Mixed Models

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# <span class="title" style="text-shadow: 0 0 100px #EBA42B;">Mixed Models</span>
## <span class="bonus-subtitle" style=""><strong>Bonus</strong></span>
### <span class="author">Michael Clark</span>
### <span class="institute"><br>m-clark.github.io <br> <span class="citation">@statsdatasci</span> <br> CSCAR, UM</span>
### <span class="date">2020-10-21</span>

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### *Overview of Random Effects*

### *More Random Effects*

### *Common Extensions*

### *Issues*

### **Bonus!**

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# Bonus!

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# Other Distributions

glmmTMB, mgcv, brms etc. all allow for more distributions
- student t
- negative binomial
- beta
- multinomial
- zero-inflated

...and more!

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# Other Contexts

- Spatial models
- Survival models
- Item response theory
- Multi-membership 
- Phylogenetic models
- Adjacency structures
- Gaussian processes
- Surveys & Mr. P
- Survival/frailty
- Meta-analysis
- Post-hoc comparisons and multiple testing 
- Growth mixture models
- Nonlinear Mixed Effects Models

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# Bayesian Models

.pull-left[
rstanarm and brm

Both use Stan

Use lme4 syntax

Extend well beyond 
]

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<img src="img/stan_logo.png" style="display:block; margin: 0 auto; width: 100%">
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# Connections

More generally we can think of STARs

- *St*ructure
- *A*dditive
- *R*egression

Can include any type of random effect:
- standard cluster
- spatial
- additive
- more!