Mixed Models

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# <span class="title">Mixed Models</span>
## <span class="subtitle">Issues</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**

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# More things to consider

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# Variance Accounted For

`\(R^2\)` has limited utility beyond OLS

In the mixed case...

... do you include the random effect or not?

```r
performance::r2(gpa_mixed)
```

```
# R2 for Mixed Models

Conditional R2: 0.625
     Marginal R2: 0.213
```

The difference can be quite dramatic!

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# Alternative Model Approaches

Fixed effects models
- Econometrics

Using cluster-robust standard errors

Generalized estimating equations (GEE)
- GLS, cluster-robust standard errors are a special case

Latent Growth Curve Models
- Identical to GLMM if set up appropriately

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# Sample Sizes

Small number of clusters
- variance estimates may not be good

Small number of observations within clusters
- Mixed models are fine with pre-post data!

Balanced/Missing values
- Balance not required
- Assumption is *missing at random*

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# Sample Sizes

*Big data*

- lme4 can be very fast 
  - even with single random effect and millions of observations
- glmmTMB is slower
    - but often won't have convergence issues
- mgcv faster with millions if fewer clusters

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# Sample Sizes

Randome effects from 1000, 100 levels

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# Model Comparison

ANOVA/Likelihood Ratio

Compare models with different fixed effects:
- change the default estimation from REML to ML
- models must have the same random effects structure

Compare models with different random effects:
- keep default REML
- models must have the same fixed effects

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# Model Comparison

AIC is probably okay, but can use AICc or CAIC

```r
AIC(standard_lme4_model)
AICcmodavg::AICc(standard_lme4_model)
cAIC4::cAIC(standard_lme4_model)
```

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# Convergence

Data is as data does.

You will eventually have issues:
- such as lack of convergence
- estimates of zero variance
- other warnings

These are not easy models to estimate, so don't be surprised if all doesn't go smoothly.

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# Convergence

Common sources of problems:

- Unscaled variables
- Other data problems (e.g. severe imbalance)
- Few clusters to estimate variances

Common solutions:

- Standardize, center, log numeric
- Consider simpler model
- Use different optimizer, more iterations

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# Summary

Mixed models will take more effort...

...because they're interesting!

That shouldn't keep you from exploring!

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# Moving on...

# [Part 1](https://m-clark.github.io/mixed-models-with-R-workshop/part-1.html)  <span class="" style = "width: 50px; display: inline-block"></span>[Part 2](https://m-clark.github.io/mixed-models-with-R-workshop/part-2.html)  <span class="" style = "width: 50px; display: inline-block"></span>[Part 3](https://m-clark.github.io/mixed-models-with-R-workshop/part-3.html)  <span class="" style = "width: 50px; display: inline-block"></span>[Part 5](https://m-clark.github.io/mixed-models-with-R-workshop/part-5.html)