Exercise: Power simulation for longitudinal data
================

## Risperidone vs. haloperidol and schizophrenia

``` 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)
```

1)  Analyze the original 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

    - What is the sample size in each treatment group?

    - Estimate the by-group random-slope model.

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

    - Interpret the interaction effect.

    - Test the interaction effect.
2)  Run a power simulation for a replication study:
    - Set up a data frame containing the study design and sample size.

    - Specify the minimum relevant effect.

    - Set the fixed effects and variance components to plausible values.

    - How many participants are required for the test of the interaction
      to detect the specified effect with a power of 80%?

    - Recover the parameters of the by-group random-slope model for one
      simulated data set.
3)  Create a renderable R script or an R Markdown file that includes
    - a header with title, author, date
    - at least one section head line
    - the questions from above and your answers
    - the R code, output, and plots (if any)

    Render the R or Rmd file to HTML.