Exercise: Growth curve model with interaction
================

## Risperidone vs. haloperidol and schizophrenia (Möller et al. 2008)

Analyze the data from [moeller.csv](../data/moeller.csv):

- `pans`: Positive and Negative Symptom Scale for schizophrenia
- `treat`: medication group
  - `risp`: atypical neuroleptic risperidone
  - `halo`: conventional neuroleptic haloperidol

``` r
dat       <- read.table("../data/moeller.csv", header = TRUE, sep = ",")
dat$id    <- factor(dat$id)
dat$treat <- factor(dat$treat, levels = c("risp", "halo"))

lattice::xyplot(pans ~ week, data = dat, groups = treat,
                type = c("g", "p", "a"), auto.key = TRUE)
```

<img src="schizo_files/figure-gfm/unnamed-chunk-2-1.png" alt="" style="display: block; margin: auto;" />

- What is the sample size in each treatment group?

- Estimate a random slope model

  - What are the estimates for the fixed effects and variance
    components?

- Fit a model with quadratic time trends for the population and
  individual subjects

- Add an interaction with treatment for the linear and the quadratic
  effects for week and test them

- Interpret your results: Which model would you choose?

- Refit the model that you chose with a centered week variable:

  - Compare the estimates for your fixed effects and the covariance
    components
  - Which estimates change and why?

### Reference

<div id="refs" class="references csl-bib-body hanging-indent">

<div id="ref-Moeller08" class="csl-entry">

Möller, H.-J., M. Riedel, M. Jäger, F. Wickelmaier, W. Maier, K.-U.
Kühn, G. Buchkremer, et al. 2008. “Short-Term Treatment with Risperidone
or Haloperidol in First-Episode Schizophrenia: 8-Week Results of a
Randomized Controlled Trial Within the German Research Network on
Schizophrenia.” *International Journal of Neuropsychopharmacology* 11
(7): 985–97. <https://doi.org/10.1017/S1461145708008791>.

</div>

</div>