Talk:Mixed model

Linear models
Except for the first couple of sentences, this article is about linear mixed-effects models. I have recently added a stand-alone article about nonlinear mixed-effects models, so I suggest that this article is renamed to linear mixed-effects model. --larslau (talk) 4 August 2020 —Preceding undated comment added 13:59, 4 August 2020 (UTC)
 * @larslau Good point. But the disadvantage of renaming this page is that we also need a page for mixed models and it would be inconvenient if that page was just a disambiguation page, given that most readers will be most interested in the linear mixed-effects models, so will appreciate coming here directly. Rather than renaming the page I added the sentence "This page will discuss mainly linear mixed-effects models rather than generalized linear mixed models or nonlinear mixed-effects models". I will also redirect linear mixed-effects model here. Delius (talk) 16:41, 2 May 2021 (UTC)

Incorrect redirect (resolved)
This article redirects to multilevel model, but this is incorrect. A multilevel model may be mixed, but not necessarily so. A mixed model is one in which some of the effects are considered to be fixed and others are considered to be random. Someone with a bit more statistical knowledge than I have could perhaps re-write the mixed-model article. --Crusio (talk) 09:57, 2 September 2008 (UTC)
 * Done, better late than never. I acknowledged the undoing of the redirect at WikiProject Statistics, so there will be higher visibility. Baccyak4H (Yak!) 02:55, 19 June 2009 (UTC)

Computation
There was a nebulous explanation of the details on how the mixed models (linear) are fit computationally. I gave a reference to the Lindstrom Bates article which describes iteratively fitting the linear model and estimating the variance components using the EM algorithm. I also cited R and SAS since this is how they do it. Might be good to format the procedures as computed code, instead of appearing as garbled jargon. My wiki-fu is not good enough to code them as such, yet.Saffloped (talk) 22:00, 12 September 2011 (UTC)

It seems that this sentence was added:
 * More recently, methods for maximum likelihood estimation of mixed models have become more widely used than least-squares based methods.[7]

This is not right nor is it wrong: it's confusing. Ordinary least squares minimizes the variance of the unweighted residuals. The point of the mixed model is that the variance components are not equal, so a more efficient estimation method is inverse variance weighting. The EM algorithm is necessary because it iteratively estimates the variance, applies the weights, and estimates model parameters. I say either remove the line, or don't speak of methods in terms of their "popularity" but their justification Saffloped (talk) 20:30, 27 September 2011 (UTC)

Definition
Can we add dimensions to all the matrices, i.e. * y is a vector of n observations * beta is a vector of fixed effects of length n * X is a matrix of ... with dimensions n x p where p is ... * u is a matrix of ... with dimensions n x q where q is ... I think this would make things way more clear for people seeing things for the first time (fill in the ellipsis's, I don't feel qualified to do so) MATThematical (talk) 06:30, 31 December 2013 (UTC)

Proposed merge of Multilevel model with Mixed model
As far as I can tell, "mixed model" and "multilevel model" are synonyms. Neil Shah-Quinn (talk) 21:28, 4 June 2021 (UTC)

I do agree these should be merged. Neuropsychologist (talk) 09:36, 17 January 2022 (UTC)

From the Multilevel model page: "Multilevel models are particularly appropriate for research designs where data for participants are organized at more than one level", whereas Mixed models can have only one level. Thus, it sounds like all multilevel models are mixed models but not all mixed models are multilevel models, since mixed models need not have more than one level. If they do get merged, I would suggest retaining the more general term "Mixed model", and including a bit about multilevel models within. 20 January 2022. — Preceding unsigned comment added by 161.98.8.9 (talk) 16:45, 20 January 2022 (UTC)

Mixed models have _two_ levels, whereas multilevel models can have more. — Preceding unsigned comment added by 2A02:A44C:86AA:1:B801:BDC6:AD3C:1357 (talk) 12:58, 25 January 2022 (UTC)

I am not sure where does the idea that "mixed models" can only have two levels. As far as I know, the "mixed" term is the shorthand for mixed-effects which refers to the presence of both fixed and random effects. It does not make any assumptions as to how the number / type of these effects. Are there any papers / reference about this distinction? 14:06, 25 January 2022 (UTC) — Preceding unsigned comment added by Neuropsychologist (talk • contribs)
 * Oppose; these are talking about different model features, and should be treated separately. Levels (the example from the page being of of schools: pupil, class, school, district), versus effects (say socioeconomic status, gender, ethnicity, etc.). So, I think that these should certainly be treated separately. Klbrain (talk) 12:44, 28 October 2022 (UTC)
 * Closing, given the uncontested objection and stale discussion. Klbrain (talk) 09:54, 26 November 2022 (UTC)