brms VS tests-as-linear

[2] https://paul-buerkner.github.io/brms/

Maybe something like the Logistic Normal ? (e.g. see this issue from brms). If that fits what you are looking for, you can use brms to generate the Stan code for you (brms::make_stan_code()) and work from that.

Okay so first off, I recommend that you read [this](https://link.springer.com/article/10.3758/s13423-016-1221-4) article about "The Bayesian New Statistics", which highlights estimation rather than hypothesis testing from a Bayesian perspective (see Fig. 1, second row, second column). Instead of a t-test, then, we can *estimate the difference* between two groups/variables. If you want to go deeper than JASP etc, I recommend that you use [brms](https://paul-buerkner.github.io/brms/), or, if you want to go even deeper, [Stan](https://mc-stan.org/) (brms is a front-end to Stan).

I think the brms package (https://github.com/paul-buerkner/brms) or the blavaan package (http://ecmerkle.github.io/blavaan/) have support for SEM. I've never done it myself, so I unfortunately can't give you any direction for that in particular. However, I have used stan in multi-level meta-analysis regression (combining multiple CRISPRa experiments to find determinants of CRISPRa activity, see https://github.com/timydaley/CRISPRa-sgRNA-determinants/blob/master/metaAnalysis/NeuronAndSelfRenewalMetaMixtureRegression.Rmd) and had some success.

brms baby

Could also be done using brms and the gr term. See this for the motivation behind this syntax.

Anyway, I found I can include weights into the brm function by using gr(RE, by = var) to deal with the heterogeneous variance and it should automatically assume that each observation within a group is correlated according to the brms reference manual.

This is what actually should work- I must be declaring my variables incorrectly. The issue I'm having is that what you refer to as lin , I tried calling a few things, from b to LinPred (which worked in the link here: brms issue 47). When I've tried doing this, I receive errors that say "The following variables are missing from the dataset....[insert variable used to symbolize linear part of the model)". But I believe you're code is on the right path for what needs to be done- I'll try altering my syntax to be sure it resembles yours let you know if it works.

1) All common statistical tests are linear models: https://lindeloev.github.io/tests-as-linear/

I knew the linked-in-the-article https://lindeloev.github.io/tests-as-linear/ which is also great. A bit meta on the widespread use of linear models: "Transcending General Linear Reality" by Andrew Abbott, DOI:10.2307/202114

Maybe you would find it useful to read a textbook on bayesian stats for inspiration. I can recommend Richard McElreath's "Statistical Rethinking" which makes it very clear how inflexible it is to just know recipes like t-tests or anovas.

The canonical approach is to build a generative model with a parameter (or multiple for ~anova) that codes for the difference between groups and do inference on that parameter of interest. Most of the recipes taught in statistics classes can be modelled as a regression of some kind (this counts for frequentist stats too, see https://lindeloev.github.io/tests-as-linear/ ). Some advocate to do that inference with bayes factors. Others, like discussed elsewhere in this thread, advocate combining the resulting posterior with a cost/value function, but either way the lesson is that there is less focus on "t-test-vs-anova" because they're the same thing anyways.

I understand where you're coming from, and I like the idea for a certain kind of people: those who are very good at handling abstractions. Software engineers do have this skill, but the majority of statistics users do not. Trying to explain the similarities between these linear methods and how all is one [1] to a social scientist who doesn't like numbers nor formulas to begin with would only lead to more confusion.

But if you ever do a randomized test with a suitable linear model to estimate the efficacy of these two methods, do let us know, that would be 10/10 :)

[1]: https://lindeloev.github.io/tests-as-linear/#41_one_sample_t...

My main critique is that these classical tests are often better explained and introduced in the concept of a regression framework. The fact that you even need a flowchart demonstrates how confusing and unintuitive the classical approach to teaching statistics is. If you learn regression, everything else becomes a special case of this much more expressive way of thinking about how to measure variation. This point is made convincingly in this post: https://lindeloev.github.io/tests-as-linear/

Most parametric tests don’t assume normality. If you feel that assuming normality is not viable, you are free to choose any other distribution. This may not be immediately obvious, since most intro courses teach inference as a bunch of disjointed formulas, but it will make more sense once one learns about generalized linear models framework and realizes that common statistical tests are all linear models. There is no need to jump straight for nonparametric tests just because something isn’t normal, as cool as they are. (Also a pedantic nitpick: Mann-Whitney and Co. test difference in average ranks, not difference in means. So they are not really a nonparametric equivalent to T tests).