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attempt to get math working in a footnote
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venpopov committed Feb 7, 2024
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3 changes: 3 additions & 0 deletions .Rbuildignore
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^_pkgdown\.yml$
^docs$
^pkgdown$
^vignettes/articles$
^doc$
^Meta$
2 changes: 2 additions & 0 deletions .gitignore
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local/
docs
inst/doc
/doc/
/Meta/
7 changes: 6 additions & 1 deletion vignettes/mixture_models.Rmd
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}
</style>
```




```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
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1) The response variable `error` is predicted by a constant term, which is internally fixed to have a mean of 0
2) The precision parameter `kappa` is predicted by set size, and the effect of set size varies across participants
3) The mixture weight^[`brms` does not directly estimate the probabilities that each response comes from each distribution (e.g. $p_{mem}$ and $p_{guess}$). Instead, brms estimates mixing proportions that are weights applied to each of the mixture distributions and they are transformed into probabilities (e.g. $p_{mem}$ and $p_{guess}$) using a softmax normalization. To get $p_{mem}$ we can use the softmax function, that is: $p_{mem} = \frac{exp(\theta_{target})}{1+exp(\theta_{target})}$] for memory responses `thetat` is predicted by set size, and the effect of set size varies across participants
3) The mixture weight[^fn-1] for memory responses `thetat` is predicted by set size, and the effect of set size varies across participants.

[^fn-1]: `brms` does not directly estimate the probabilities that each response comes from each distribution (e.g. $p_{mem}$ and $p_{guess}$). Instead, brms estimates mixing proportions that are weights applied to each of the mixture distributions and they are transformed into probabilities (e.g. $p_{mem}$ and $p_{guess}$) using a softmax normalization. To get $p_{mem}$ we can use the softmax function, that is: $p_{mem} = \frac{exp(\theta_{target})}{1+exp(\theta_{target})}$

```{r}
ff <- brms::bf(error ~ 1,
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