Hello. I have a question about the variance of Y. I have the model 𝒀=𝑿𝛽+𝒁𝑏+𝜀 with 𝜀 ~ 𝑁(0,𝜎^2 𝐼) and 𝑏 ~ 𝑁 (0,Γ). Thus, 𝑌 ~ 𝑁(𝑋𝛽, 𝑍Γ𝑍^𝑇+𝜎^2 𝐼). Intuitively I would have guessed that Var(Y) = Γ+𝜎^2 𝐼. Why is the variance Var(Y)=𝑍Γ𝑍^𝑇+𝜎^2 𝐼 ? Why do I need to multiply Z and Z^T on both sides of Γ? I hope you can help me :)
@@mronkko the "covariance matrix" part. You emphasize that the variance is equal to the variance of the random effects + the variance of the error term.
Great video! Very helpful conceptual explanation. Thank you.
Glad it was helpful!
This is great! Thank you!
You are welcome
Hello.
I have a question about the variance of Y.
I have the model 𝒀=𝑿𝛽+𝒁𝑏+𝜀 with 𝜀 ~ 𝑁(0,𝜎^2 𝐼) and 𝑏 ~ 𝑁 (0,Γ). Thus, 𝑌 ~ 𝑁(𝑋𝛽, 𝑍Γ𝑍^𝑇+𝜎^2 𝐼).
Intuitively I would have guessed that Var(Y) = Γ+𝜎^2 𝐼. Why is the variance Var(Y)=𝑍Γ𝑍^𝑇+𝜎^2 𝐼 ? Why do I need to multiply Z and Z^T on both sides of Γ?
I hope you can help me :)
Can you give me a timestamp of the relevant part of the video?
@@mronkko the "covariance matrix" part. You emphasize that the variance is equal to the variance of the random effects + the variance of the error term.
@@PeterBTerkelsen Can you give a time in the video so it is easier to answer?