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Add exercise and clean up code for example

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Nora Wickelmaier
2025-06-20 13:59:41 +02:00
parent 72bd3fcaa7
commit 40fdb67b67
6 changed files with 186 additions and 40 deletions
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slides/lead_lmm.pdf
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slides/lead_lmm.tex
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@@ -78,7 +78,9 @@
\item I will explain the general concepts with the slides
\item We will switch to R and use the lme4 package to fit the models
\item You will use R to fit an extension of the model
\item We will discuss the results\\~\\
\item We will discuss the results
\item All the materials are here: \url{https://gitea.iwm-tuebingen.de/nwickelmaier/lead_lmm}
\\~\\
\item[$\to$] Try to go along in R! Ask as many questions as possible, also
the ones you usually do not dare to ask (because you are supposed to know
them already or something\dots)
@@ -162,7 +164,7 @@
\begin{column}{.6\textwidth}
Model equation
\begin{align*}
\text{(Level 1)} \quad y_{ij} &= b_{0i} + \varepsilon_{ij}\\
\text{(Level 1)} ~\quad y_{ij} &= b_{0i} + \varepsilon_{ij}\\
\text{(Level 2)} \quad b_{0i} &= \beta_0 + \upsilon_{0i}\\
\text{(2) in (1)} \quad y_{ij} &= \beta_0 + \upsilon_{0i} + \varepsilon_{ij}
\end{align*}
@@ -236,7 +238,7 @@
\end{frame}
\begin{frame}{Regression with random school effects}
\begin{frame}{Adding socioeconomic status as a predictor}
\begin{itemize}
\item How strong is the relationship between students' socioeconomic status
and their math achievement on average?
@@ -267,7 +269,7 @@
\begin{column}{.6\textwidth}
Model equation
\begin{align*}
\text{(Level 1)} \quad y_{ij} &= b_{0i} + b_{1i}\,x_{ij} + \varepsilon_{ij}\\
\text{(Level 1)} ~\quad y_{ij} &= b_{0i} + b_{1i}\,x_{ij} + \varepsilon_{ij}\\
\text{(Level 2)} \quad b_{0i} &= \beta_0 + \upsilon_{0i}\\
\quad b_{1i} &= \beta_1\\
\text{(2) in (1)} \quad y_{ij} &= \beta_0 + \beta_1\,x_{ij} +
@@ -322,7 +324,7 @@
\end{itemize}\pause
\item How can we interpret the random slopes for this model?\pause
\item How do we add random slopes to a random intercept model using
\texttt{lme4::lmer()}?
\texttt{lme4::lmer()}?\pause
\item Fit a model with random slopes for socioeconomic status in R
\end{itemize}
\end{block}
@@ -381,12 +383,12 @@
\begin{frame}{Hierarchical regression model}
Model equation
\begin{align*}
\text{(Level 1)} \quad y_{ij} =&~b_{0i} + b_{1i}\,cses_{ij} + \varepsilon_{ij}\\
\text{(Level 1)} ~\quad y_{ij} =&~b_{0i} + b_{1i}\,cses_{ij} + \varepsilon_{ij}\\
\text{(Level 2)} \quad b_{0i} =&~\beta_0 + \beta_2 meanses_i + \beta_4 sector_i + \upsilon_{0i}\\
\quad b_{1i} =&~\beta_1 + \beta_3 meanses_i + \beta_5 sector_i + \upsilon_{1i}\\
\text{(2) in (1)} \quad y_{ij} =&~\beta_0 + \beta_1\,cses_{ij} + \beta_2 meanses_i + \beta_4 sector_i\\
& + \beta_3 (cses_{ij} \times meanses_i) + \beta_5 (cses_{ij} \times sector_i) \\
& + \upsilon_{0i} + cses_{ij}\upsilon_{1i} + \varepsilon_{ij}
& + \upsilon_{0i} + \upsilon_{1i}cses_{ij} + \varepsilon_{ij}
\end{align*}
with
\begin{align*}
@@ -424,7 +426,7 @@ with
\item Compute the model in R using \texttt{lme4::lmer()}
{\scriptsize
\begin{align*}
\text{(Level 1)} \quad y_{ij} =&~b_{0i} + b_{1i}\,cses_{ij} + \varepsilon_{ij}\\
\text{(Level 1)} ~\quad y_{ij} =&~b_{0i} + b_{1i}\,cses_{ij} + \varepsilon_{ij}\\
\text{(Level 2)} \quad b_{0i} =&~\beta_0 + \beta_2 meanses_i + \beta_4 sector_i + \upsilon_{0i}\\
\quad b_{1i} =&~\beta_1 + \beta_3 meanses_i + \beta_5 sector_i + \upsilon_{1i}\\
\text{(2) in (1)} \quad y_{ij} =&~\beta_0 + \beta_1\,cses_{ij} + \beta_2 meanses_i + \beta_4 sector_i