From 306623f06586ceae49b00541c40617d8adf3e575 Mon Sep 17 00:00:00 2001 From: Hassen Allegue Date: Sat, 19 Oct 2024 01:18:46 +0000 Subject: [PATCH] Clarifying the structure of the X design matrix --- index.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/index.Rmd b/index.Rmd index fe2c812..ce1511e 100644 --- a/index.Rmd +++ b/index.Rmd @@ -221,7 +221,7 @@ We can also write this in matrix notation: $\boldsymbol{y} = X\boldsymbol{\beta} + \boldsymbol{\epsilon}$ -where $X$ is a matrix of predictors and $\boldsymbol{\beta}$ is a (column) vector of slopes/effect sizes. This matrix notation is a bit more compact and relates most easily the structure of the `simulate_population()` function. However it becomes more complex when we have things varying at different levels, as we have to start getting design matrices for the random effects involved e.g. +where $X$ is a matrix of predictors (one per column) and $\boldsymbol{\beta}$ is a vector of slopes/effect sizes. This matrix notation is a bit more compact and relates most easily the structure of the `simulate_population()` function. However it becomes more complex when we have things varying at different levels, as we have to start getting design matrices for the random effects involved e.g. $\boldsymbol{y} = X\boldsymbol{\beta} + Z\boldsymbol{u} + \boldsymbol{\epsilon}$