0_simulate.Rmd

---
title: "Simulating Mixed-model datasets"
output: html_notebook
---

In this document, we're describing how to generate datasets that have a within-subject (i.e. requiring mixed-models) design as commonly encountered in decision making experiments. 

## Step 1: Generate independent variable structure

We're starting by mimicking Catalina's Ritalin Trust Game dataset structure.

We have - all within subject:
* two session: drug on/off
* within each session
** three partners: computer, face trustworthy, face untrustworthy
** two behaviors: high reciprocation, low reciprocation
** for each combination of the above, we have 12 rounds

And let's have 24 subjects, half of which do drug in order AB, while other half do drug in order BA. 

So let's create the dataframe. Being lazy, I'm first defining the dataframe like this:

```{r}
df_trustgame <- expand.grid (drug=c("on","off"),
                             partner=c("computer","face trusty","face untrusty"),
                             behavior=c("high reciprocation","low reciprocation"),
                             round=seq(1,12),
                             order=c("on/off","off/on"),
                             subjects=paste(seq(1,12)) # force subject to be a factor
                             )
str(df_trustgame)
```

However, in this format, subject "1" shows up with both orders:
```{r}
summary(df_trustgame[df_trustgame$subjects=="1",])
```
So, to make it clear that subject "1" in one order is not the same person as subject "1" in the other order, I create the interaction term, and replace subject with that.
```{r}
df_trustgame$subjects_new <- as.factor(paste(df_trustgame$subjects,df_trustgame$order))

summary(df_trustgame[df_trustgame$subjects_new=="1 on/off",])
str(df_trustgame$subjects_new)
```
The `subject_new` factor has the correct number of levels, namely 24. Let's just recode the subject into number 1-24 and delete the old, incorrect numbers.

```{r}
levels(df_trustgame$subjects_new) <- paste(seq(1,24))
df_trustgame$subjects <- df_trustgame$subjects_new
df_trustgame$subjects_new <- NULL
```

So let's inspect the basic structure of the dataframe
```{r}
str(df_trustgame)
```

This contains all the necessary information.

For convenience, we already create a `session` variable, which indicates whether the subject is participating the first or the second time.
```{r}
df_trustgame$session <- factor( ifelse( (df_trustgame$drug=="on" & df_trustgame$order == "on/off" ) | 
                                  (df_trustgame$drug=="off" & df_trustgame$order == "off/on" ),
                                "first", "second"))
str(df_trustgame)
summary(df_trustgame$session)
```


## Step 2: Calculate dependent variable value

The main thing is that the DV is in a within-subject design, with at least a random intercept for subject. So, what other factors contribute as random factors (intercepts or slopes) is unknown for the real datasets, so we're going to create a bunch of DVs, with some/all combinations that we think are potentially relevant. 

Then, we can fit the mixed models to these different DVs, and see how the fitted parameters change/match the known true values. This way, we can check model specification mismatch and its effects on the estimated parameters. 

For now, we start only with a continuous dependent variable. 

### fixed effect-sizes
First, let's define the effect sizes of the fixed effects. Note that to make comparison easier to the real datasets, we're using the same coding of effects.
```{r}
#### Main effects
b_drug <- 0.5 # on - off

b_parntner_com_trusty <- 0.5 # trustworthy face - computer
b_parntner_com_untrusty <- 0.5 # untrustworthy face - computer

b_behavior <- 0.5 # high - low

b_round <- 0.5 # continuous variable

b_order <- 0.5 # off/on - on/off

b_session <- 0.5 # second - first

#### Interactions


```


### random intercept for subject
This is the minimalistic within-subject model
```{r}
# make random numbers reproducible
set.seed(123456)


```




## Step 3: Visualize data