From 64344d87af3f90956a34593cfe950cd0c5acd331 Mon Sep 17 00:00:00 2001 From: Eduardo Junior <edujrrib@gmail.com> Date: Tue, 28 Jun 2016 03:08:24 -0300 Subject: [PATCH] =?UTF-8?q?Corre=C3=A7=C3=B5es=20e=20complementos=20aos=20?= =?UTF-8?q?slides=20da=20apresenta=C3=A7=C3=A3o=20do=20tcc?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- presentations/preambulo-beamer.tex | 31 +- presentations/slides-tcc.Rmd | 947 +++++++++++++++++++++++++---- presentations/slides-tcc.pdf | Bin 518397 -> 662066 bytes 3 files changed, 821 insertions(+), 157 deletions(-) diff --git a/presentations/preambulo-beamer.tex b/presentations/preambulo-beamer.tex index 5048c23..5f794df 100644 --- a/presentations/preambulo-beamer.tex +++ b/presentations/preambulo-beamer.tex @@ -14,8 +14,8 @@ % --- % date: "`r format(Sys.time(), '%d de %B de %Y')`" % fontsize: "10pt" -% output: -% beamer_presentation: +% output: +% beamer_presentation: % fig_caption: yes % highlight: zenburn % includes: @@ -68,7 +68,7 @@ \setbeamertemplate{frametitle}{ \nointerlineskip - \begin{beamercolorbox}[sep=0.3cm, ht=1.8em, + \begin{beamercolorbox}[sep=0.3cm, ht=1.8em, wd=\paperwidth]{frametitle} \vbox{}\vskip-2ex% \strut\hspace*{3ex}\large\bfseries\insertframetitle\strut @@ -92,7 +92,7 @@ %% ====================================================================== %% Página Inicial -\setbeamertemplate{title page}[default] +\setbeamertemplate{title page}[default][plain] \setbeamercolor{title}{fg=teal} \setbeamercolor{author}{fg=black!70} \setbeamercolor{institute}{fg=black!70} @@ -106,7 +106,7 @@ \setbeamertemplate{headline}{\bfseries \leavevmode% \hbox{% - \begin{beamercolorbox}[wd=.5\paperwidth, ht=2.2ex, dp=1ex, right, + \begin{beamercolorbox}[wd=.5\paperwidth, ht=2.2ex, dp=1ex, right, rightskip=1em]{section in head/foot} \hspace*{2ex}\insertsectionhead \end{beamercolorbox}% @@ -122,7 +122,7 @@ \setbeamertemplate{footline}{\ttfamily\bfseries \leavevmode% \hbox{% - \begin{beamercolorbox}[wd=.3\paperwidth, ht=2.4ex, dp=1ex, right, + \begin{beamercolorbox}[wd=.3\paperwidth, ht=2.4ex, dp=1ex, right, rightskip=1em]{footlinecolor} \insertshortauthor% \end{beamercolorbox}% @@ -147,18 +147,6 @@ \usefonttheme{professionalfonts} \usefonttheme{serif} -%% \usepackage{palatino} -%% \usepackage{eulervm} -%% \usepackage[none]{ubuntu} -%% \usepackage{verbatim} -%% -%% \usefonttheme{professionalfonts} -%% \usefonttheme{serif} -%% \renewcommand{\ttdefault}{ubuntumono} -%% \renewcommand{\ttfamily}{\fontUbuntuMono} -%% \makeatletter -%% \def\verbatim@font{\normalsize\fontUbuntuMono} -%% \makeatother %% ====================================================================== %% Colorindo ambiente verbatim @@ -187,7 +175,7 @@ %% Formatando slides para seções e subseções \AtBeginSection[]{ - \begin{frame}[c, allowframebreaks] + \begin{frame}[c, allowframebreaks, noframenumbering, plain] \begin{center} \textcolor{teal}{\thesection} \\ \vspace{0.3cm} \parbox{0.6\textwidth}{ @@ -197,7 +185,7 @@ } \AtBeginSubsection{ - \begin{frame}[c, allowframebreaks] + \begin{frame}[c, allowframebreaks, noframenumbering, plain] \begin{center} \textcolor{teal}{\thesection.\thesubsection} \\ \vspace{0.3cm} \parbox{0.6\textwidth}{ @@ -212,7 +200,7 @@ \title[Extensões e Aplicações do Modelo COM-Poisson]{Extensões e Aplicações do Modelo de Regressão Conway-Maxwell-Poisson para - Modelagem de Dados de Contagem} + Modelagem de Dados de Contagem} \author[Eduardo E. R. Junior \& Walmes M. Zeviani]{ Eduardo Elias Ribeiro Junior \\ Orientação: Prof. Dr. Walmes Marques Zeviani} @@ -229,4 +217,3 @@ % como `template: template.tex`. Assim não são sobrepostas as definição % padrão do knitr com as modificações feitas. Utilizar como base o arquivo % em ~/.../rmarkdown/rmd/latex/default.tex - diff --git a/presentations/slides-tcc.Rmd b/presentations/slides-tcc.Rmd index b7240f5..754157e 100644 --- a/presentations/slides-tcc.Rmd +++ b/presentations/slides-tcc.Rmd @@ -43,21 +43,20 @@ library(cmpreg) ### Dados de contagem ### \begin{figure}[t] - \includegraphics[height=1cm]{./images/count} + \includegraphics[height=0.9cm]{./images/count} \end{figure} São variáveis aleatórias aleatórias que representam o número de ocorrências de um evento em um dominÃo discreto ou contÃnuo. \vspace{0.5cm} -Se $Y$ é uma v.a. de contagem, $y = 0, 1, 2, \ldots$ +Se $Y$ é uma variável aleatória de contagem, $y = 0, 1, 2, \ldots$ \vspace{0.5cm} Exemplos: * Número de filhos por casal; * Número de indivÃduos infectados por uma doença; - * Número de acidentes de trânsito em um mês; * Número de _posts_ em uma rede social durante um dia; * Número de frutos produzidos; * ... @@ -79,7 +78,7 @@ Exemplos: ### ### -```{r, fig.height = 4, fig.cap = "Ilustração de processos pontuais que levam a contagens com diferentes nÃveis de dispersão."} +```{r, fig.height = 3.5, fig.cap = "Ilustração de processos pontuais que levam a contagens com diferentes nÃveis de dispersão."} mygrid <- expand.grid(xc = 1:3, yc = 1:3) mygrid <- data.frame(mygrid) @@ -111,8 +110,9 @@ xyplot(y ~ x | caso, data = da, "Superdispersão", "Subdispersão")), panel = function(x, y, subscripts, ...) { - l <- seq(min(x), max(x), length.out = 10) - panel.abline(h = l, v = l, col = col, lty = 2) + ## l <- seq(min(x), max(x), length.out = 10) + panel.grid(h = 10, v = 10, col = col, lty = 2, ...) + ## panel.abline(h = l, v = l, col = col, lty = 2) panel.xyplot(x, y, ...) }) @@ -120,6 +120,8 @@ xyplot(y ~ x | caso, data = da, ### Distribuições de probabilidades para dados de contagem ### +Com base em @Winkelmann2008 e @Kokonendji2014 + \begin{table} \centering \small @@ -152,16 +154,16 @@ Katz & \checkmark & \checkmark & \chec \cline{2-4} \\[-0.3cm] & Equidispersão & Superdispersão & Subdispersão \\[0.1cm] \hline - \rowcolor{teal!20} -\textbf{Poisson} & \checkmark & & \\ - \rowcolor{teal!20} -\textbf{Binomial Negativa} & \checkmark & \checkmark & \\ + \rowcolor{teal!30} +Poisson & \checkmark & & \\ + \rowcolor{teal!30} +Binomial Negativa & \checkmark & \checkmark & \\ \textit{Inverse Gaussian Poisson} & \checkmark & \checkmark & \\ \textit{Compound Poisson} & \checkmark & \checkmark & \\ Poisson Generalizada & \checkmark & \checkmark & \checkmark \\ \textit{Gamma-Count} & \checkmark & \checkmark & \checkmark \\ - \rowcolor{teal!20} -\textbf{COM-Poisson} & \checkmark & \checkmark & \checkmark \\ + \rowcolor{teal!30} +COM-Poisson & \checkmark & \checkmark & \checkmark \\ Katz & \checkmark & \checkmark & \checkmark \\ \textit{Poisson Polynomial} & \checkmark & \checkmark & \checkmark \\ \textit{Double-Poisson} & \checkmark & \checkmark & \checkmark \\ @@ -171,6 +173,181 @@ Katz & \checkmark & \checkmark & \chec } \end{table} +### Distribuição COM-Poisson ### + +Proposta por @Conway1962. + +\begin{block}{Função massa de probabilidade} +\begin{equation} + \label{eqn:pmf-compoisson} + \Pr(Y=y \mid \lambda, \nu) = \frac{\lambda^y}{(y!)^\nu Z(\lambda, \nu)}, + \qquad \qquad + Z(\lambda, \nu) = \sum_{j=0}^\infty\frac{\lambda^j}{(j!)^\nu} +\end{equation} +\end{block} + +* Não tem expressão fechada para média e variância; +* Apresenta distribuições bastante conhecidas como casos particulares: + - Poisson - $\nu = 1$; + - Bernoulli - $\nu \to \infty$; + - Geométrica - $\nu = 0$ e $\lambda < 1$. + +### Distribuição COM-Poisson ### + +```{r distr-compoisson, fig.height=3.4, fig.width=6.7, fig.cap="Probabilidades pela distribuição COM-Poisson."} + +library(cmpreg) +##------------------------------------------- +## Parametros da distribuição +pars <- list("p1" = log(c(1.362, 0.4)), + "p2" = log(c(8, 1)), + "p3" = log(c(915, 2.5))) +mus <- sapply(pars, function(p) calc_mean_cmp(p[1], p[2], sumto = 50)) +vars <- sapply(pars, function(p) calc_var_cmp(p[1], p[2], sumto = 50)) + +##------------------------------------------- +## Calculando as probabilidades +y <- 0:30 + +## COM-Poisson +py.co <- sapply(pars, function(p) dcmp(y, p[1], p[2], sumto = 50)) +da.co <- as.data.frame(py.co) +da.co <- cbind(y, stack(da.co)) + +## Poisson +py.po <- sapply(mus, function(p) dpois(y, lambda = p)) +da.po <- as.data.frame(py.po) +da.po <- cbind(y, stack(da.po)) + +##------------------------------------------- +## Objetos para grafico da lattice +l <- sapply(pars, function(p) exp(p[1])) +n <- sapply(pars, function(p) exp(p[2])) +fl <- substitute( + expression(lambda == l1~","~nu == n1, + lambda == l2~","~nu == n2, + lambda == l3~","~nu == n3), + list(l1 = l[1], l2 = l[2], l3 = l[3], + n1 = n[1], n2 = n[2], n3 = n[3])) +cols <- trellis.par.get("superpose.line")$col[1:2] +yaxis <- pretty(da.po$values, n = 2) +ylim <- c(-0.1, max(da.po$values)*1.2) +key <- list( + columns = 2, + lines = list(lty = 1, col = cols), + text = list(c("Poisson", "COM-Poisson"))) + +##------------------------------------------- +## Grafico +xyplot(values ~ c(y - 0.15) | ind, data = da.po, + type = c("h", "g"), + xlab = "y", ylab = expression(Pr(Y == y)), + ylim = ylim, xlim = extendrange(y), + scales = list(y = list(at = yaxis)), + layout = c(NA, 1), + key = key, + strip = strip.custom(factor.levels = fl)) + + as.layer(xyplot( + values ~ c(y + 0.15) | ind, data = da.co, + type = "h", col = cols[2])) +for(i in 1:3){ + trellis.focus("panel", i, 1, highlight=FALSE) + grid::grid.text(label = sprintf("E[Y]: %.1f\nV[Y]: %.1f", + mus[i], mus[i]), + x = .57, y = 0.03, + default.units = "npc", + gp = grid::gpar(col = cols[1]), + just = c("left", "bottom")) +grid::grid.text(label = sprintf("E[Y]: %.1f\nV[Y]: %.1f", + mus[i], vars[i]), + x = .05, y = 0.03, + default.units = "npc", + gp = grid::gpar(col = cols[2]), + just = c("left", "bottom")) +} +trellis.unfocus() + +``` + +### Relações média-variância ### + +```{r mv, fig.height=4, fig.width=8, fig.cap="Relações Média e Variância COM-Poisson e Binomial Negativa."} + +##------------------------------------------- +## Parâmetros considerados +nu <- seq(0.3, 4, length.out = 50) +col <- brewer.pal(n = 8, name = "RdBu") +col <- colorRampPalette(colors = col)(length(nu)) + +##------------------------------------------- +## Etiquetas da legenda +labels <- substitute( + expression(nu == p1, nu == p2, nu == p3), + list(p1 = min(nu), p2 = median(nu), p3 = max(nu))) + +##------------------------------------------- +## Gráfico + +par(mfrow = c(1,2), mar = c(6.5, 5, 3, 4) + 0.1, las = 1) +## Curva identidade representando a Poisson +curve((1/1)*(mu + (1 - 1)/(2*1)), xlab = "", ylab = "", + from = 0, to = 10, xname = "mu") +title(ylab = expression(V(X) == frac(nu*(E(X) + 1)-1, nu^2)), + line = 2.5) +title(xlab = expression(E(X) == lambda^{1/nu} - frac(nu-1, 2*nu)), + line = 4) +grid() + +## Curvas da relação média e variância da COM-Poisson +for (a in seq_along(nu)) { + curve((1/nu[a])*(mu + (nu[a] - 1)/(2*nu[a])), + add = TRUE, xname = "mu", col = col[a], lwd = 2) +} +plotrix::color.legend( + xl = 11, yb = 2.5, xr = 12, yt = 6.5, + gradient = "y", align = "rb", + legend = round(fivenum(nu)[c(1, 3, 5)]), + rect.col = col) +mtext(text = expression(nu), side = 3, cex = 1.3, + line = -3.5, at = 11.5) + +##------------------------------------------- +## Parâmetros considerados +theta <- seq(0.5, 50, length.out = 50) +col <- rev(brewer.pal(n = 8, name = "RdBu")) +col <- colorRampPalette(colors = col)(length(theta)) + +##------------------------------------------- +## Etiquetas da legenda +labels <- substitute( + expression(theta == p1, theta == p2, theta == p3), + list(p1 = min(theta), p2 = median(theta), p3 = max(theta))) + +##------------------------------------------- +## Gráfico + +## Curva identidade representando a Poisson +## par(mar = c(5.5, 4.2, 3, 3), las = 1) +curve(mu + 1*0, + from = 0, to = 10, xname = "mu", + ylab = expression(V(Y) == mu + mu^2~"/"~theta), + xlab = expression(E(Y) == mu)) +grid() +## Curvas da relação média e variância da Binomial Negativa +for (a in seq_along(theta)) { + curve(mu + (mu^2)/theta[a], + add = TRUE, xname = "mu", col = col[a], lwd = 2) +} +plotrix::color.legend( + xl = 11, yb = 2.5, xr = 12, yt = 6.5, + gradient = "y", align = "rb", + legend = round(fivenum(theta)[c(1, 3, 5)]), + rect.col = col) +mtext(text = expression(theta), side = 3, cex = 1.3, + line = -3.5, at = 11.5) + +``` + # Objetivos # ### Objetivos gerais ### @@ -185,7 +362,6 @@ dados de contagem: * Disponibilizando os recursos computacionais para ajuste dos modelos, em formato de pacote R. - # Materiais e Métodos # ## Materiais ## @@ -197,27 +373,28 @@ Seis conjuntos de dados analisados: \only<1>{ \begin{itemize} \tightlist - \item Capulhos de algodão sob desfolha artificial - \item Produtividade de algodão sob infestação de Mosca-branca - \item Produtividade de soja sob umidade e adubação potássica - \item Ocorrência de ninfas de Mosca-branca em lavoura de soja - \item Peixes capturados por visitantes de um parque Estadual - \item Número de nematoides em raizes de feijoeiro + \item Capulhos de algodão sob desfolha artificial; + \item Produtividade de algodão sob infestação de Mosca-branca; + \item Produtividade de soja sob umidade e adubação potássica; + \item Ocorrência de ninfas de Mosca-branca em lavoura de soja; + \item Peixes capturados por visitantes de um parque Estadual; + \item Número de nematoides em raizes de feijoeiro. \end{itemize} } \only<2>{ \begin{itemize} \tightlist \setbeamercolor{itemize item}{fg=teal!30} - \item \textcolor{teal!30}{Capulhos de algodão sob desfolha artificial} + \item \textcolor{teal!30}{Capulhos de algodão sob desfolha artificial;} \setbeamercolor{itemize item}{fg=teal} - \item \textbf{Produtividade de algodão sob infestação de Mosca-branca} + \item Produtividade de algodão sob infestação de Mosca-branca; \setbeamercolor{itemize item}{fg=teal!30} - \item \textcolor{teal!30}{Produtividade de soja sob umidade e adubação potássica} + \item \textcolor{teal!30}{Produtividade de soja sob umidade e adubação + potássica;} \setbeamercolor{itemize item}{fg=teal} - \item \textbf{Ocorrência de ninfas de Mosca-branca em lavoura de soja} - \item \textbf{Peixes capturados por visitantes de um parque Estadual} - \item \textbf{Número de nematoides em raizes de feijoeiro} + \item Ocorrência de ninfas de Mosca-branca em lavoura de soja; + \item Peixes capturados por visitantes de um parque Estadual; + \item Número de nematoides em raizes de feijoeiro. \end{itemize} } \end{center} @@ -227,10 +404,14 @@ Seis conjuntos de dados analisados: Software R versão `r with(R.version, paste0(major, ".", minor))`. Principais pacotes: -* `MASS` (modelo binomial negativo) -* `pscl` (modelagem de excesso de zeros) -* `lme4` (modelo Poisson com efeito aleatório Normal) -* `bbmle` (ajuste de modelos via máxima verossimilhança) +* `MASS` - `r packageVersion("MASS")`: + ajuste dos modelos binomial negativo; +* `pscl` - `r packageVersion("pscl")`: + modelagem de excesso de zeros; +* `lme4` - `r packageVersion("lme4")`: + ajuste dos modelos Poisson com efeito aleatório Normal; +* `bbmle` - `r packageVersion("bbmle")`: + ajuste de modelos via máxima verossimilhança. ## Métodos ## ### Estimação via máxima verossimilhança ### @@ -252,9 +433,9 @@ $$\hat{\Theta} = \underset{\Theta}{\textrm{arg max }} \ell(\Theta \mid - $\phi = 0 \Rightarrow \textrm{Equidispersão}$ - $\phi > 0 \Rightarrow \textrm{Subdispersão}$ -\begin{block}{log-verossimilhança} +\begin{block}{Log-verossimilhança} \begin{equation} - \label{loglik-compoissonr} +\label{loglik-compoisson} \ell(\phi, \beta \mid \underline{y}) = \sum_{i=1}^n y_i \log(\lambda_i) - e^\phi \sum_{i=1}^n \log(y!) - \sum_{i=1}^n \log(Z(\lambda_i, \phi)) \end{equation} @@ -272,7 +453,7 @@ em que $\lambda_i = e^{X_i\beta}$, com $X_i$ o vetor $(x_{i1}, x_{i2}, * $\underline{\lambda}=\exp(X\beta)$ o parâmetro de locação da distribuição COM-Poisson truncada. -\begin{block}{verossimilhança} +\begin{block}{Verossimilhança} \begin{equation} \label{eqn:loglik-hurdlecmp} \Ell(\phi, \beta, \gamma \mid \underline{y}) = @@ -310,14 +491,13 @@ $$\begin{aligned} \right ) db_i \end{equation} -\noindent -sendo $m$ o número de grupos que compartilham do mesmo efeito aleatório, -$q$ o número de efeitos aleatórios (intercepto aleatório, inclinação e -intercepto aleatórios, etc.) e $n_i$ o número de observações no i-ésimo -grupo. +$m:$ o número de grupos que compartilham do mesmo efeito aleatório; \\ +$q:$ o número de efeitos aleatórios (intercepto aleatório, inclinação e +intercepto aleatórios, etc.); e \\ +$n_i:$ o número de observações no i-ésimo grupo. \end{block} -# Resultados # +# Resultados e Discussões # <!--------------------------------------------- --> ## Pacote R ## @@ -325,7 +505,7 @@ grupo. ### `cmpreg`: Ajuste de Modelos de Regressões COM-Poisson ### Implementação em R de um _framework_ para ajuste dos modelos de -regressão COM-Poisson, pacote `cmpreg` +regressão COM-Poisson, pacote `cmpreg`. ```{r pacote, echo=TRUE, eval=FALSE} @@ -416,16 +596,16 @@ prof.nnos <- profile(m3C.nnos, which = "phi") Conduzido na UFGD em casa de vegetação [@Martelli2008]. -* Delineamento: inteiramente casualizado com cinco repetições * Objetivo: avaliar o impacto da praga Mosca-branca na produção de - algodão. -* Unidade amostral: vaso com duas plantas. + algodão; +* Delineamento: inteiramente casualizado com cinco repetições +* Unidade amostral: vaso com duas plantas; * Covariável experimental: - - Tempo de exposição das plantas à praga, em dias. (`dexp`) + - Tempo de exposição das plantas à praga, em dias (`dexp`); * Variáveis resposta: - - Número de capulhos produzidos - - Número de estruturas reprodutivas - - Número de nós + - Número de capulhos produzidos; + - Número de estruturas reprodutivas; + - Número de nós. ### Modelagem ### @@ -462,34 +642,24 @@ anQ.nnos <- myanova(m1Q.nnos, m2Q.nnos, m3Q.nnos) ## Tabela com medidas de ajuste tab.ncapu <- data.frame( - modelos = paste("Preditor", 1:3), + ## 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), + ## 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), + ## 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) - -##------------------------------------------- -## Estimativas e testes para o parametro phi -phis <- cmptest(m3C.ncapu, m2C.nerep, m3C.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)) +digits <- c(1, 0, 2, 2, 4, 2, 2, 4, 2, 4) ``` @@ -497,31 +667,204 @@ phis <- cmptest(m3C.ncapu, m2C.nerep, m3C.nnos) \footnotesize \centering \caption{Medidas de ajuste para avaliação e comparação} -\begin{tabular}{lccccccccc} +\only<1>{ +\begin{tabular}{ccccccccc} + \toprule + & \multicolumn{3}{c}{Poisson} & \multicolumn{3}{c}{COM-Poisson} & \multicolumn{2}{c}{Quasi-Poisson} \\ + \cmidrule(lr){2-4} \cmidrule(lr){5-7} \cmidrule(lr){8-9} + np & $\ell$ & AIC & P($>\rchi^2$) & $\ell$ & AIC & P($>\rchi^2$) & deviance & P($>F$) \\ + \midrule + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \multicolumn{9}{l}{{\bfseries \footnotesize Número de capulhos produzidos}} \\[0.0cm] + \cline{1-5} \\[-0.2cm] +```{r body11, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ncapu, digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \multicolumn{9}{l}{{\bfseries \footnotesize Número de estruturas reprodutivas}} \\[0.0cm] + \cline{1-5} \\[-0.2cm] +```{r body12, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nerep, digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \multicolumn{9}{l}{{\bfseries \footnotesize Número de nós da planta}} \\[0.0cm] + \cline{1-5} \\[-0.2cm] +```{r body13, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nnos, digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \bottomrule +\end{tabular} +} +\only<2>{ +\begin{tabular}{ccccccccc} \toprule - & & \multicolumn{3}{c}{Poisson} & \multicolumn{3}{c}{COM-Poisson} & \multicolumn{2}{c}{Quasi-Poisson} \\ - \cmidrule(lr){3-5} \cmidrule(lr){6-8} \cmidrule(lr){9-10} - & np & $\ell$ & AIC & P($>\rchi^2$) & $\ell$ & AIC & P($>\rchi^2$) & deviance & P($>F$) \\ + & \multicolumn{3}{c}{Poisson} & \multicolumn{3}{c}{COM-Poisson} & \multicolumn{2}{c}{Quasi-Poisson} \\ + \cmidrule(lr){2-4} \cmidrule(lr){5-7} \cmidrule(lr){8-9} + 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] + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \multicolumn{9}{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] +```{r body11b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ncapu, digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(2), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \multicolumn{9}{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] +```{r body12b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nerep, digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \multicolumn{9}{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 \\ +```{r body13b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nnos, digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(2), command = "\\rowcolor{teal!30}" + )) + +``` \bottomrule \end{tabular} +} \end{table} +### Avaliação da dispersão ### + +```{r prof-cottonBolls2, fig.height=3, fig.width=7, fig.cap="Perfis de log-verossimilhança para o parâmetro de precisão da COM-Poisson."} + +##====================================================================== +## 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]) +## +cols <- trellis.par.get("superpose.line")$col[1:2] +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, ...) { + conf <- c(0.9, 0.95, 0.99) + hl <- sqrt(qchisq(conf, 1)) + ##------------------------------------------- + mle <- x[y == 0] + xl <- x[x < mle]; yl <- y[x < mle] + xr <- x[x > mle]; yr <- y[x > mle] + ##------------------------------------------- + funleft <- approxfun(x = yl, y = xl) + funright <- approxfun(x = yr, y = xr) + vxl <- funleft(hl) + vxr <- funright(hl) + vz <- c(hl, hl) + ##------------------------------------------- + panel.xyplot(x, y, ...) + panel.arrows(c(vxl, vxr), 0, c(vxl, vxr), vz, + code = 1, length = 0.1, lty = 2, + col = "gray40") + panel.segments(vxl, vz, vxr, vz, lty = 2, + col = "gray40") + panel.abline(h = 0, v = mle, lty = 3) + panel.text(x = rep(mle, 2), y = vz+0.1, + labels = paste(conf*100, "%"), + col = "gray20") + panel.abline(v = 0, col = cols[2]) + }) + +``` + +### Avaliação da matriz de covariância ### + +```{r corr-cottonBolls2, fig.height=1.7, fig.width=5, out.width="1\\linewidth", 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) + +pnames <- c("phi", "beta0", "beta1") +Vcov <- vcov(m2C.nerep) +Corr.nerep <- cov2cor(Vcov) +dimnames(Corr.nerep) <- list(pnames, pnames) + +par(mfrow = c(1, 3)) +mycorrplot(Corr.ncapu, mar = c(1.5, 0, 0, 0)) +mtext(text = "Capulhos produzidos", side = 1, cex = 0.7) +mycorrplot(Corr.nerep, mar = c(1.5, 0, 0, 0)) +mtext(text = "Estruturas reprodutivas", side = 1, cex = 0.7) +mycorrplot(Corr.nnos, mar = c(1.5, 0, 0, 0)) +mtext(text = "Número de nós", side = 1, cex = 0.7) + +``` + ### Valores preditos ### ```{r pred-cottonBolls2, fig.height=3.5, fig.width=7, fig.cap="Curva dos valores preditos com intervalo de confiança de (95\\%) como função dos dias de exposição a alta infestação de Mosca-branca."} @@ -625,13 +968,13 @@ xyplot(count ~ dexp | va, data = da, scales = list( y = list(relation = "free", rot = 0)), strip = strip.custom( - factor.levels = c("Estruturas reprodutivas ", - "Capulhos produzidos", - "Nós da planta")), + factor.levels = c( + "Capulhos produzidos", + "Estruturas reprodutivas", + "Nós da planta")), alpha = 0.3, spread = 0.15, - panel = panel.beeswarm, - par.settings = ps.sub)+ + panel = panel.beeswarm)+ as.layer( xyplot(fit + lwr + upr ~ dexp | var, data = predP, layout = c(NA, 1), @@ -696,16 +1039,16 @@ prof.ntot <- profile(m1C.ntot, which = "phi") Conduzido na UFGD em casa de vegetação [@Suekane2011]. -* Delineamento: blocos casualizados com quatro blocos. -* Objetivo: avaliar a propensão de cultivares de soja à praga - Mosca-branca. -* Unidade experimental: dois vasos com duas plantas. +* Objetivo: avaliar a ocorrência de mosca-branca nas diferentes + cultivares de soja; +* Delineamento: blocos casualizados, quatro blocos; +* Unidade experimental: dois vasos com duas plantas; * Covariáveis experimentais: - - Indicadora de bloco, I, II, III e IV, (`bloco`), + - Indicadora de bloco, I, II, III e IV, (`bloco`); - Dias decorridos após a primeira avaliação, 0, 8, 13, 22, 31 e 38 - dias. (`dias`), + dias, (`dias`); - Indicadora de cultivar de soja, BRS 239, BRS 243 RR, BRS 245 RR, - BRS246 RR, (`cult`). + BRS246 RR, (`cult`); * Variável resposta: - Número de ninfas de Mosca-branca nos folÃolos dos terços superior, médio e inferior. @@ -714,9 +1057,9 @@ Conduzido na UFGD em casa de vegetação [@Suekane2011]. Preditores considerados: -* $\eta_1 = g(\mu_{ijk}) = \beta_0 + \tau_i + \gamma_j + \delta_k$ -* $\eta_2 = g(\mu_{ijk}) = \beta_0 + \tau_i + \gamma_j + \delta_k + -\alpha_{jk}$ +* Preditor 1: $g(\mu_{ijk}) = \beta_0 + \tau_i + \gamma_j + \delta_k$ +* Preditor 2: $g(\mu_{ijk}) = \beta_0 + \tau_i + \gamma_j + \delta_k + + \alpha_{jk}$ \hspace{0.3cm} \begin{minipage}[t]{0.9\textwidth} @@ -769,10 +1112,9 @@ 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) -## print(xtable(tab.ajuste, digits = digits)) +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +digits <- c(1, 1, 0, 2, 2, 2, 0, 4, 2) ``` @@ -780,28 +1122,169 @@ tab.ajuste <- data.frame( \centering \footnotesize \caption{Medidas de ajuste para avaliação e comparação} +\only<1>{ +\begin{tabular}{lcccccrcr} + \toprule + Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & \\ + \midrule +```{r body21, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[1:2, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ \\ + \midrule +```{r body22, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[3:4, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + Binomial Neg. & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\theta}$ \\ + \midrule +```{r body23, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[5:6, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + Quase-Poisson & np & deviance & AIC & F & diff np & P(>F) & $\hat{\sigma}^2$ \\ + \midrule +```{r body24, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[7:8, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \bottomrule +\end{tabular} +} +\only<2>{ \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] +```{r body21b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[1:2, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ \\ \midrule - Preditor 1 & 13 & -410,44 & 846,89 & & & & -3,08 \\ - Preditor 2 & 28 & -407,15 & 870,30 & 6,59 & 15 & 9,68E-01 & -2,95 \\[0.3cm] +```{r body22b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[3:4, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(0), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento Binomial Neg. & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\theta}$ \\ \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] +```{r body23b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[5:6, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(0), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento Quase-Poisson & np & deviance & AIC & F & diff np & P(>F) & $\hat{\sigma}^2$ \\ \midrule - Preditor 1 & 12 & 1371,32 & & & & & 17,03 \\ - Preditor 2 & 27 & 1283,82 & & 0,31 & 15 & 9,93E-01 & 19,03 \\ +```{r body24b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.ajuste[7:8, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(0), command = "\\rowcolor{teal!30}" + )) + +``` \bottomrule \end{tabular} +} \end{table} +### Avaliando a dispersão e convergência de Z ### + +```{r convergez-prof-whiteFly, fig.height=3.5, fig.width=7, fig.cap="Convergência das constantes de normalização e perfil de log-verossimilhança para o parâmetro de precisão da COM-Poisson."} + +##------------------------------------------- +## Constante normalizadora + +## Para nvag +lam.ntot <- predict(m2C.ntot) +zs.ntot <- sapply(lam.ntot, function(l) { + funZ(exp(l), exp(m2C.ntot@coef[1]), maxit = 1500, tol = 0.001) +}) +names(zs.ntot) <- 1:nrow(whiteFly) +const.ntot <- plyr::ldply(zs.ntot) +const.ntot <- rbind(data.frame(const.ntot, var = "ntot")) + +xy1 <- xyplot(z ~ j | var, data = const.ntot, + type = c("l", "g"), + scales = "free", + yscale.components = yscale.components.logpower, + ylab = list( + expression(frac(lambda[i]^j, "(j!)"^nu)), + rot = 0), + strip = strip.custom( + factor.levels = c("Número de ninfas"))) + +##------------------------------------------- +## Perfil de log-verossimilhanca para phi +xy2 <- myprof(prof.ntot, namestrip = expression(phi), subset = 4) + +print(xy1, split = c(1, 1, 2, 1), more = TRUE) +print(xy2, split = c(2, 1, 2, 1), more = FALSE) + +``` + ### Valores preditos ### ```{r pred-whiteFly, fig.height=4.2, fig.width=7.5, fig.cap="Valores preditos com intervalos de confiança (95\\%)."} @@ -986,12 +1469,11 @@ dispHB <- sapply(list(m1HB, m2HB), function(m) m$theta) dispersions <- c(NA, NA, dispHB, dispHC) ## Empilhando -tab <- data.frame(pred = rep(paste("Preditor", 1:2), 3)) -tab <- cbind(tab, rbind(anHP, anHB, anHC), dispersions) +tab.fish <- data.frame(pred = rep(paste("Preditor", 1:2), 3)) +tab.fish <- cbind(tab.fish, rbind(anHP, anHB, anHC), dispersions) -## ## Gerando o código latex -## digits <- c(1, 1, 0, 2, 2, 2, 0, -2, 2) -## xtable(tab, digits = digits) +## Gerando o código latex +digits <- c(1, 1, 0, 2, 2, 2, 0, 4, 2) ``` @@ -1000,22 +1482,107 @@ tab <- cbind(tab, rbind(anHP, anHB, anHC), dispersions) \footnotesize \caption{Medidas de ajuste para avaliação e comparação} \label{tab:ajuste-fish} +\only<1>{ +\begin{tabular}{lcccccrc} + \toprule +Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & \\ + \midrule +```{r body31, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +digits[8] <- -1 +print(xtable(tab.fish[1:2, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento +Binomial Neg. & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\theta}$ \\ + \midrule +```{r body32, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +digits[8] <- 4 +print(xtable(tab.fish[3:4, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento +COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ \\ + \midrule +```{r body33, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.fish[5:6, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \bottomrule +\end{tabular} +} +\only<2>{ \begin{tabular}{lcccccrc} \toprule Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & \\ \midrule - Preditor 1 & 7 & -857,48 & 1728,96 & & & & \\ - Preditor 2 & 10 & -744,58 & 1509,17 & 225,79 & 3 & 1,12E-48 & \\[0.3cm] +```{r body31b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +digits[8] <- -1 +print(xtable(tab.fish[1:2, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento Binomial Neg. & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\theta}$ \\ \midrule - Preditor 1 & 8 & -399,79 & 815,58 & & & & 0,20 \\ - Preditor 2 & 11 & -393,72 & 809,44 & 12,14 & 3 & 6,91E-03 & 0,37 \\[0.3cm] +```{r body32b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +digits[8] <- 4 +print(xtable(tab.fish[3:4, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ \\ \midrule - Preditor 1 & 8 & -409,85 & 835,71 & & & & -8,77 \\ - Preditor 2 & 11 & -402,30 & 826,59 & 15,12 & 3 & 1,72E-03 & -3,77 \\ +```{r body33b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.fish[5:6, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` \bottomrule \end{tabular} +} \end{table} ### Valores preditos ### @@ -1131,14 +1698,15 @@ load("../docs/mixedcmp_models.rda") Conduzido no IAPAR em casa de vegetação. -* Delineamento: inteiramente casualizado com cinco repetições. -* Objetivo: avaliar a resistência à nematoides de linhagens de feijoeiro. +* Objetivo: avaliar a resistência de linhagens de feijoeiro à nematoides; +* Delineamento: inteiramente casualizado com cinco repetições; * Unidade amostral: alÃquota de 1ml da solução de raizes lavadas, - trituradas, peneiradas e diluÃdas em água provida por um vaso com duas - plantas. + trituradas, peneiradas, diluÃdas em água. Provida por um vaso com duas + plantas; * Covariáveis: - - Indicador de linhagem de feijoeiro, A, B, C, $\ldots$, S (`cult`) - - Concentração de raiz na solução. (`sol`) + - Indicador de linhagem de feijoeiro, A, B, C, $\ldots$, S, + (`cult`); + - Concentração de raiz na solução, (`sol`); * Variáveis resposta: - Número de nematoides. @@ -1146,13 +1714,19 @@ Conduzido no IAPAR em casa de vegetação. Preditores considerados: -* Preditor 1: $g(\mu_{ij}) = \beta_0 + b_j$ -* Preditor 2: $g(\mu_{ij}) = \beta_0 + \beta_1 \log(\textrm{sol})_i + - b_j$ +* Preditor 1: $g(\mu_{ij}) = \beta_0 + b_i$ +* Preditor 2: $g(\mu_{ij}) = \beta_0 + \beta_1 \log(\textrm{sol})_{ij} + + b_i$ \hspace{0.35cm} \begin{minipage}[t]{0.9\textwidth} -$b_j \sim \textrm{Normal}(0,\, \sigma^2)$ +$b_i \sim \textrm{Normal}(0,\, \sigma^2)$ +\vspace{0.2cm} + +\small +$i: $ varia entre as linhagens, $i=1, 2, \ldots, 19$; e \\ +$j: $ varia entre as observações dentro das linhagens, $j=1, 2, \ldots, +n_i$. \end{minipage} \vspace{0.5cm} @@ -1163,24 +1737,126 @@ Modelos concorrentes: ### Medidas de ajuste ### +```{r logLik-nematodes, include=FALSE} + +## Anova +anP <- myanova(m1PM, m2PM) +anC <- myanova(m1CM, m2CM) + +## TRV entre Mixed-Poisson e Mixed-COMPoisson +trv <- 2 * (anC[, 2] - anP[, 2]) +pvs <- pchisq(q = trv, df = 1, lower.tail = FALSE) +phi <- sapply(list(m1CM, m2CM), function(model) model@fullcoef[1]) + +## Empilha na tabela +tab.nema <- data.frame( + preditor = rep(paste("Preditor", 1:2), 2), + rbind(cbind(anP, cbind(c(NA, NA)), c(NA, NA)), + cbind(anC, phi, pvs))) + +digits <- c(1, 1, 0, 2, 2, 2, 0, 4, 2, 4) + +``` + \begin{table}[ht] \centering \footnotesize \caption{Medidas de ajuste para avaliação e comparação} +\only<1>{ +\begin{tabular}{lcccccrcr} + \toprule + Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & \\ + \midrule +```{r body41, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nema[1:2, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ & P($>\rchi^2$) \\ + \midrule +```{r body42, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nema[3:4, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento + \bottomrule +\end{tabular} +} +\only<2>{ \begin{tabular}{lcccccrcr} \toprule Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & \\ \midrule - Preditor 1 & 2 & -237,20 & 478,40 & & & & & \\ - Preditor 2 & 3 & -234,66 & 475,32 & 5,07 & 1 & 2,43E-02 & & \\[0.3cm] +```{r body41b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nema[1:2, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento COM-Poisson & np & $\ell$ & AIC & 2(diff $\ell$) & diff np & P($>\rchi^2$) & $\hat{\phi}$ & P($>\rchi^2$) \\ \midrule - Preditor 1 & 3 & -236,85 & 479,71 & & & & 0,15 & 4,06E-01 \\ - Preditor 2 & 4 & -233,86 & 475,72 & 5,99 & 1 & 1,44E-02 & 0,23 & 2,05E-01 \\ +```{r body42b, results="asis"} + +##---------------------------------------------------------------------- +## Copiar e colar o corpo do resultado na customização latex abaixo +print(xtable(tab.nema[3:4, ], digits = digits), + include.colnames = FALSE, + hline.after = NULL, + only.contents = TRUE, + add.to.row = list( + pos = list(1), command = "\\rowcolor{teal!30}" + )) + +``` + \specialrule{0em}{0.5em}{0em} %% Apenas para espaçamento \bottomrule \end{tabular} +} \end{table} +### Avaliação dos perfis de verossimilhança ### + +```{r prof-nematodes, fig.height=3, fig.width=7, fig.cap="Perfis de verossimilhança dos parâmetros estimados no modelo COM-Poisson Misto."} + +fl <- expression(phi, log(sigma), beta[0], beta[1]) +myprof(profCM, subset = 3.5, + namestrip = fl, xlab = "Parâmetros do modelo") + +``` + +### Imagem da matriz de covariância ### + +```{r corr-nematodes, fig.width=3.2, fig.height=3.2, out.width="0.5\\textwidth", fig.cap="Imagem da matriz de covariância entre os parâmetros do modelo COM-Poisson."} + +pnames <- c("phi", "lsigma", paste0("beta", 0:1)) + +Vcov <- vcov(m2CM) +Corr <- cov2cor(Vcov) +dimnames(Corr) <- list(pnames, pnames) +mycorrplot(Corr) + +``` + ### Valores preditos ### ```{r pred-nematodes, fig.height=4.2, fig.width=7.4, fig.cap="Valores preditos nos modelos de efeitos mistos."} @@ -1274,13 +1950,13 @@ print(xy1, position = c(0.57, 0, 1, 1), more = FALSE) * Similaridade entre inferências via modelo Quasi-Poisson e COM-Poisson; * Desempenho do modelo Binomial Negativo; -* Interpretação dos parâmetros nos modelos baseados na COM-Poisson +* Interpretação dos parâmetros nos modelos baseados na COM-Poisson; * Problemas numéricos para determinação da matriz hessiana no modelo Hurdle COM-Poisson; * Procedimentos computacionalmente intensivos na avaliação da verossimilhança no caso COM-Poisson de efeitos aleatórios; * Não ortogonalidade observada (empÃrica) entre os parâmetros de locação - e de precisão no modelo COM-Poisson; + e de precisão no modelo COM-Poisson; e * Comportamento simétrico dos perfis de log-verossimilhança para o parâmetro $\phi$ da COM-Poisson. @@ -1294,10 +1970,11 @@ Aplicação do modelo COM-Poisson: * Resultados similares aos providos pela abordagem semi-paramétrica via quasi-verossimilhança; * A não ortogonalidade entre os parâmetros de locação e precisão no - modelo COM-Poisson se mostra como caracterÃstica da distrição; + modelo COM-Poisson se mostra como caracterÃstica da distribuição; * A simetria nos perfis de verossimilhança do parâmetro de precisão - também. -* A avaliação da constante de normalização é problemática no modelo. + também; e +* A avaliação da constante de normalização é uma dificuldade + computacional do modelo. ### Conclusões ### @@ -1307,7 +1984,7 @@ Análise de dados de contagem: * Modelo Poisson inadequado na maioria das aplicações, mostrando que a suposição de equidispersão é de fato restritiva; * Modelos alternativos ao Poisson devem ser empregados na análise de - dados de contagem; + dados de contagem; e * Sugere-se o modelo COM-Poisson como alternativa totalmente paramétrica e bastante flexÃvel. @@ -1316,7 +1993,7 @@ Análise de dados de contagem: * Estudar reparametrizações do modelo COM-Poisson; * Avaliar aproximações da constante de normalização; * Realizar estudos de simulação para avaliar a robustez do modelo; -* Implementar o modelo COM-Poisson inflacionado de zeros; +* Implementar o modelo COM-Poisson inflacionado de zeros; e * Implementar o modelo COM-Poisson com efeitos aleatórios dependentes. <!--------------------------------------------- --> diff --git a/presentations/slides-tcc.pdf b/presentations/slides-tcc.pdf index 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