Mathematical Notation for Mixed Models

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[@cofi9659]

Great video

[@galenseilis5971]

Linear mixed effects are a good starting point for pedagogy, but I would also recommend mentioning in passing non-linear mixed effects are sometimes useful. For keen students it may be further worth noting that the notion of a mixed effect can be generalized to other operators beyond addition.

[@derekcaramella8730]

Here’s a fun topic I would love to see. If I have K groups on a time series trend & I want to model each group K, what is the best approach? An initial assessment shows that these time series operate on different frequencies and magnitudes. So, a mixed linear model would not work since the frequency depends on the group K. Hypothetically, if the frequencies did not depend on K, just the magnitude was different, then I could use a mixed model. Any ideas? I always could use intersection variables with an GLM, but I have many K. Would love your thoughts!

[@QuantPsych]

Mixed models don't work so well for time-series data. Time series analyses try to plot the change in value over time. With mixed models, you can estimate the change in value over time, but it wasn't designed to do that. (And it's going to be limited to linear change over time, or perhaps a polynomial). It's been a long time since I've done time series, so I'm not sure how helpful I can be. There's probably an extension of arima models you could use.

[@galenseilis5971]

@@QuantPsych Not only can mixed effects models work well for times series forecasting, but I recommend them for that purpose. They are one of the ways of having hierarchical time series models without resorting to reconciliation methods on existing forecasts. Mixed effects are not limited to linear models. I expect, but have not researched, that the first usages of mixed effects were in linear models. But that's incidental to where mixed effects models are useful.

[@galenseilis5971]

I'm not sure what you're working on, but by the mentioning of frequencies and magnitudes I am guessing that you are dealing with something where Fourier series would be useful. Consider evaluating whether a model that uses Fourier series whose parameter are mixed effects would be useful in your case. I cannot guarantee that they will be based on so little information about the problem, but it sounds promising on the face of it.

[@diegonicolasnabaesjodar8580]

@@QuantPsych What do you think about decomposing a time series (e.g. with STL) and modelling the remainder component (=noise, ~=residuals)? (and include a random factor if needed, plus an ARMA structure for the autocorrelation, using the nlme package).

[@lisbonn8623]

Hello, I have this data to work with, collected to determine the factors associated with height change for their first-year growth characteristics. 400 infants were enrolled in the study. The variables included were: ind, sex, weight, length, breastfeeding (bf), age, and numdays, help. my question is how do we indetermine which variables will be fixed and random plus the exploratory individual profile and mean profile show a quadratic relation so do we have to model a classical model to start with for comparison?

[@QuantPsych]

I have some videos published that show you how to identify whether a variable is fixed or random. You can also include quadratic terms in mixed models, just as you would with regular linear models.

[@diegonicolasnabaesjodar8580]

I am a big fan. ...but: "Depression ij" (Yij) states that you have data from multiple "i's" and "j's". Not that "the scores are different across the i's and j's". Stupid detail, but I like to favor the YT algorthm towards QP. Cheers.

[@galenseilis5971]

If someone is intent on mastering mixed effects then they should really understand the mathematics. Just knowing how to make a function call is a superficial understanding that will be less helpful when you need to troubleshoot or implement your own modified solution to a novel problem.

[@stephenomenal1245]

I would appreciate it if you could tell us what specific mathematics is required for mixed models. Matrix notation??

[@QuantPsych]

Unless you're writing algorithms yourself, it's probably enough to just understand the notation. I don't think you need matrix algebra to understand it.