--- title: 'CSSS/POLS 510 Maximum Likelihood Estimation: Lab 7' editor_options: chunk_output_type: console date: '2020-11-20' output: beamer_presentation: colortheme: seagull fonttheme: structurebold keep_tex: yes theme: Szeged slidy_presentation: default fontsize: 12pt subtitle: Multinomial Logistic Regression author: Kenya Amano --- # Agenda 1. Recap lectures 2. Multinomial Logistic Regression 3. Homework: HW4 & HW5 # 1. Recap Where are we at right now? 1. Learn distribution and MLE $\rightarrow$ HW1 & HW2 2. Logit model $\rightarrow$ HW3 3. Ordered Probit model $\rightarrow$ HW4 4. Multinomial logit $\rightarrow$ HW5 5. Count data $\rightarrow$ HW5 # 2. Multinomial logit model Review the lecture materials to understand the concept # 2 Simulating QoI 1. Estimate: MLE $\hat{\beta}_{(M+1)\times(P+1)}$ and its variance $\hat{V}(\hat{\beta}_{(M+1)\times(P+1)})$\ $\textcolor{red}{\rightarrow \texttt{optim(), multinom()}}$ 2. Simulate estimation uncertainty from a multivariate normal distribution:\ Draw $\tilde{\beta} \sim MVN \big[\hat{\beta}, \hat{V}(\hat{\beta})\big]$\ $\textcolor{red}{\rightarrow \texttt{MASS::mvrnorm()}}$ 3. Create hypothetical scenarios of your substantive interest:\ Choose valuese of X: $X_c$ $\textcolor{red}{\rightarrow \texttt{simcf::cfmake(), cfchange()} \dots}$ # 2 Simulating QoI 4. Calculate expected values:\ $\tilde{\pi_c} = g(X_c, \tilde{\beta})$ \ 5. Compute EVs, First Differences or Relative Risks\ EV: $\mathbb{E}(y = j|X_{c1},\tilde{\beta})$\ $\textcolor{red}{\rightarrow \texttt{simcf::mlogitsimev()} \dots}$\ FD: $\mathbb{E}(y = j|X_{c2},\tilde{\beta},) - \mathbb{E}(y = j|X_{c1},\tilde{\beta})$\ $\textcolor{red}{\rightarrow \texttt{simcf::mlogitsimfd()} \dots}$\ RR: $\frac{\mathbb{E}(y = j|X_{c2},\tilde{\beta})}{\mathbb{E}(y = j|X_{c1},\tilde{\beta})}$\ $\textcolor{red}{\rightarrow \texttt{simcf::mlogitsimrr()} \dots}$\ # 3. Homework: Question HW4 + Due on Nov 24 + Email subject: **MLE510HW4** + File name: **MLE510HW4KenyaAmano** + *slack chanel: #hw4 + One common problem when knitting: the math mode environment doesn't like white space or empty line + Try \begin{alinged} instead of \begin{split} + R Markdown guide is [\underline{here}](https://bookdown.org/yihui/rmarkdown)