From da7870757b487d8a9624bbe3020d0e6aa467e4b9 Mon Sep 17 00:00:00 2001 From: Walmes Zeviani <walmes@ufpr.br> Date: Fri, 27 May 2016 23:01:31 -0300 Subject: [PATCH] Adiciona slides do modelo misto. --- inst/slides/images/winkelman95.jpeg | Bin inst/slides/modelo_misto.Rnw | 79 ++++++++++++++++++++++++++++ inst/slides/slides-mrdcr.Rnw | 12 +++-- inst/slides/slides-mrdcr.pdf | Bin 479389 -> 487306 bytes 4 files changed, 87 insertions(+), 4 deletions(-) mode change 100755 => 100644 inst/slides/images/winkelman95.jpeg create mode 100644 inst/slides/modelo_misto.Rnw diff --git a/inst/slides/images/winkelman95.jpeg b/inst/slides/images/winkelman95.jpeg old mode 100755 new mode 100644 diff --git a/inst/slides/modelo_misto.Rnw b/inst/slides/modelo_misto.Rnw new file mode 100644 index 0000000..76a2b44 --- /dev/null +++ b/inst/slides/modelo_misto.Rnw @@ -0,0 +1,79 @@ +<<setup-childmisto, eval=FALSE, include=FALSE>>= +set_parent("slides-mrdcr.Rnw") +@ + +\begin{frame}[allowframebreaks] + \frametitle{Modelos de efeito aleatório} + \begin{itemize} + \item Acomodam o efeito de termos aleatórios no modelo (ex: blocos, + indivÃduos). + \item Podem representar estruturas hierárquicas de efeitos (ex: + municÃpios $>$ bairros $>$ escolas $>$ salas). + \item Podem acomodar superdispersão com efeito aleatório ao nÃvel de + observação. + \end{itemize} +\end{frame} + +\begin{frame}[allowframebreaks] + \frametitle{A formulação do modelo de efeito aleatório} + \begin{itemize} + \item Seja $b_{i}$ o vetor $q$-dimensional, $q \geq 1$, de efeito do + $i$-ésimo nÃvel de um fator categórico. + \item Seja $Y_{ij}$ o valor observado da $j$-amostra sob efeito de + $b_{i}$ com o vetor linha de covariáveis $X_{ij}$. + \item Considere que uma função monótona $g$ da média de $Y$ seja + função linear do vetor de covariáveis $X_{ij}$ e do vetor de efeitos + aleatórios $b_{i}$ + \begin{equation} + g(\mu_{ij}) = \eta_{ij} = X_{ij}\beta + Z_{i} b_{i}. + \end{equation} + + \item A distribuição condicional de $Y_{ij}$ em relação a $b_{i}$ é + \begin{equation} + Y_{ij}|b_{i} \sim f(y_{ij}|b_{i}, \theta), + \end{equation} + em que $f$ é uma função densidade apropriada para $Y$ e + $\theta \subseteq \beta$ o vetor de parâmetros dessa distribuição. + + \framebreak + + \item Seja a distribuição do efeito aleatório $b_{i}$ + \begin{equation} + b_i \overset{iid}{\sim} \text{Normal}(0, D(\alpha)). + \end{equation} + + \item A esperança de $Y$ marginal é + \begin{equation} + \text{E}(Y_{ij}) = \mu_{ij}, + \end{equation} + no qual $\alpha$ é o vetor de parâmetros presentes na especificação + da covariância dos efeitos aleatórios. + \end{itemize} + + \framebreak + + A função de verossimilhança do modelo + \begin{equation} + L(\theta, \alpha) = \prod_{i=1}^{m} \int_{\mathbb{R}^q} + \left[ \prod_{j=1}^{n_i} f(y_{ij}, \theta, b_i) \right ] + \times f(b_i, \alpha)\, \text{d}b_i. + \end{equation} + + \framebreak + + O problema é + \begin{itemize} + \item Calcular a verossimilhança requer avaliar a integral + \item Pode ser em muitas dimensões ($q > 1$,intercepto, inclinação, + etc) + \item Efeitos podem ser múltiplos, aninhados ou cruzados + \item Para modelar subdispersão com efeito ao nÃvel de observação, + tem-se que $b_{i}$ é $b_{ij}$, ou seja, na mesma dimensão dos dos + dados. + \end{itemize} +\end{frame} + +\begin{frame}{Estudos de caso} + {\it Vignette} \href{run:../doc/v8_misto.html}{\tt + misto.html} +\end{frame} diff --git a/inst/slides/slides-mrdcr.Rnw b/inst/slides/slides-mrdcr.Rnw index 0321b1f..05e59e2 100644 --- a/inst/slides/slides-mrdcr.Rnw +++ b/inst/slides/slides-mrdcr.Rnw @@ -138,16 +138,16 @@ %% ====================================================================== %% Metadados do documento \title{Modelos de Regressão para Dados de Contagem com R} -\author[Walmes Zeviani, Eduardo Jr \& Cesar Taconelli]{ +\author[Walmes Zeviani, Eduardo Jr \& Cesar Taconeli]{ Prof. Dr. Walmes M. Zeviani\\ Eduardo E. Ribeiro Jr\\ - Prof. Dr. Cesar A. Taconelli + Prof. Dr. Cesar A. Taconeli } \institute[UFPR]{ Laboratório de EstatÃstica e Geoinformação \\ Departamento de EstatÃstica \\ Universidade Federal do Paraná} -\date{\today \\[0.1cm] \url{edujrrib@gmail.com}} +\date{\today \\[0.1cm] \url{{walmes,eduardo.jr,taconeli}@ufpr.br}} %\titlegraphic{\includegraphics[width=2cm]{images/MRDCr_logo}} %% ====================================================================== @@ -245,9 +245,13 @@ source("_setup.R") \section{Modelos com Efeitos Aleatórios} \label{sec-efeito-aleatorio} +<<misto, child = "modelo_misto.Rnw">>= +@ + \begin{frame}[allowframebreaks]{Referências} \small -\begin{thebibliography}{} + +\begin{thebibliography}{99} \bibitem{Conway1962} Conway, R. W., Maxwell, W. L. (1962). 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