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I recall seeing an answer to some question about linear mixed models where the answer showed an elegant notation for the model. Something like:

$$p(y|x,\gamma)=\mathcal{N}(\beta x+\gamma z,\sigma^2I),\quad \gamma\sim \mathcal{N}(0,\sigma_{\gamma}^2I)$$

I can't find it anymore, though. I saw it last year, but I can't remember whether it was from last year or earlier. I also thought it was @amoeba's, but it's not. I tried both Googling, and using the site search for [linear mixed model]. Can you help me find it?

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    $\begingroup$ How much nicer was it than what you wrote here? :) Are you just looking for a reference answer for this quoted notation, or are you looking for a better notation? $\endgroup$
    – amoeba
    Commented Feb 23, 2018 at 16:14
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    $\begingroup$ @amoeba hey, thanks for the compliments :-) I'm (have been, actually) more of a user of LMMs than a learner, so I wasn't sure my notation was correct and thus yes, I was looking for a reference answer which would confirm this quoted notation. But I also seem to remember it was a nice answer overall, so I would have probably enjoyed reading it again during the weekend. $\endgroup$
    – DeltaIV
    Commented Feb 23, 2018 at 16:18
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    $\begingroup$ stats.stackexchange.com/questions/304374 ? $\endgroup$
    – amoeba
    Commented Feb 23, 2018 at 21:52
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    $\begingroup$ If not, it might help to review stats.stackexchange.com/… (26 hits). $\endgroup$
    – amoeba
    Commented Feb 23, 2018 at 21:53
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    $\begingroup$ @amoeba adding mathcal to the search query was clever...I was halfway through your list but I got bored (weekend laziness :) and I decided to use the notation of Doug Bates from lme4 vignette cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf which is very similar to mine, but it allows for correlations among random effects. $\endgroup$
    – DeltaIV
    Commented Feb 24, 2018 at 10:49
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    $\begingroup$ @DeltaIV: I almost always use the notation $...+Z\gamma+...$ when it comes to LME, I based this on the notation used in Faraway's in Extending the Linear Model with R. While I view Bates` opinions on LMEMs almost as laws, I dislike the idea of using $b$ instead of $\gamma$. The reason is that in multivariate settings where we just want to change our vectors $\alpha$, $\beta$ to matrices $A$, $B$, using both $b$ and $\beta$ becomes cumbersome, $\gamma$ generalised to $\Gamma$ without any issues. (But Bates' notation can't ever be wrong so +1) $\endgroup$
    – usεr11852
    Commented Mar 10, 2018 at 20:34
  • $\begingroup$ @usεr11852 ah, I just used $\gamma$ "unconsciously": I felt that using $b$ and $\beta$ in the same equation "didn't feel right", but I didn't realize about the implications for multivariate linear mixed models (probably because I never use them). $\endgroup$
    – DeltaIV
    Commented Mar 12, 2018 at 11:17

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