perception_memory_coordination-study_1.Rmd

---
title: "Data preparation: Interpersonal coordination in perception and memory (Study 1)"
author: "A. Paxton, T. J. H. Morgan, J. Suchow, & T. L. Griffiths"
output:
  html_document:
    keep_md: yes
    number_sections: yes
---

This R markdown provides the data preparation for our manuscript, "Interpersonal coordination in perception and memory" (Paxton, Morgan, Suchow, & Griffiths, *in preparation*). This R markdown file presents the data preparation for Study 1, which includes only the neutral condition.

To run this from scratch, you will need the following files:

* `./data/study_1-neutral/`: Contains experimental data. All data for included dyads are freely available in the OSF repository for the project: `https://osf.io/8fu7x/`.
* `./supplementary-code/required_packages-pmc.r`: Installs required libraries, if they are not already installed. **NOTE**: This should be run *before* running this script.
* `./supplementary-code/libraries_and_functions-pmc.r`: Loads in necessary libraries and creates new functions for our analyses.

Additional files will be created during the initial run that will help reduce processing time. Several of these files are available as CSVs from the OSF repository listed above.

As part of our manuscript for the proceedings of the 2018 annual meeting of the Cognitive Science Society (see `study_1-cogsci2018/` directory within this repository), this R markdown file will be converted into an .R script and embedded into the manuscript. Each time the CogSci proceeding is compiled, it will generate a new .R version of this file, dated to the last time this file was changed.

**Code written by**: A. Paxton (University of California, Berkeley)

**Date last modified**: 03 July 2018

***

# Data import

***

## Preliminaries

```{r prep-prelim, warning = FALSE, error = FALSE, message = FALSE}

# clear our workspace
rm(list=ls())

# read in libraries and create functions
source('./supplementary-code/required_packages-pmc.r')
source('./supplementary-code/libraries_and_functions-pmc.r')

```

***

## Concatenate experiment files

```{r concatenate-data, warning = FALSE, error = FALSE, message = FALSE}

# get list of individual experiments included in the data
experiment_files = list.dirs('./data/study_1-neutral', recursive=FALSE)

# concatenate the files
vector_files = data.frame()
info_files = data.frame()
questionnaire_files = data.frame()
node_files = data.frame()
participant_files = data.frame()
for (experiment in experiment_files){
  
  # read in the next experiment's files and add ID to each
  exp_id = basename(experiment)
  next_vector = read.table(paste(experiment,'/vector.csv',sep=''), sep=',',
                           header=TRUE, stringsAsFactors = FALSE) %>%
    mutate(experiment = exp_id)
  next_info = read.table(paste(experiment,'/info.csv',sep=''), sep=',',
                         header=TRUE, stringsAsFactors = FALSE) %>%
    mutate(experiment = exp_id)
  next_q = read.table(paste(experiment,'/question.csv',sep=''), sep=',',
                           header=TRUE, stringsAsFactors = FALSE) %>%
    mutate(experiment = exp_id)
  next_node = read.table(paste(experiment,'/node.csv',sep=''), sep=',',
                           header=TRUE, stringsAsFactors = FALSE) %>%
    mutate(experiment = exp_id)
  next_participant = read.table(paste(experiment,'/participant.csv',sep=''), sep=',',
                           header=TRUE, stringsAsFactors = FALSE) %>%
    mutate(experiment = exp_id)

  # append to group files
  vector_files = rbind.data.frame(vector_files, next_vector)
  info_files = rbind.data.frame(info_files, next_info)
  questionnaire_files = rbind.data.frame(questionnaire_files, next_q)
  node_files = rbind.data.frame(node_files, next_node)
  participant_files = rbind.data.frame(participant_files, next_participant)

}

```

## Grab duration and bonus data

```{r merge-duration-and-bonuses}

# clean up the questionnaire files
question_trimmed = questionnaire_files %>%
  dplyr::select(experiment, participant_id, number, question, response)

# clean up the participant files
participant_trimmed = participant_files %>%
  dplyr::filter(status=='approved') %>%
  mutate(creation_time = ymd_hms(creation_time)) %>%
  mutate(end_time = ymd_hms(end_time)) %>%
  mutate(duration = (end_time - creation_time)) %>%
  dplyr::select(experiment, worker_id, status, base_pay, bonus, duration)

# join the files and omit any folks that aren't completely included in both dataframes
participation_descriptives = full_join(question_trimmed, participant_trimmed,
                                     by = c('experiment',
                                            'participant_id' = 'worker_id')) %>%
  na.omit() %>%
  
  # remove actual question data
  dplyr::select(-response, -question, -status, -number)

```

## Identify dyads from vector data

In order to figure out which participants' nodes were connected to one another in dyads, we use the vectors created between nodes (excluding the stimulus-creating node). We then use that information to identify which stimuli were sent to which dyads.

```{r identify-dyads, warning = FALSE, error = FALSE, message = FALSE}

# use the vectors connecting the nodes to identify pairs
vector_df = vector_files %>%
  
  # convert time to integer and winnow out unnecessary variables and nodes
  mutate(t = round(as.numeric(ymd_hms(creation_time)), 0)) %>%
  dplyr::select(experiment, t, origin_id, destination_id, network_id) %>%
  dplyr::filter(!origin_id == 1) %>%
  
  # find pairs from vector files
  group_by(experiment, t) %>%
  mutate(min_id = pmin(origin_id,destination_id)) %>%
  mutate(max_id = pmax(origin_id,destination_id)) %>%
  ungroup() %>%
  
  # get unique pairs and number them
  dplyr::select(-origin_id, -destination_id) %>%
  distinct() %>%
  mutate(dyad = seq_along(min_id)) %>%

  # gather the participants into a single column
  gather(key="id",value="participant", min_id, max_id) %>%
  dplyr::select(-id)

# figure out which stimuli were sent to which dyads
dyad_df = info_files %>%
  mutate(t = round(as.numeric(ymd_hms(creation_time)), 0)) %>%
  dplyr::filter(origin_id == 1) %>%
  dplyr::select(experiment, t, contents) 

# combine the contents and the dyad info, allowing room for error with timestamp
dyad_df = data.table(dyad_df)
vector_df = data.table(vector_df)
setkey(dyad_df, experiment, t)
setkey(vector_df, experiment, t)
dyad_df = dyad_df[vector_df,roll="nearest"] %>%
  dplyr::select(-t)

```

## Prepare dataframe

We now take the concatenated files and begin processing, including de-duplication of dataset.

The structure of the experiment sometimes led to near-duplicate rows to be sent to the server to manage partner communication. We must now identify these near-duplicates and strip them out. We can best identify these by using the `response_counter` variable: A properly de-duplicated dataset should have only 1 row per `response_counter` value in each trial for each participant.

```{r process-infos, warning = FALSE, error = FALSE, message = FALSE}

info_df = info_files %>% ungroup() %>%
  
  # filter out stimulus nodes
  dplyr::filter(!origin_id == 1) %>%
  
  # convert time and get rid of unnecessary variables
  mutate(t = round(as.numeric(ymd_hms(creation_time)), 0)) %>%
  dplyr::select(experiment, t, property3, origin_id, network_id, contents) %>%
    
  # read in `contents` as JSONs
  cbind(., jsonlite::stream_in(textConnection(.$contents))) %>%

  # rename a whole slew of variables
  dplyr::rename(participant = origin_id,
                trial_type = trialType,
                trial_number = trialNumber,
                guess_counter = guessCounter,
                response_counter = responseCounter,
                accept_type = acceptType,
                stimulus_number = chosenStimulusNumber,
                length = chosenStimulusLength) %>%
  
  # get rid of unnecessary variables and arrange rows
  dplyr::select(-property3, -finalAccuracy, -contents) %>%
  dplyr::arrange(experiment, participant, trial_number, response_counter) %>%
  
  # remove the automatically generated infos that produced NAs in `guess`
  dplyr::filter(!is.na(guess)) %>%
  
  # determine uniqueness without considering time
  group_by(experiment, participant, network_id, trial_type,
           trial_number, guess_counter, response_counter) %>%
  dplyr::summarise_all(first) %>%
  ungroup() %>%
  
  # replace NAs from guesses and calculate error with each guess
  mutate(guess = replace(guess, guess<0, NA)) %>%
  mutate(guess_error = length - guess) %>%
  
  # merge info dataframe with dyad number information
  full_join(., dyad_df,
            by = c('experiment', 'participant','network_id')) %>%
  dplyr::rename(stimulus_list = contents)

```

```{r print-sanity-check-for-duplicate-issues, invisible=TRUE, echo=FALSE}

# sanity check
sanity_df = info_df %>% ungroup() %>%
  
  # count number of times we see the same response counter
  group_by(experiment, participant, trial_type, trial_number, guess_counter, response_counter) %>%
  dplyr::summarise(n = n()) %>%
  ungroup() %>%
  
  # filter to include only test-condition duplicates
  dplyr::filter(n!=1 & trial_type=="test") %>%
  
  # join with the main dataset to check it out
  inner_join(., info_df, 
             by = c("experiment", "participant", "trial_type", 
                    "trial_number", "guess_counter", "response_counter")) %>%
  
  # identify whether any identified duplicate rows have diferent accept_type values
  group_by(experiment, participant, trial_type, trial_number, guess_counter, response_counter) %>%
  dplyr::filter(length(unique(accept_type))!=1) %>%
  ungroup()

# print sanity check
cat('Problematic rows identified (i.e., duplicates with differing accept types): ',dim(sanity_df)[1],sep='')

```

***

# Data cleaning

***

## Identify pairs 

Next, we identify all dyads in which both participants completed all trials.

```{r identify-paired-individuals}

# identify usable dyads
paired_individuals = info_df %>%
  
  # count the number of infos and trials per participant
  group_by(experiment,participant) %>%
  dplyr::summarise(trials = max(trial_number),
            dyad = ifelse(length(unique(dyad)==1),
                          unique(dyad),
                          NA),
            infos = n()) %>%
  ungroup() %>%
  na.omit() %>%
  dplyr::filter(infos > 23) %>%
  
  # count the infos sent by each participant in each dyad
  dplyr::mutate(original_participant = participant) %>%
  group_by(experiment, dyad) %>%
  dplyr::mutate(participant_num = 1:n()) %>%
  dplyr::mutate(participant_num = participant_num-1) %>%
  mutate(participant = paste('p',participant_num,sep='')) %>%
  dplyr::select(-participant_num,-original_participant) %>%
  spread(key = participant, value = infos) %>%
  ungroup() %>%
  mutate(difference_in_responses = abs(p1-p0)) %>%

  # remove any participants who weren't paired with someone
  na.omit() %>%
  
  # only include pairs in which both individuals completed 24 trials
  dplyr::filter(trials==24)

```

```{r print-paired-individuals, invisible=TRUE, echo=FALSE}

total_paired_individuals = paired_individuals %>% ungroup() %>%
  dplyr::select(experiment, dyad) %>%
  distinct()

cat('Total pairs who finished: ',dim(total_paired_individuals)[1], sep='')

```

## Remove problematic trials

Some dyads became mismatched in their progress throughout the game. Essentially, in some trials, one player would move on to the next trial, while their partner would "hang" in the previous one. The program would automatically move someone forward after this mismatched state persisted for a few seconds.

To deal with this issue, we strike the entire trial for that dyad.

```{r identify-problem-trials}

# exclude trials with mismatched data
discarded_trials_df = info_df %>%
  dplyr::filter(dyad %in% paired_individuals$dyad & trial_type=="test") %>%  
  
  # count the number of infos per trial per participant
  group_by(experiment,participant,trial_number) %>%
  dplyr::summarise(dyad = ifelse(length(unique(dyad)==1),
                          unique(dyad),
                          NA),
            infos = n()) %>%
  ungroup() %>%
  na.omit() %>%
  
  # count the infos sent by each participant in each dyad
  group_by(experiment, dyad) %>%
  mutate(participant = paste('p',(participant - min(participant)),sep='')) %>%
  spread(key = participant, value = infos) %>%
  ungroup() %>%
  mutate(difference_in_responses = abs(p1-p0)) %>%
  
  # single out the trials with mismatching responses
  dplyr::filter(!difference_in_responses==0)

```

```{r print-problem-trials, invisible=TRUE, echo=FALSE}

# share information on how many trials will be removed
total_removed_trials = discarded_trials_df %>% ungroup() %>%
  group_by(experiment, dyad) %>%
  dplyr::summarise(total_discarded = n())

cat('Total trials discarded: ',sum(total_removed_trials$total_discarded),' (across ', length(unique(total_removed_trials$dyad)),' dyads) ', sep='')

```

## Winnow the data

```{r winnow-data}

# winnow and recorder columns
winnowed_info_df = info_df %>% ungroup() %>%
  dplyr::filter(dyad %in% paired_individuals$dyad & experiment %in% paired_individuals$experiment) %>%
  dplyr::left_join(., discarded_trials_df,
                   by = c("experiment","dyad","trial_number")) %>%
  dplyr::filter(is.na(difference_in_responses)) %>%
  mutate(t = round(t,-1)) %>%
  dplyr::select(experiment, t, dyad, participant, 
         trial_type, trial_number, response_counter, guess_counter, accept_type, 
         length, guess, guess_error, network_id) %>%
  na.omit()

winnowed_info_df = unique(setDT(winnowed_info_df), by = c('experiment', 'dyad',
        'participant', 'trial_type', 'trial_number', 'response_counter', 'guess_counter',
        'accept_type', 'length', 'guess', 'guess_error', 'network_id'))

```

```{r print-included-dyad-stats, invisible=TRUE, echo=FALSE}

included_trial_info = winnowed_info_df %>% ungroup() %>%
  dplyr::filter(trial_type == 'test') %>%
  group_by(experiment, dyad) %>% 
  summarize(included_trials = length(unique(trial_number)))

cat('Mean included trials per dyad: ',mean(included_trial_info$included_trials), sep='')

```

## Quick sanity check

For sanity, let's also check that everyone included in our winnowed dataset completed both training and test trials.

```{r sanity-check-for-training-and-test}

# ensure that everyone completed both training and test
only_one_trial_type = winnowed_info_df %>% ungroup() %>%
  dplyr::select(experiment, participant, trial_type) %>%
  distinct() %>%
  group_by(experiment, participant) %>%
  summarize(n=n()) %>%
  dplyr::filter(n!=2)

```

```{r print-problem-participants, invisible=TRUE, echo=FALSE}

cat('Included participants who did not submit guesses during any training trials: ',dim(only_one_trial_type)[1], sep='')

```

It looked like some participants chose not to complete the training trials or struggled with getting their guesses submitted in time.  We'll need to handle this when we create training slopes.

***

# Data processing

***

## Add questionnaire data

In the experiment's current form, different tables include different information, and some tables present the same information under different labels. This is true for questionnaire data. To accurately pair individuals' guess data with their questionnaire responses, we match the `participant_id` variables in `node_df` and `question_df`, and we join the `id` variable in `node_df` with the `participant` variable in `info_df`.

```{r add-questionnaire-data}

# clean up questionnaire data by converting the stringified JSONs to a new variable
question_df = questionnaire_files %>% ungroup() %>%
  dplyr::select(experiment, participant_id, response) %>%
  cbind(., jsonlite::stream_in(textConnection(.$response))) %>%
  dplyr::select(-response)

# clean up the node dataframe
node_df = node_files %>% ungroup() %>%
  dplyr::select(experiment, participant_id, id) %>%
  na.omit()

# join questionnaire data wth infos and remove any participants whose survey data we don't have
winnowed_info_df = left_join(question_df, node_df,
                                by=c('experiment','participant_id')) %>%
  left_join(winnowed_info_df, .,
                              by=c('experiment','participant' = 'id')) %>%
  drop_na(cooperative_partner, cooperative_self, trust_partner, trust_self, engagement, difficulty)

```

```{r identify-questionnaire-dyads}

# identify how many dyads have matching infos and complete questionnaire data
usable_question_dyads = winnowed_info_df %>% ungroup() %>%
  dplyr::select(experiment, dyad, participant) %>%
  distinct() %>%
  group_by(experiment, dyad) %>%
  dplyr::summarise(included_p = n()) %>%
  ungroup() %>%
  dplyr::filter(included_p==2)

# if needed, remove dyads who didn't have questionnaire data
winnowed_info_df = winnowed_info_df %>% ungroup() %>%
  dplyr::filter(dyad %in% usable_question_dyads$dyad)

```

```{r print-quesionnaire-dyads, invisible=TRUE, echo=FALSE}

cat('Total dyads with all guess and questionnaire data: ',dim(usable_question_dyads)[1], sep='')

```

## Export duration and bonus data for participants

```{r link-participants-to-bonus-data}

# link participants to their bonus and duration data
participation_descriptives = node_files %>%
  dplyr::select(experiment, id, participant_id, network_id) %>%
  full_join(., participation_descriptives,
            by = c('participant_id',
                   'experiment')) %>%
  full_join(., dyad_df,
             by = c('id' = 'participant',
                    'experiment',
                    'network_id')) %>%
  dplyr::filter(dyad %in% usable_question_dyads$dyad & experiment %in% usable_question_dyads$experiment) %>%
  dplyr::select(-contents, -network_id)

```

```{r export-bonus-and-duration-data}

# export bonuses
write.table(participation_descriptives, './data/study_1-neutral/participation_descriptives.csv', 
            sep=',', append = FALSE, quote = FALSE, row.names = FALSE, col.names = TRUE)

```

## Create unique dyad and participant IDs across all experiments

Dallinger provides numeric IDs for each participant that are unique only within each experiment. Therefore, we create participant and dyad identifiers that are unique across the entire dataset.

```{r create-unique-ids}

# create unique dyad IDs
unique_dyad_ids = winnowed_info_df %>% ungroup() %>%
  dplyr::select(experiment, dyad) %>%
  distinct() %>%
  mutate(unique_dyad = row_number())

# create unique participant IDs
unique_participant_ids = winnowed_info_df %>% ungroup() %>%
  dplyr::select(experiment, participant) %>%
  distinct() %>%
  mutate(unique_participant = row_number())

# merge both into the main dataframe and rename
winnowed_info_df = right_join(unique_participant_ids, winnowed_info_df,
                             by=c('experiment', 'participant')) %>%
  right_join(unique_dyad_ids, ., by=c('experiment','dyad')) %>%
  dplyr::rename(original_participant = participant,
                original_dyad = dyad,
                participant = unique_participant,
                dyad = unique_dyad) %>%
  dplyr::arrange(experiment, participant, trial_number, response_counter)

```

## Increment all counters by 1

Data were collected using Pythonic counters (i.e., starting from 0). We'll here update the dataframe to reflect R conventions (i.e., starting from 1).

```{r r-counters}

winnowed_info_df = winnowed_info_df %>%
  mutate(trial_number = trial_number + 1) %>%
  mutate(response_counter = response_counter + 1) %>%
  mutate(guess_counter = guess_counter + 1)

```

## Normalize error by maximum possible error

Because stimuli line lengths could range from 1-100, each trial provided a bound on the total possible guess error.  As a result, we need to normalize each guess error by the maximum *possible* error for that trial.

```{r normalize-error}

winnowed_info_df = winnowed_info_df %>% ungroup() %>%
  mutate(normalized_error = guess_error/max(abs(100-length),abs(length-100)))

```

## Create training accuracy metric

We next create a training metric that quantifies the *non-directional* improvement over the training rounds. Essentially, this captures the change in relative accuracy over training, regardless of whether participants began by over- or under-estimating line lengths.

```{r training-improvement}

# create a slope to see how quickly they improved
winnowed_info_df = winnowed_info_df %>% ungroup() %>%
  
  # if they didn't do training, give them a flat training performance
  mutate(normalized_error = replace(normalized_error, 
                                    which(normalized_error<0L), 
                                    0)) %>%
  
  dplyr::select(participant, trial_type, trial_number, normalized_error) %>%
  na.omit() %>%
  dplyr::filter(trial_type == 'train') %>%
  group_by(participant) %>%
  do(broom::tidy(lm(abs(.$normalized_error) ~ .$trial_number))) %>%
  dplyr::filter(term=='.$trial_number') %>%
  dplyr::select(participant, estimate) %>%
  dplyr::rename(training_improvement = estimate) %>%
  left_join(winnowed_info_df, .,
            by='participant') %>%
  
  # if they didn't complete training, give them a 0
  mutate(training_improvement = replace(training_improvement, 
                                    which(training_improvement<0L), 
                                    0))

```

```{r plot-training_slopes, echo=FALSE, warning = FALSE, error = FALSE, message = FALSE}

# create a plot to show training slopes
training_slope_plot = ggplot(dplyr::filter(winnowed_info_df, 
                                           trial_type=='train'), 
                             aes(x = trial_number,
                                 y = abs(normalized_error))) +
  geom_line(aes(color=as.factor(participant))) +
  scale_color_viridis(discrete=TRUE) +
  stat_smooth() +
  ylab('Absolute error of guess') +
  scale_x_continuous(breaks=c(1,5,10)) +
  xlab('Training trial') +
  ggtitle('Accuracy of individual participants over training') +
  theme(legend.position="none")

# save a high-resolution version of the plot
ggsave(plot = training_slope_plot,
       height = 3,
       width = 5,
       filename = './figures/pmc-training_slopes.jpg')

# save a smaller version of the plot for knitr
ggsave(plot = training_slope_plot,
       height = 3,
       width = 5,
       dpi=100,
       filename = './figures/pmc-training_slopes-knitr.jpg')

```

![**Figure**. Included participants' absolute normalized error over all training trials and best-fit line (in blue).](./figures/pmc-training_slopes-knitr.jpg)

```{r plot-normalized-error-over-all-trials, echo=FALSE, warning = FALSE, error = FALSE, message = FALSE}

# figure out what our equal x-axis limits will be
x_limit = winnowed_info_df %>% ungroup() %>%
  na.omit() %>%
  dplyr::summarise(lim = max(abs(normalized_error))) %>%
  .$lim

# create plot
normalized_error_hist = ggplot(winnowed_info_df,
                               aes(x = normalized_error)) + 
  geom_histogram(aes(fill = factor(trial_number)),bins=30) +
  scale_fill_viridis(discrete=TRUE,
                     breaks=c('1',
                              '5',
                              '10',
                              '15',
                              '20',
                              '25'),
                     labels=c('First',
                              '',
                              '',
                              '',
                              '',
                              'Last'),
                     name = "Trial") +
  xlab('Normalized error') +
  ylab('Count') +
  xlim(-x_limit, x_limit) +
  ggtitle('Normalized error over all trials')
  
# save a high-resolution version of the plot
ggsave(plot = normalized_error_hist,
       height = 4,
       width = 5,
       filename = './figures/pmc-error_hist.jpg')

# save a smaller version of the plot for knitr
ggsave(plot = normalized_error_hist,
       height = 4,
       width = 5,
       dpi=100,
       filename = './figures/pmc-error_hist-knitr.jpg')

```

![**Figure**. Histogram of individual participants' normalized error for each guess over all trials. Histogram is further broken down by the trial number at which each guess was given.](./figures/pmc-error_hist-knitr.jpg)

## Widen data to include partner's guess

```{r create-column-for-partner-guess}

# create a column for the partner's guess at that time
winnowed_info_df = winnowed_info_df %>% ungroup() %>%
  
  # create participant binary values
  group_by(experiment, dyad) %>%
  mutate(self_id = (min(participant)+max(participant)) - participant) %>%
  mutate(partner_id = participant) %>%
  ungroup() %>%

  # gather into multiple values
  dplyr::select(self_id, partner_id, normalized_error, trial_number, response_counter) %>%
  dplyr::rename(partner_error = normalized_error) %>%
  distinct() %>%
  
  # merge
  left_join(winnowed_info_df, .,
            by=c('participant'='self_id',
                 'trial_number',
                 'response_counter'))

```

## Export raw data

```{r export-data}

write.table(winnowed_info_df, './data/study_1-neutral/winnowed_data.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", row.names = FALSE, col.names = TRUE)

```

***

# Data exploration and descriptive statistics

***

## Preliminaries

```{r exploration-prelim, warning = FALSE, error = FALSE, message = FALSE}

# clear our workspace
rm(list=ls())

# read in libraries and create functions
source('./supplementary-code/libraries_and_functions-pmc.r')

# read in dataset
winnowed_info_df = read.table('./data/study_1-neutral/winnowed_data.csv', sep=',',header = TRUE)

```

## Bonuses and duration

```{r import-bonuses-and-duration}

participation_descriptives = read.table('./data/study_1-neutral/participation_descriptives.csv', 
                                        sep=',', header = TRUE)

```

```{r print-mean-duration-for-participants, echo=FALSE}
cat('Average participation duration: ',mean(participation_descriptives$duration),' minutes',sep='')
```

```{r print-mean-bonuses-for-participants, echo=FALSE}
cat('Average particpant performance bonus (minus flat completion bonus):  $',
          mean(participation_descriptives$bonus-.33),sep='')
```


## Variable distributions

```{r plot-all-variables, echo = FALSE}

# adapted from https://drsimonj.svbtle.com/quick-plot-of-all-variables
all_variable_plot = winnowed_info_df %>%
  mutate_all(funs(as.numeric)) %>%
  dplyr::select(one_of(questionnaire_variables),
         normalized_error, experiment, dyad, training_improvement) %>%
  gather() %>%                
  ggplot(aes(value)) +
    facet_wrap(~ key, scales = "free") +
    geom_density() +
    xlab('Value') +
    ylab('Density') +
    ggtitle('Density plots of questionnaire data and outcome variables')

# save a high-resolution version of the plot
ggsave(plot = all_variable_plot,
       height = 4,
       width = 8,
       filename = './figures/pmc-all_variables.jpg')

# save a smaller version of the plot for knitr
ggsave(plot = all_variable_plot,
       height = 4,
       width = 8,
       dpi=100,
       filename = './figures/pmc-all_variables-knitr.jpg')

```

![**Figure**. Density plots of questionnaire responses, normalized error, and improvement over training trials.](./figures/pmc-all_variables-knitr.jpg)
***

# Data manipulation

***

## Preliminaries

```{r manipulation-prelim, warning = FALSE, error = FALSE, message = FALSE}

# clear our workspace
rm(list=ls())

# read in libraries and create functions
source('./supplementary-code/libraries_and_functions-pmc.r')

# read in dataset
winnowed_info_df = read.table('./data/study_1-neutral/winnowed_data.csv', 
                              sep=',',header = TRUE)

```

## Calculate cross-correlation between partners' normalized error

First, we prepare the dataframe for cross-correlation by transitioning from long-form data for both participants within the dyad to using wide-form data for each dyad, with one column for each constituent participant's `normalized_error` at each `trial_number` and `response_counter`.

```{r reformat-df-for-cross-corr}

# strip out unnecessary information
infos = winnowed_info_df %>% ungroup() %>%
  dplyr::select(experiment,dyad,participant,t,normalized_error,trial_number,response_counter) %>%
  
  # create participant binary values
  group_by(experiment, dyad) %>%
  mutate(partner_id = (min(participant)+max(participant)) - participant) %>%
  mutate(self_id = participant) %>%
  ungroup() %>%
  
  # create binary ID
  group_by(experiment, dyad) %>%
  mutate(partner_binary = participant - min(participant)) %>%
  ungroup() %>%
  
  # remove training trials
  dplyr::filter(trial_number > 10)

# create a dataframe with one dyad per row and separate columns for each participant's error data
binary_dfs = split(infos, infos$partner_binary)
p0_df = data.frame(binary_dfs[[1]]) %>%
  dplyr::rename(error0 = normalized_error) %>%
  dplyr::select(experiment, dyad, trial_number, response_counter, error0)
p1_df = data.frame(binary_dfs[[2]]) %>%
  dplyr::rename(error1 = normalized_error) %>%
  dplyr::select(experiment, dyad, trial_number, response_counter, error1)

```

Once the data are prepared, we calculate the cross-correlation coefficients between participants' `normalized_error` during all test rounds. The maximum lag is specified within the `libraries_and_functions-pmc.r` file.

```{r calculate-cross-correlation}

# calculate cross-correlation
ccf_df = full_join(p0_df,p1_df,
                   by= c("experiment", "dyad", "trial_number", "response_counter")) %>%
  
  # calculate cross-correlation for each dyad's error scores
  group_by(experiment,dyad) %>%
  do(ccf = ccf(.$error0, .$error1, lag.max = ccf_max_lag, type = 'correlation',
               na.action = na.pass, plot=FALSE)) %>%
  ungroup() %>%
  
  # extract cross-correlations from the embedded list
  dplyr::select(ccf) %>%
  dplyr::pull(ccf) %>%
  unlist() %>%
  matrix(.,ncol=length(unique(winnowed_info_df$dyad))) %>%
  
  # convert it into a proper dataframe and select only the coefficients
  as.data.frame() %>%
  slice(1:(ccf_max_lag*2+1)) %>%
  t() %>%
  as.data.frame %>%
  rowid_to_column(var='dyad') %>%

  # rename variables and strip rownames
  rename_(.dots=setNames(names(.), 
                         gsub("V", "", names(.)))) %>%
  remove_rownames() %>%
  
  # reshape the data to combine lag and r
  gather(key = 'lag' , value='r', -dyad) %>%
  mutate_all(as.numeric) %>%
  mutate(lag = lag - ccf_max_lag - 1)

```

Because we don't have any theoretical expectations about or experimental manipulations to change *who* might be leading and following, we ignore directionality for this first-pass analysis.

```{r ignore-lag-directionality}

# ignore lag directionality
ccf_df = ccf_df %>% ungroup() %>%
  mutate(lag = abs(lag)) %>%
  group_by(dyad,lag) %>%
  dplyr::summarise(r = mean(r))

```

Once we've calculated the cross-correlation coefficients for each dyad, we merge it into the questionnaire data.

```{r merge-into-main-df}

# grab what we need for the cross-correlation analyses
questions_only = winnowed_info_df %>%
  dplyr::select(one_of(c('experiment','dyad','participant',
                  questionnaire_variables, 'training_improvement'))) %>%
  
  # create a mean training improvement score for the dyad
  group_by(experiment, dyad) %>%
  mutate(training_improvement = mean(training_improvement)) %>%
  ungroup() %>%
  
  # select only the unique rows
  distinct() 

# merge into the ccf dataframe
ccf_df = full_join(questions_only, ccf_df,
                   by='dyad','experiment')

```

Let's clean up a bit before we move on.

```{r clean-up-variables}

# clean up unneeded variables
rm(p0_df,p1_df,binary_dfs, infos, questions_only)

```

## Create interaction terms

### For `winnowed_info_df`

```{r create-interactions-winnowed}

# create interactions
winnowed_info_df = winnowed_info_df %>% ungroup() %>%
  
  # create a turn variable across trials and responses
  as.data.frame() %>%
  group_by(experiment,dyad,participant) %>%
  mutate(turn = row_number()) %>%
  ungroup() %>%
  
  # exclude training data
  dplyr::filter(trial_type=='test') %>%

  # survey interactions
  mutate(cooperative.both = cooperative_self * cooperative_partner) %>%
  mutate(trust.both = trust_self * trust_partner) %>%
  mutate(cooperative.trust.self = cooperative_self * trust_self) %>%
  mutate(cooperative.trust.partner = cooperative_partner * trust_partner) %>%
  
  # error interactions
  mutate(error.length = (normalized_error+.00001) * length) %>%
  mutate(error.turn = (normalized_error+.00001) * turn) %>%
  mutate(error.length.turn = (normalized_error+.00001) * turn * length) %>%
  
  # other interactions
  mutate(turn.training = turn * training_improvement)

```

```{r create-first-guess-df}

# spin off a dataset for only first answers
first_guess_df = winnowed_info_df %>% ungroup() %>%
  
  # grab just the final guess on each trial guess
  dplyr::filter(response_counter==1) %>%
  
  # filter out "turn" variables
  dplyr::select(-contains("turn")) %>%
  
  # recreate the interactions at the trial level
  mutate(error.length = (normalized_error+.00001) * length) %>%
  mutate(error.trial = (normalized_error+.00001) * trial_number) %>%
  mutate(error.length.trial = (normalized_error+.00001) * trial_number * length) %>%
  mutate(trial.training = trial_number * training_improvement)

```

```{r create-final-guess-df}

# spin off a dataset for only final answers
final_guess_df = winnowed_info_df %>% ungroup() %>%
  
  # grab just the final guess on each trial guess
  group_by(experiment,dyad,participant,trial_number) %>%
  slice(n()) %>%
  ungroup() %>%
  
  # filter out "turn" variables
  dplyr::select(-contains("turn")) %>%
  
  # recreate the error interactions at the trial level
  mutate(error.length = (normalized_error+.00001) * length) %>%
  mutate(error.trial = (normalized_error+.00001) * trial_number) %>%
  mutate(error.length.trial = (normalized_error+.00001) * trial_number * length) %>%
  mutate(trial.training = trial_number * training_improvement)

```

### For `ccf_df`

```{r create-orthogonal-polynomials-ccf}

# create first- and second-order orthogonal polynomials for lag 
raw_lag = min(ccf_df$lag):max(ccf_df$lag)
lag_vals = data.frame(raw_lag)
lag_offset = (0-min(raw_lag)) + 1
t = stats::poly((raw_lag + lag_offset), 2)
lag_vals[, paste("lag_ot", 1:2, sep="")] = t[lag_vals$raw_lag + lag_offset, 1:2]

# join it to the original data table
ccf_df = left_join(ccf_df,lag_vals, by = c("lag" = "raw_lag"))

```

```{r create-interactions-ccf}

ccf_df = ccf_df %>% ungroup() %>%
  
  # create interactions among static variables of interest
  mutate(cooperative.both = cooperative_self * cooperative_partner) %>%
  mutate(trust.both = trust_self * trust_partner) %>%
  mutate(cooperative.trust.self = cooperative_self * trust_self) %>%
  mutate(cooperative.trust.partner = cooperative_partner * trust_partner) %>%

  # first-order polynomials with lag
  mutate(cooperative_self.lag_ot1 = cooperative_self * lag_ot1) %>%
  mutate(cooperative_partner.lag_ot1 = cooperative_partner * lag_ot1) %>%
  mutate(cooperative.both.lag_ot1 = cooperative_self * cooperative_partner * lag_ot1) %>%
  mutate(trust_self.lag_ot1 = trust_self * lag_ot1) %>%
  mutate(trust_partner.lag_ot1 = trust_partner * lag_ot1) %>%
  mutate(trust.both.lag_ot1 = trust_self * trust_partner * lag_ot1) %>%

  # first-order polynomials with lag
  mutate(cooperative_self.lag_ot2 = cooperative_self * lag_ot2) %>%
  mutate(cooperative_partner.lag_ot2 = cooperative_partner * lag_ot2) %>%
  mutate(trust_self.lag_ot2 = trust_self * lag_ot2) %>%
  mutate(trust_partner.lag_ot2 = trust_partner * lag_ot2) %>%
  
  # polynomial interactions
  mutate(lag_ot1.lag_ot2 = lag_ot1 * lag_ot2) %>%
  mutate(cooperative.both.lag_ot1.lag_ot2 = cooperative.both * lag_ot1 * lag_ot2) %>%
  mutate(trust.both.lag_ot1.lag_ot2 = trust_self * trust_partner * lag_ot1 * lag_ot2) %>%
  mutate(cooperative.trust.self.lag_ot1.lag_ot2 = cooperative_self * trust_self * lag_ot1 * lag_ot2) %>%
  mutate(cooperative.trust.partner.lag_ot1.lag_ot2 = cooperative_partner * trust_partner * lag_ot1 * lag_ot2)

```

## Create standardized datasets

### For `winnowed_info_df`

```{r standardize-winnowed}

info_plot = winnowed_info_df %>% ungroup() %>%
  mutate_at(vars(participant,dyad),
            funs(factor))

info_st = winnowed_info_df %>% ungroup() %>%
  mutate_all(funs(as.numeric(scale(as.numeric(.))))) %>%
  mutate_at(vars(participant,dyad),
            funs(factor))

first_guess_plot = first_guess_df %>% ungroup() %>%
  mutate_at(vars(participant,dyad),
            funs(factor))

first_guess_st = first_guess_df %>% ungroup() %>%
  mutate_all(funs(as.numeric(scale(as.numeric(.))))) %>%
  mutate_at(vars(participant,dyad),
            funs(factor))
  
final_guess_plot = final_guess_df %>% ungroup() %>%
  mutate_at(vars(participant,dyad),
            funs(factor))
  
final_guess_st = final_guess_df %>% ungroup() %>%
  mutate_all(funs(as.numeric(scale(as.numeric(.))))) %>%
  mutate_at(vars(participant,dyad),
            funs(factor))

```

### For `ccf_df`

```{r standardize-ccf}

# create unstandardized dataframe and convert relevant variables to factors
ccf_plot = ccf_df %>% ungroup() %>%
  mutate_at(vars(participant,dyad),
            funs(factor))
  
# create standardized dataframe and convert relevant variables to factors
ccf_st = ccf_df %>%
  mutate_all(funs(as.numeric(scale(as.numeric(.))))) %>%
  mutate_at(vars(participant,dyad),
            funs(factor))

```

## Export analysis-ready datasets

```{r export-analysis-datasets}

# export standardized and plotting info datasets
write.table(info_plot, './data/study_1-neutral/info_plot.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)
write.table(info_st, './data/study_1-neutral/info_st.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)

# export standardized and plotting first-guess datasets
write.table(first_guess_plot, './data/study_1-neutral/first_guess_plot.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)
write.table(first_guess_st, './data/study_1-neutral/first_guess_st.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)

# export standardized and plotting final-guess datasets
write.table(final_guess_plot, './data/study_1-neutral/final_guess_plot.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)
write.table(final_guess_st, './data/study_1-neutral/final_guess_st.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)

# export standardized and plotting ccf datasets
write.table(ccf_plot, './data/study_1-neutral/ccf_plot.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)
write.table(ccf_st, './data/study_1-neutral/ccf_st.csv', sep=',',
            append = FALSE, quote = FALSE, na = "NA", 
            row.names = FALSE, col.names = TRUE)

```