores + e modelos ajustados} +\label{tab:ajuste-cottonBolls2} +\begin{tabular}{lccccccccc} + \toprule + & & \multicolumn{3}{c}{Poisson} & \multicolumn{3}{c}{COM-Poisson} & \multicolumn{2}{c}{Quasi-Poisson} \\ + \cmidrule{3-5} \cmidrule{6-8} \cmidrule{9-10} + & np & $\ell$ & AIC & P($>\rchi^2$) & $\ell$ & AIC & P($>\rchi^2$) & deviance & P($>F$) \\ + \midrule + \multicolumn{10}{l}{{\bfseries \footnotesize Número de capulhos produzidos}} \\[0.0cm] + \cline{1-5} \\[-0.2cm] + & 1 & -105,27 & 212,55 & & -92,05 & 188,09 & & 20,80 & \\ + & 2 & -105,03 & 214,05 & 4,83E-01 & -91,31 & 188,62 & 2,25E-01 & 20,31 & 2,23E-01 \\ + & 3 & -104,44 & 214,88 & 2,78E-01 & -89,47 & 186,95 & 5,52E-02 & 19,13 & 6,16E-02 \\[0.2cm] + \multicolumn{10}{l}{{\bfseries \footnotesize Número de estruturas reprodutivas}} \\[0.0cm] + \cline{1-5} \\[-0.2cm] + & 1 & -104,74 & 211,49 & & -86,41 & 176,82 & & 16,23 & \\ + & 2 & -104,27 & 212,54 & 3,32E-01 & -84,59 & 175,18 & 5,66E-02 & 15,29 & 6,19E-02 \\ + & 3 & -104,06 & 214,12 & 5,16E-01 & -83,73 & 175,47 & 1,90E-01 & 14,87 & 2,07E-01 \\[0.2cm] + \multicolumn{10}{l}{{\bfseries \footnotesize Número de nós da planta}} \\[0.0cm] + \cline{1-5} \\[-0.2cm] + & 1 & -143,79 & 289,59 & & -120,58 & 245,16 & & 12,69 & \\ + & 2 & -143,48 & 290,95 & 4,25E-01 & -119,03 & 244,06 & 7,87E-02 & 12,05 & 7,39E-02 \\ + & 3 & -142,95 & 291,89 & 3,04E-01 & -116,27 & 240,54 & 1,88E-02 & 11,00 & 2,23E-02 \\ + \bottomrule +\end{tabular} +\begin{tablenotes} + \footnotesize +\item np, número de parâmetros. +\item Fonte: Elaborado pelo autor. +\end{tablenotes} +\end{table} + + +\lipsum[1] + +<<prof-cottonBolls2, fig.height=3.5, fig.width=7, fig.cap="Perfis de log-verossimilhança para o parâmetro extra da COM-Poisson nos modelos para número de capulhos produzidos (esquerda), número de estruturas reprodutivas (central) e número de nós (direira).">>= + +##====================================================================== +## Causa +da.ncapu <- as.data.frame(prof.ncapu) +da.nerep <- as.data.frame(prof.nerep) +da.nnos <- as.data.frame(prof.nnos) +## +levels(da.nerep$param) <- "phi2" +levels(da.nnos$param) <- "phi3" +## +vars <- c("param", "z", "focal") +da <- rbind(da.ncapu[, vars], da.nerep[, vars], da.nnos[, vars]) +## +xyplot(abs(z) ~ focal | param, data = da, + layout = c(NA, 1), + scales = list(x = "free"), + subset = abs(z) < 3.5, + type = c("l", "g"), + strip = strip.custom( + factor.levels = c( + "Capulhos produzidos", + "Estruturas reprodutivas", + "Nós da planta" + ) + ), + ylab = expression(abs(z)~~(sqrt(~Delta~"deviance"))), + xlab = expression(phi), + panel = function(x, y, subscripts = subscripts, ...) { + mle <- x[y == 0] + panel.xyplot(x, y, subscripts = subscripts, ...) + panel.abline(h = 0, v = mle, lty = 3) + }, sub = "Fonte: Elaborado pelo autor.") + +## xy1 <- myprof(prof.ncapu, par.settings = ps.sub) +## xy2 <- myprof(prof.nerep, par.settings = ps.sub, ylab = "") +## xy3 <- myprof(prof.nnos, par.settings = ps.sub, ylab = "") +## print(xy1, split = c(1, 1, 3, 1), more = TRUE) +## print(xy2, split = c(2, 1, 3, 1), more = TRUE) +## print(xy3, split = c(3, 1, 3, 1), more = FALSE) +## fonte.xy("Fonte: Elaborado pelo autor.") + +@ + +\lipsum[1] + +<<corr-cottonBolls2a, fig.height=4, fig.width=8, fig.cap="Imagem da matriz de correlação entre os parâmetros do modelo COM-Poisson">>= + +pnames <- c("phi", "beta0", "beta1", "beta2") + +Vcov <- vcov(m3C.ncapu) +Corr.ncapu <- cov2cor(Vcov) +dimnames(Corr.ncapu) <- list(pnames, pnames) + +Vcov <- vcov(m3C.nnos) +Corr.nnos <- cov2cor(Vcov) +dimnames(Corr.nnos) <- list(pnames, pnames) + +par(mfrow = c(1, 2)) +mycorrplot(Corr.ncapu) +mycorrplot(Corr.nnos) + +fonte("Fonte: Elaborado pelo autor.") + +@ + +<<corr-cottonBolls2b, fig.height=4, fig.width=4, results="asis", fig.show="hide", fig.cap="Imagem da matriz de correlação entre os parâmetros do modelo COM-Poisson">>= + +pnames <- c("phi", "beta0", "beta1") + +Vcov <- vcov(m2C.nerep) +Corr.nerep <- cov2cor(Vcov) +dimnames(Corr.nerep) <- list(pnames, pnames) + +mycorrplot(Corr.nerep) + +fonte("Fonte: Elaborado pelo autor.") + +wrapfigure() + +@ + + +\lipsum[1] + +<<pred-cottonBolls2, fig.height=3.5, fig.width=7, fig.cap="Curva dos valores preditos com intervalo de confiança de (95\\%) como função do nÃvel de desfolha e do estágio fenológico da planta.">>= + +qn <- qnorm(0.975) * c(fit = 0, lwr = -1, upr = 1) + +## Predição pontual/intervalar +pred <- data.frame(dexp = with(cottonBolls2, + seq(min(dexp), max(dexp), l = 50))) + +##====================================================================== +## Considerando a Poisson +##------------------------------------------- +## Para nerep +aux <- predict(m2P.nerep, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Poisson", aux) +predP.nerep <- cbind(var = "nerep", pred, aux) +##------------------------------------------- +## Para ncapu +aux <- predict(m3P.ncapu, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Poisson", aux) +predP.ncapu <- cbind(var = "ncapu", pred, aux) +##------------------------------------------- +## Para nnos +aux <- predict(m3P.nnos, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Poisson", aux) +predP.nnos <- cbind(var = "nnos", pred, aux) +## +predP <- rbind(predP.nerep, predP.ncapu, predP.nnos) + +##====================================================================== +## Considerando a COM-Poisson +##------------------------------------------- +## Para nerep +aux <- predict(m2C.nerep, newdata = pred, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux) +predC.nerep <- cbind(var = "nerep", pred, aux) +##------------------------------------------- +## Para ncapu +aux <- predict(m3C.ncapu, newdata = pred, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux) +predC.ncapu <- cbind(var = "ncapu", pred, aux) +##------------------------------------------- +## Para nnos +aux <- predict(m3C.nnos, newdata = pred, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux) +predC.nnos <- cbind(var = "nnos", pred, aux) +## +predC <- rbind(predC.nerep, predC.ncapu, predC.nnos) + +##====================================================================== +## Considerando a Quasi-Poisson +##------------------------------------------- +## Para nerep +aux <- predict(m2Q.nerep, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ.nerep <- cbind(var = "nerep", pred, aux) +##------------------------------------------- +## Para ncapu +aux <- predict(m3Q.ncapu, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ.ncapu <- cbind(var = "ncapu", pred, aux) +##------------------------------------------- +## Para nnos +aux <- predict(m3Q.nnos, newdata = pred, se.fit = TRUE) +aux <- with(aux, exp(fit + outer(se.fit, qn, FUN = "*"))) +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ.nnos <- cbind(var = "nnos", pred, aux) +## +predQ <- rbind(predQ.nerep, predQ.ncapu, predQ.nnos) + +##====================================================================== +##------------------------------------------- +## Gráfico com os valores preditos +data(cottonBolls2) +vars <- c("dexp", "vaso", "planta", "nerep", "ncapu", "nnos") +cottonBolls2 <- cottonBolls2[, vars] +da <- reshape2::melt(cottonBolls2, id = c("dexp", "vaso", "planta"), + variable.name = "va", value.name = "count") +cols <- trellis.par.get("superpose.line")$col[1:3] + +key <- list( + column = 3, + lines = list(lty = c(3, 1, 2), lwd = 1, col = cols), + text = list(c("Poisson", "COM-Poisson", "Quasi-Poisson"))) + +xyplot(count ~ dexp | va, data = da, + key = key, + type = c("p", "g"), + layout = c(NA, 1), + ylab = "Contagens", + xlab = "Dias de exposição a alta infestação de Mosca-branca", + scales = list( + y = list(relation = "free", rot = 0)), + strip = strip.custom( + factor.levels = c("Estruturas reprodutivas ", + "Capulhos produzidos", + "Nós da planta")), + alpha = 0.3, + spread = 0.15, + panel = panel.beeswarm, + par.settings = ps.sub)+ + as.layer( + xyplot(fit + lwr + upr ~ dexp | var, data = predP, + layout = c(NA, 1), + scales = list( + y = list(relation = "free", rot = 0)), + type = "l", col = cols[1], lty = c(1, 3, 3), lwd = 1) + ) + + as.layer( + xyplot(fit + lwr + upr ~ dexp | var, data = predC, + layout = c(NA, 1), + scales = list( + y = list(relation = "free", rot = 0)), + type = "l", col = cols[2], lty = c(1, 1, 1), lwd = 1) + ) + + as.layer( + xyplot(fit + lwr + upr ~ dexp | var, data = predQ, + layout = c(NA, 1), + scales = list( + y = list(relation = "free", rot = 0)), + type = "l", col = cols[3], lty = c(1, 2, 2), lwd = 1) + ) + +fonte.xy("Fonte: Elaborado pelo autor.") + +@ + +\lipsum[1] + +\section{Análise de produção de soja sob efeito de umidade e adubação + potássica} + +<<ajuste-soyaBeans, include=FALSE, cache=TRUE>>= + +## Dados +library(tccPackage) +data(soyaBeans) +soyaBeans <- soyaBeans[-74, ] +soyaBeans <- transform(soyaBeans, K = factor(K)) + +##------------------------------------------- +## Para o número de vagens viáveis por parcela + +## Preditores considerados + +f1.nv <- nvag ~ bloc + umid + K +f2.nv <- nvag ~ bloc + umid * K + +f1.ng <- ngra ~ bloc + umid + K +f2.ng <- ngra ~ bloc + umid * K + +## Ajustando os modelos Poisson +m1P.nv <- glm(f1.nv, data = soyaBeans, family = poisson) +m2P.nv <- glm(f2.nv, data = soyaBeans, family = poisson) + +m1P.ng <- glm(f1.ng, data = soyaBeans, family = poisson) +m2P.ng <- glm(f2.ng, data = soyaBeans, family = poisson) + +## Ajustando os modelos COM-Poisson +m1C.nv <- cmp(f1.nv, data = soyaBeans, sumto = 300) +m2C.nv <- cmp(f2.nv, data = soyaBeans, sumto = 300) + +m1C.ng <- cmp(f1.ng, data = soyaBeans, sumto = 700) +m2C.ng <- cmp(f2.ng, data = soyaBeans, sumto = 700) + +## Ajustando os modelos Binomial Negativo +library(MASS) +m1B.nv <- glm.nb(f1.nv, data = soyaBeans) +m2B.nv <- glm.nb(f2.nv, data = soyaBeans) + +m1B.ng <- glm.nb(f1.ng, data = soyaBeans) +m2B.ng <- glm.nb(f2.ng, data = soyaBeans) + +## Ajustando os modelos Quasi-Poisson +m1Q.nv <- glm(f1.nv, data = soyaBeans, family = quasipoisson) +m2Q.nv <- glm(f2.nv, data = soyaBeans, family = quasipoisson) + +m1Q.ng <- glm(f1.ng, data = soyaBeans, family = quasipoisson) +m2Q.ng <- glm(f2.ng, data = soyaBeans, family = quasipoisson) + +##====================================================================== +## Perfil de log-verossimilhanca para o parametro phi +prof.nv <- profile(m2C.nv, which = "phi") +prof.ng <- profile(m2C.ng, which = "phi") + +@ + +\lipsum[1] + +<<loglik-soyaBeans, include=FALSE>>= + +## Análise de desvios dos modelos +anP.nv <- myanova(m1P.nv, m2P.nv) +anC.nv <- myanova(m1C.nv, m2C.nv) +anB.nv <- myanova(m1B.nv, m2B.nv) +anQ.nv <- myanova(m1Q.nv, m2Q.nv) + +anP.ng <- myanova(m1P.ng, m2P.ng) +anC.ng <- myanova(m1C.ng, m2C.ng) +anB.ng <- myanova(m1B.ng, m2B.ng) +anQ.ng <- myanova(m1Q.ng, m2Q.ng) + +## Tabelas com medidas de ajuste +tab.nv <- rbind( + anP.nv[, c("np", "ll", "AIC", "P(>Chisq)")], + anC.nv[, c("np", "ll", "AIC", "P(>Chisq)")], + anB.nv[, c("np", "ll", "AIC", "P(>Chisq)")], + anQ.nv[, c("np", "dev", "AIC", "P(>F)")]) + +tab.ng <- rbind( + anP.ng[, c("ll", "AIC", "P(>Chisq)")], + anC.ng[, c("ll", "AIC", "P(>Chisq)")], + anB.ng[, c("ll", "AIC", "P(>Chisq)")], + anQ.ng[, c("dev", "AIC", "P(>F)")]) + +## Obtem as estimativas dos parâmetros de dispersão/precisão +dispersions.nv <- c( + c(rep(NA, 2)), + sapply(list(m1C.nv, m2C.nv), function(m) coef(m)[1]), + sapply(list(m1B.nv, m2B.nv), function(m) m$theta), + sapply(list(m1Q.nv, m2Q.nv), function(m) summary(m)$dispersion)) + +dispersions.ng <- c( + c(rep(NA, 2)), + sapply(list(m1C.ng, m2C.ng), function(m) coef(m)[1]), + sapply(list(m1B.ng, m2B.ng), function(m) m$theta), + sapply(list(m1Q.ng, m2Q.ng), function(m) summary(m)$dispersion)) + +## Adicionando os parametros de dispersão à tabela +tab.nv <- cbind(tab.nv, dispersions.nv) +tab.ng <- cbind(tab.ng, dispersions.ng) + +## Juntando as tabelas +## tab.ajuste <- data.frame(pred = rep(paste0("$\\eta_", 1:2, "$"), 4)) +## tab.ajuste <- cbind(tab.ajuste, as.data.frame(cbind(tab.nv, tab.ng))) +## tab.ajuste <- as.data.frame(cbind(tab.nv, tab.ng)) + +## ##---------------------------------------------------------------------- +## ## Copiar e colar o corpo do resultado na customização latex abaixo +## digits <- c(1, 0, 2, 2, -2, -2, 2, 2, -2, -2) +## print(xtable(tab.ajuste, digits = digits)) @ +\begin{table}[ht] +\centering +\small +\caption{Medidas de ajuste para avaliação e comparação entre preditores + e modelos ajustados} +\label{tab:ajuste-soyaBeans} +\begin{tabular}{lcccrcccrc} + \toprule + & & \multicolumn{4}{c}{{\bfseries Número de vagens}} & \multicolumn{4}{c}{{\bfseries Número de grãos}} \\ + \cmidrule{3-6} \cmidrule{7-10} +{\footnotesize Poisson} & np & $\ell$ & AIC & P($>\rchi^2$) & & $\ell$ & AIC & P($>\rchi^2$) & \\ + \midrule + $\eta_1$ & 11 & -266,69 & 555,38 & & & -343,16 & 708,33 & & \\ + $\eta_2$ & 19 & -259,62 & 557,23 & 7,79E-02 & & -321,67 & 681,34 & 8,83E-07 & \\[0.3cm] +{\footnotesize COM-Poisson} & np & $\ell$ & AIC & P($>\rchi^2$) & $\hat{\phi}$ & $\ell$ & AIC & P($>\rchi^2$) & $\hat{\phi}$ \\ + \midrule + $\eta_1$ & 12 & -266,60 & 557,20 & & -6,75E-02 & -326,61 & 677,21 & & -8,17E-01 \\ + $\eta_2$ & 20 & -259,33 & 558,65 & 6,85E-02 & 1,29E-01 & -315,64 & 671,29 & 5,06E-03 & -5,18E-01 \\[0.3cm] +{\footnotesize Binomial-Neg.} & np & $\ell$ & AIC & P($>\rchi^2$) & $\hat{\phi}$ & $\ell$ & AIC & P($>\rchi^2$) & $\hat{\phi}$ \\ + \midrule + $\eta_1$ & 12 & -266,69 & 557,37 & & 4,59E+03 & -326,54 & 677,07 & & 1,42E+02 \\ + $\eta_2$ & 20 & -259,62 & 559,23 & 7,82E-02 & 1,03E+06 & -315,39 & 670,77 & 4,39E-03 & 2,61E+02 \\[0.3cm] +{\footnotesize Quasi-Poisson} & np & $\ell$ & AIC & P($>\rchi^2$) & $\hat{\phi}$ & $\ell$ & AIC & P($>\rchi^2$) & $\hat{\phi}$ \\ + \midrule + $\eta_1$ & 11 & 79,43 & & & 1,28E+00 & 167,71 & & & 2,71E+00 \\ + $\eta_2$ & 19 & 65,28 & & 1,87E-01 & 1,20E+00 & 124,72 & & 3,00E-02 & 2,29E+00 \\ + \bottomrule +\end{tabular} +\begin{tablenotes} + \footnotesize +\item np, número de parâmetros. +\item Fonte: Elaborado pelo autor. +\end{tablenotes} +\end{table} -Verificando \textit{outputs} R \textit{inline} \Sexpr{1/3}. A -referenciação de figuras produzidas em \textit{chunks} R é -\texttt{fig: + chunkname}, assim como vemos nas figuras \ref{fig:capmosca} -e \ref{fig:capdesfo}. Para as tabelas a referenciação também é simples, -conforme tabela \ref{tab:01}. +\lipsum[1] -\lipsum[1-2] +<<prof-soyaBeans, fig.height=3.5, fig.width=7, fig.cap="Perfis de log-verossimilhança para o parâmetro extra da COM-Poisson nos modelos para número de vagens viáveis por parcela (esquerda) e número grãos de soja por parcela (direira).">>= -<<results='asis'>>= -xtable::xtable(mtcars[, 1:8], caption = "Dados de automóveis", - label = "tab:01") +xy1 <- myprof(prof.nv, par.settings = ps.sub, + namestrip = "Número de vagens") +xy2 <- myprof(prof.ng, par.settings = ps.sub, + namestrip = "Número de grãos") +print(xy1, split = c(1, 1, 2, 1), more = TRUE) +print(xy2, split = c(2, 1, 2, 1), more = TRUE) +fonte.xy("Fonte: Elaborado pelo autor.") -## print(head(xt, 1), booktabs = FALSE) @ -Entendendo citações: -\begin{itemize} - \item \citeonline{Zeviani2014} - \item \citeonline[p.~281]{Paula2013} - \item \cite{Sellers2010} - \item \cite[cap.~4]{RibeiroJr2012} - \item \apud[p.~2--3]{Zeviani2014}{Park2009} - \item \apudonline{Lord2010}{Shmueli2005} -\end{itemize} +<<corr-soyaBeansa, fig.height=7, fig.width=7, fig.cap="Imagem da matriz de correlação entre os parâmetros do modelo COM-Poisson ajustados ao número de vagens por parcela.">>= + +pnames <- c("phi", "beta0", + paste0("tau", 1:4), + paste0("gama", 1:2), + paste0("delta", 1:4), + paste0("alpha", 1:8)) + +Vcov <- vcov(m2C.nv) +Corr.nv <- cov2cor(Vcov) +dimnames(Corr.nv) <- list(pnames, pnames) +mycorrplot(Corr.nv) + +fonte("Fonte: Elaborado pelo autor.") + +@ + +<<corr-soyaBeansb, fig.height=7, fig.width=7, fig.cap="Imagem da matriz de correlação entre os parâmetros do modelo COM-Poisson ajustados ao número de grãos por parcela.">>= + +pnames <- c("phi", "beta0", + paste0("tau", 1:4), + paste0("gama", 1:2), + paste0("delta", 1:4), + paste0("alpha", 1:8)) + +Vcov <- vcov(m2C.ng) +Corr.ng <- cov2cor(Vcov) +dimnames(Corr.ng) <- list(pnames, pnames) +mycorrplot(Corr.ng) + +fonte("Fonte: Elaborado pelo autor.") + +@ + +\lipsum[1] + +<<pred-soyaBeans, fig.height=5, fig.width=7.5, fig.cap="Valores preditos com intervalos de confiança (95\\%) como função do nÃvel de adubação com potássio e do percentual de umidade do solo para cada variável de interesse mensurada (número de vagens e número de grãos por parcela).">>= +library(multcomp) + +## Predição pontual/intervalar +pred <- with(soyaBeans, + expand.grid( + bloc = factor(levels(bloc)[1], levels = levels(bloc)), + umid = levels(umid), + K = levels(K) + )) + +## Matrix de delineamento para predição, considera o efeito médio de +## bloco +X <- model.matrix(~bloc + umid * K, data = pred) +bl <- attr(X, "assign") == 1 +X[, bl] <- X[, bl] * 0 + 1/(sum(bl) + 1) + + +##====================================================================== +## Considerando a Poisson +##------------------------------------------- +## Para nv +aux <- exp(confint(glht(m2P.nv, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Poisson", aux) +predP.nv <- cbind(var = "nvag", pred, aux) +##------------------------------------------- +## Para ng +aux <- exp(confint(glht(m2P.ng, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Poisson", aux) +predP.ng <- cbind(var = "ngra", pred, aux) +## +predP <- rbind(predP.nv, predP.ng) + +##====================================================================== +## Considerando a COM-Poisson +##------------------------------------------- +## Para nv +aux <- predict(m2C.nv, newdata = X, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux[, c("fit", "lwr", "upr")]) +predC.nv <- cbind(var = "nvag", pred, aux) +##------------------------------------------- +## Para ng +aux <- predict(m2C.ng, newdata = X, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux[, c("fit", "lwr", "upr")]) +predC.ng <- cbind(var = "ngra", pred, aux) +## +predC <- rbind(predC.nv, predC.ng) + +##====================================================================== +## Considerando a Binomial Negativa +##------------------------------------------- +## Para nv +aux <- family(m2B.nv)$linkinv( + confint(glht(m2B.nv, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Binomial Negativa", aux) +predB.nv <- cbind(var = "nvag", pred, aux) +##------------------------------------------- +## Para ng +aux <- family(m2B.ng)$linkinv( + confint(glht(m2B.ng, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Binomial Negativa", aux) +predB.ng <- cbind(var = "ngra", pred, aux) +## +predB <- rbind(predB.nv, predB.ng) + +##====================================================================== +## Considerando a Quasi-Poisson +##------------------------------------------- +## Para nv +aux <- exp(confint(glht(m2Q.nv, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ.nv <- cbind(var = "nvag", pred, aux) +##------------------------------------------- +## Para ng +aux <- exp(confint(glht(m2Q.ng, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ.ng <- cbind(var = "ngra", pred, aux) +## +predQ <- rbind(predQ.nv, predQ.ng) + +##------------------------------------------- +pred.all <- rbind(predP, predC, predB, predQ) +pred.all <- pred.all[with(pred.all, order(var, umid, K, modelo)), ] + +##====================================================================== +##------------------------------------------- +## Gráfico com os valores preditos +data(soyaBeans) +soyaBeans <- soyaBeans[-74, ] ## outlier identificado +soyaBeans <- soyaBeans[, c("K", "umid", "bloc", "ngra", "nvag")] + +da <- reshape2::melt( + soyaBeans, id = c("K", "umid", "bloc"), + variable.name = "var", value.name = "count") + +key <- list(type = "o", divide = 1, + lines = list(pch = 1:nlevels(pred.all$model) + 4), + text = list(c("Poisson", "COM-Poisson", + "Binomial Negativa", "Quasi-Poisson")) + ) + +useOuterStrips( + segplot( + K ~ lwr + upr | umid + var, + key = key, + ylab = "Contagens", + xlab = "NÃvel de adubação Potássica", + centers = fit, groups = modelo, data = pred.all, + horizontal = FALSE, draw = FALSE, + lwd = 2, pch = 1:nlevels(pred.all$modelo) + 4, + panel = panel.groups.segplot, as.table = TRUE, + gap = 0.3, + scales = list( + y = list(relation = "free", rot = 0)) + ), strip = strip.custom( + strip.names = TRUE, var.name = "Umidade"), + strip.left = strip.custom( + factor.levels = c("Nº de vagens", "Nº de grãos")) +) + +## ## as.layer() não funciona quando usado duas variaveis para strip +## xyplot(count ~ factor(K) | umid, data = da, +## key = key, +## type = c("p", "g"), +## alpha = 0.3, +## scales = list( +## y = list(relation = "free", rot = 0)) +## ) + +fonte.xy("Fonte: Elaborado pelo autor.") + +@ + + +\lipsum[1] + +\section{Análise de ninfas de mosca-branca em lavoura de soja} + +<<ajuste-whiteFly, include=FALSE, cache=TRUE>>= +data(whiteFly) +whiteFly <- droplevels(subset(whiteFly, grepl("BRS", x = cult))) +whiteFly$aval <- factor(whiteFly$dias) +## Preditores considerados +f1 <- ntot ~ bloco + cult + aval +f2 <- ntot ~ bloco + cult * aval + +## Ajustando os modelos Poisson +m1P.ntot <- glm(f1, data = whiteFly, family = poisson) +m2P.ntot <- glm(f2, data = whiteFly, family = poisson) + +## Ajustando os modelos COM-Poisson +m1C.ntot <- cmp(f1, data = whiteFly, sumto = 800) +m2C.ntot <- cmp(f2, data = whiteFly, sumto = 800) + +## Ajustando os modelos Binomial Negativo +library(MASS) +m1B.ntot <- glm.nb(f1, data = whiteFly) +m2B.ntot <- glm.nb(f2, data = whiteFly) + +## Ajustando os modelos Quasi-Poisson +m1Q.ntot <- glm(f1, data = whiteFly, family = quasipoisson) +m2Q.ntot <- glm(f2, data = whiteFly, family = quasipoisson) + +##====================================================================== +## Perfil de log-verossimilhanca para o parametro phi +prof.ntot <- profile(m1C.ntot, which = "phi") + +@ + +\lipsum[1] + +<<loglik-whiteFly, include=FALSE>>= + +## Análise de desvios dos modelos +anP.ntot <- myanova(m1P.ntot, m2P.ntot) +anC.ntot <- myanova(m1C.ntot, m2C.ntot) +anB.ntot <- myanova(m1B.ntot, m2B.ntot) +anQ.ntot <- myanova(m1Q.ntot, m2Q.ntot) + +## Tabelas com medidas de ajuste +tab.ntot <- rbind(anP.ntot, anC.ntot, anB.ntot, anQ.ntot) + +## Obtem as estimativas dos parâmetros de dispersão/precisão +dispersions.ntot <- c( + c(rep(NA, 2)), + sapply(list(m1C.ntot, m2C.ntot), function(m) coef(m)[1]), + sapply(list(m1B.ntot, m2B.ntot), function(m) m$theta), + sapply(list(m1Q.ntot, m2Q.ntot), function(m) summary(m)$dispersion)) + +## Teste para o parâmetro de dispersão +pvs <- rep(NA, 8) +pvs[3:4] <- cmptest(m1C.ntot, m2C.ntot)[, 2] + +## Agrupando +dispersions.ntot <- cbind(dispersions.ntot, pvs) + +## Adicionando os parametros de dispersão à tabela +tab.ntot <- cbind(tab.ntot, dispersions.ntot) +rownames(tab.ntot) <- NULL + +## Juntando as tabelas +tab.ajuste <- data.frame( + pred = rep(paste("Preditor", 1:2), 4), + tab.ntot) + +## ##---------------------------------------------------------------------- +## ## Copiar e colar o corpo do resultado na customização latex abaixo +## digits <- c(1, 1, 0, 2, 2, 2, 0, -2, 2, -2) +## print(xtable(tab.ajuste, digits = digits)) +@ + +\begin{table}[ht] +\small +\caption{Medidas de ajuste para avaliação e comparação entre preditores + e modelos ajustados} +\label{tab:ajuste-whiteFly} +\begin{tabular}{lcccccrcr} + \toprule + Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & & \\ + \midrule + Preditor 1 & 12 & -922,98 & 1869,96 & & & & & \\ + Preditor 2 & 27 & -879,23 & 1812,46 & 87,50 & 15 & 2,90E-12 & & \\[0.3cm] + COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ & P($>\rchi^2$) \\ + \midrule + Preditor 1 & 13 & -410,44 & 846,89 & & & & -3,08 & 6,39E-225 \\ + Preditor 2 & 28 & -407,15 & 870,30 & 6,59 & 15 & 9,68E-01 & -2,95 & 2,47E-207 \\[0.3cm] + Binomial Neg. & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\theta}$ & P($>F^2$) \\ + \midrule + Preditor 1 & 13 & -406,16 & 838,31 & & & & 3,44 & \\ + Preditor 2 & 28 & -400,55 & 857,10 & 11,21 & 15 & 7,38E-01 & 3,99 & \\[0.3cm] + Quase-Poisson & np & deviance & AIC & F & diff np & P(>F) & $\hat{\sigma}^2$ & P($>F$) \\ + \midrule + Preditor 1 & 12 & 1371,32 & & & & & 17,03 & \\ + Preditor 2 & 27 & 1283,82 & & 0,31 & 15 & 9,93E-01 & 19,03 & \\ + \bottomrule +\end{tabular} +\begin{tablenotes} + \footnotesize +\item np, número de parâmetros, diff $\ell$, diferença entre + log-verossimilhanças, F, estatÃstica F baseada nas quasi-deviances, + diff np, diferença entre o np. +\item Fonte: Elaborado pelo autor. +\end{tablenotes} +\end{table} + +\lipsum[1] + +<<prof-whiteFly, fig.height=4, fig.width=4, fig.show="hide", results="asis", fig.cap="Perfil de log-verossimilhança para o parâmetro extra da COM-Poisson">>= + +myprof(prof.ntot, subset = 4, par.settings = ps.sub) +fonte.xy("Fonte: Elaborado pelo autor.") + +wrapfigure() + +@ + + +\lipsum[1] + +<<corr-whiteFly, fig.width=7, fig.height=7, fig.cap="Imagem da matriz de correlação entre os parâmetros do modelo COM-Poisson">>= + +pnames <- c("phi", "beta0", + paste0("tau", 1:3), + paste0("gama", 1:3), + paste0("delta", 1:5)) + +Vcov <- vcov(m1C.ntot) +Corr <- cov2cor(Vcov) +dimnames(Corr) <- list(pnames, pnames) +mycorrplot(Corr) + +fonte("Fonte: Elaborado pelo autor.") + +@ + + +\lipsum[1] + + +<<pred-whiteFly, fig.height=4.5, fig.width=7.5, fig.cap="Valores preditos com intervalos de confiança (95\\%) em função das cultivares de soja e da data de avaliação da planta.">>= + +library(multcomp) + +## Predição pontual/intervalar +pred <- with(whiteFly, + expand.grid( + bloco = factor(levels(bloco)[1], + levels = levels(bloco)), + cult = levels(cult), + aval = levels(aval) + )) + +## Matrix de delineamento para predição, considera o efeito médio de +## bloco +X <- model.matrix(~bloco + cult + aval, data = pred) +bl <- attr(X, "assign") == 1 +X[, bl] <- X[, bl] * 0 + 1/(sum(bl) + 1) + +##------------------------------------------- +## Considerando a Poisson +aux <- exp(confint(glht(m1P.ntot, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Poisson", aux) +predP <- cbind(pred, aux) + +##------------------------------------------- +## Considerando a COM-Poisson +aux <- predict(m1C.ntot, newdata = X, type = "response", + interval = "confidence") +aux <- data.frame(modelo = "COM-Poisson", aux[, c("fit", "lwr", "upr")]) +predC <- cbind(pred, aux) + +##------------------------------------------- +## Considerando a Binomial Negativa +aux <- family(m1B.ntot)$linkinv( + confint(glht(m1B.ntot, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Binomial Negativa", aux) +predB <- cbind(pred, aux) + +##------------------------------------------- +## Considerando a Quasi-Poisson +aux <- exp(confint(glht(m1Q.ntot, linfct = X), + calpha = univariate_calpha())$confint) +colnames(aux) <- c("fit", "lwr", "upr") +aux <- data.frame(modelo = "Quasi-Poisson", aux) +predQ <- cbind(pred, aux) + +##------------------------------------------- +pred.all <- rbind(predP, predC, predB, predQ) +pred.all <- pred.all[with(pred.all, order(cult, aval, modelo)), ] + +##---------------------------------------------------------------------- +## Gráfico + +key <- list(type = "o", divide = 1, + lines = list(pch = 1:nlevels(pred.all$model) + 4), + text = list(c("Poisson", "COM-Poisson", + "Binomial Negativa", "Quasi-Poisson")) + ) + +xyplot(ntot ~ aval | cult, + data = whiteFly, + layout = c(NA, 1), + as.table = TRUE, + key = key, + alpha = 0.3, + type = c("p", "g"), + xlab = "Número de dias após o inicÃo do experimento", + ylab = "Número total de moscas-brancas", + par.settings = ps.sub) + + as.layer( + segplot( + aval ~ lwr + upr | cult, + layout = c(NA, 1), + key = key, + centers = fit, groups = modelo, data = pred.all, + horizontal = FALSE, draw = FALSE, + lwd = 2, pch = 1:nlevels(pred.all$modelo) + 4, + panel = panel.groups.segplot, gap = 0.3) + ) + +fonte.xy("Fonte: Elaborado pelo autor.") + +@ + +\lipsum[1] + +\section{Análise de captura de peixes em um parque estadual} + + +<<ajuste-fish, include=FALSE, cache=TRUE>>= + + +@ -- GitLab