Firefly_Dashboard.Rmd

---
title: "PriorKnowledge"
author: "Ally Williams"
date: "2023-08-01"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(warning = FALSE, message = FALSE)

# Data Manipulation and Analysis
library(tidyverse)   # Data manipulation and visualization
library(dplyr)       # Data manipulation
library(broom)       # Statistical analysis utilities
library(reshape2)    # Data reshaping
library(glmnet)      # Regularized regression models
library(readr)       # Data import


# Graphics
library(ggplot2)     # Data visualization
library(ggridges)    # Ridgeline plots
library(ggthemes)    # Additional ggplot2 themes
library(ggrepel)     # Label placement in ggplot2
library(ppcor)       # Partial and semi-partial correlation
library(ggExtra)     # Additional ggplot2 functions
library(ggsci)       # Scientific journal-inspired color palettes
library(viridis)     # Color palettes
library(scales)      # Scale functions
library(patchwork)   # Multi-plot alignment
library(ggcorrplot)  # Correlation plot
library(gapminder)   # Dataset used to make the box plot connected by lines
library(RColorBrewer)# Color palettes
library(plotly)      # Interactive graphs
library(lubridate)   # Date functions
library(stringr)     # Text functions
library(extrafont)   # Font customization on graphs
library(htmlwidgets) # Interactive exports
library(cowplot)     # Plot arrangement
library(png)         # PNG image format support
library(apyramid)    # Create age pyramids

# Themes: "default", "bootstrap", "cerulean", "cosmo", "darkly", "flatly", "journal", "lumen", "paper", "readable", "sandstone", "simplex", "spacelab", "united", "yeti"

# Tables
library(kableExtra)  # Table formatting
library(xtable)      # Table formatting
library(reactable)   # Interactive tables
library(htmltools)   # HTML table formatting

# Date functions
library(anytime)     # Date conversion
library(lubridate)   # Date manipulation

# SlimStampen
#library(SlimStampenRData)  # SlimStampen-specific functions

# Dashboard
library(flexdashboard)  # Dashboard creation
library(lme4)
library(sjPlot)
```
### All SoF 

```{r fig.width= 10, fig.height= 4.5}
cleandata_lastRep <- read_csv("cleandata_lastrep.csv")
graph=ggplot(cleandata_lastRep, aes(x=lessonId, y=alpha, col=lessonId, fill=lessonId)) +
  geom_boxplot(width=.4,size=0.1, alpha=0.2) +
  stat_summary(fun.y=mean, geom="pointrange", size=0.1, shape=1, color="black") +
  geom_point(size=2, position=position_jitter(0.1)) +
  xlab("Lesson") +
  #scale_x_discrete(labels=xlabels) +
  ylab("SoF") +
  ylim(0.1, 0.55) +
  ggtitle("Speed of Forgetting Across Lessons") +
  theme_hc() +
  theme(legend.position="none",
        axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))
ggplotly(graph, tooltip=c("y", "text")) %>% 
  layout(legend = list(orientation = "h")) %>% 
  config(displayModeBar=FALSE)

```
### SoF by Lesson
```{r, echo=FALSE}

# Speed of Forgetting by Participant
graph=ggplot(cleandata_lastRep, aes(x=prior_knowledge, y=alpha, text=paste0(email))) +
  geom_boxplot(size=0.1, alpha=0.2) +
  geom_line(aes(group = email, col = email), size = 0.1, position = position_dodge(0)) +
  geom_point(aes(col = email), size = 2, shape = 20, stroke = 0, position = position_dodge(0)) +
  xlab("Lesson") +
  #scale_x_discrete(labels=xlabels) +
  ylab("SoF") +
  ylim(0.29, 0.31) +
  ggtitle("Speed of Forgetting by Participant") +
  labs(fill="Participant", col="Participant") +
  theme_hc() +
  theme(axis.title.x=element_blank(),
        panel.grid.major = element_blank(),
        axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))

ggplotly(graph, tooltip=c("y", "text")) %>% 
  layout(legend = list(orientation = "")) %>% 
  config(displayModeBar=FALSE)

```
#Prior Knowledge by Fact
```{r}

ggplot(cleandata_lastRep, aes(x=answer, y=alpha, col=prior_knowledge))+
  #geom_boxplot()+
  geom_point(size=0.5, position=position_jitter(0.2)) +
  #geom_line(aes(group=prior_knowledge), size=0.1, position=position_dodge(0)) +
       xlab("Fact") +
  ylab("SoF") +
  scale_color_manual(values=c("darkblue", "lightgreen")) +
  scale_fill_manual(values=c("darkblue", "lightgreen")) +
  ggtitle(paste("Prior Knowledge and SoF across Facts")) +
  labs(col="prior_knowledge") +
  theme_hc() +
  theme(legend.position = "right",
        axis.text.x = element_text (angle=90, size=8),
        panel.grid.major = element_blank())

ggsave("figures/Prior_Knowledge_Across_Facts.png")

```



## Effect of prior knowledge on SOF across ppl
```{r}
ggplot(cleandata_lastRep, aes(y = alpha, x = as.factor(userId), col = prior_knowledge, fill = prior_knowledge)) +
  stat_summary(geom="point", fun.data = "mean_sdl", size=2.5) +
  stat_summary(geom="ribbon", fun.data = "mean_se", 
               aes(group = prior_knowledge), 
               col = NA, 
               alpha = 0.25) +
  stat_summary(geom="line", fun = "mean", aes(group = prior_knowledge)) +
  xlab("Participant ID") +
  scale_color_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_fill_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_x_discrete() +
ylab(expression(paste(italic("SoF")))) +
  ylim(0.1, 0.5) +
  ggtitle(expression(paste ("Effect of Prior Knowledge Across Participants"))) +
  labs(col="Prior Knowledge", fill="Prior Knowledge") +
  theme_minimal() +
  theme(legend.position = "right",
        axis.text.x = element_text (angle=90, size=5),
        panel.grid.major = element_blank())

ggsave("figures/Prior_Knowledge_Across_Participants.png")

```



## Prior Knowledge across participants: point plot
```{r}
ggplot(cleandata_lastRep, aes(y = alpha, x = userId, col = prior_knowledge, fill = prior_knowledge)) +
  stat_summary(geom="point", fun.data = "mean_se", size=2, 
               position = position_dodge()) +
  stat_summary(geom="errorbar", size=0.3, color = "black", fun.data = "mean_se", aes(group = prior_knowledge)) +
  xlab("Participant ID") +
  scale_color_manual(values=c("darkblue", "lightgreen")) +
  scale_fill_manual(values=c("darkblue", "lightgreen")) +
  scale_x_discrete() +
ylab(expression(paste(italic("SoF")))) +
  ylim(0, 0.5) +
  ggtitle(expression(paste ("Effect of Prior Knowledge Across Participants"))) +
  labs(col="Prior Knowledge", fill="Prior Knowledge") +
  theme_minimal() +
  theme(legend.position = "right",
        axis.text.x = element_text (angle=90, size=5),
        panel.grid.major = element_blank())
```


##Prior Knowledge across participants: bar graph
```{r}
#Plot with added error bars
plot_with_stacked_bar_and_error_bars <- ggplot(cleandata_lastRep, aes(x = factor(userId), y = alpha, fill = prior_knowledge)) +
  geom_bar(stat = "summary", fun = "mean", position = "dodge", alpha = 0.7) +
  geom_errorbar(stat = "summary", fun.data = "mean_se", position = position_dodge(width = 0.75), width = 0.25, size = 0.7) +
  xlab("Participant ID") +
  ylab(expression(paste(italic("SoF")))) +
  ylim(0.0, 0.7) +
  ggtitle(expression(paste("Effect of Prior Knowledge Across Participants"))) +
  scale_fill_manual(values = c("darkblue", "lightgreen")) +
  labs(fill = "Prior Knowledge") +
  theme_minimal() +
  theme(legend.position = "right",
        axis.text.x = element_text(angle = 90),
        panel.grid.major = element_blank())

print(plot_with_stacked_bar_and_error_bars)





ggsave("figures/Prior_Knowledge_Across_Participants_bargraph.png")
```
## Correlations between known and unknwon fact SOF

Is there a correlation between the SOFs of the known and unknown facts?

```{r, fig.width=5, fig.height=5}
SOF_corr <- cleandata_lastRep %>%
  group_by(userId, prior_knowledge) %>%
  summarize(alpha = mean(alpha)) %>%
  pivot_wider(names_from = prior_knowledge, values_from = alpha)

correlation_value <- cor(SOF_corr$no, SOF_corr$yes, use = "complete.obs")

ggplot(SOF_corr, aes(x = no, y = yes)) +
  geom_smooth(method = "lm") +
  geom_point(size = 4, col = "blue", alpha = 0.5) +
  geom_text_repel(aes(label = userId)) +
  xlab("SOF: Previously Unknown") +
  ylab("SOF: Previously Known") +
  annotate(geom = "text", x = 0.25, y = 0.35, label = paste("r =", round(correlation_value, 2))) +
  ggtitle("SOF by Prior Knowledge") +
  theme_minimal()

cor_test_result <- cor.test(SOF_corr$no, SOF_corr$yes, use = "complete.obs")

p_value <- cor_test_result$p.value

print(p_value)

ggsave("figures/PriorKnowledgeCorrelations.png")
```

And finally, some MLM:

```{r}
base <- lmer(alpha ~ prior_knowledge  + (1|userId) +(0+prior_knowledge|userId), 
             cleandata_lastRep)
tab_model(base)
```

# DOES MLE WORK??? 

```{r}
recovered_blc <- read_csv("optimize/results_MLE.csv", show_col_types = FALSE)

recovered_blc$answer <- tolower(recovered_blc$answer)
recovered_blc$answer <- URLdecode(recovered_blc$answer)

#recovered_blc <- recovered_blc %>%
#  rename(userId = Subject) %>%
#  rename(answer = Fact) %>%
#  rename(lessonId = Lesson)

recovered_blc$...1 <- NULL

recovered_blc$userId <- as.character(recovered_blc$userId) 
cleandata_lastRep$userId <- as.character(cleandata_lastRep$userId)

recovered_blc <- left_join(recovered_blc, cleandata_lastRep, by = c("userId", "answer"))



```

```{r}
recovered_blc <- recovered_blc %>%
  mutate(prior_knowledge = if_else(prior_knowledge == "yes", 1, 0))

correlation <- ggplot(recovered_blc, aes(x = BLC, y = alpha)) +
  geom_point(color = "darkblue") +
  geom_smooth(method = "lm", color = "darkblue") +
  labs(title = "Scatterplot of Recovered BLC vs. SOF",
       x = "BLC",
       y = "SOF")

# Calculate correlation and p-value
test <- cor.test(recovered_blc$BLC, recovered_blc$prior_knowledge)

# Add correlation coefficient and p-value to the plot
correlation <- correlation +
  annotate("text", x = Inf, y = -Inf,
           label = paste("r =", round(test$estimate, 2),
                         "\n",
                         "p < .0001"),
           hjust = 1, vjust = -0.5)

# Display the scatterplot with correlation
print(correlation)

pv <- format(test$pv, digits = 2)
print(pv)

```

```{r}

# Create a scatterplot
scatterplot <- ggplot(recovered_blc, aes(x = BLC, y = prior_knowledge)) +
  geom_point(color = "darkblue") +
  geom_smooth(method = "lm", color = "darkblue") +
  labs(title = "Scatterplot of Recovered BLC vs. Prior Knowledge",
       x = "BLC",
       y = "Prior Knowledge")

# Calculate correlation and p-value
correlationResult <- cor.test(recovered_blc$BLC, recovered_blc$prior_knowledge)

# Add correlation coefficient and p-value to the plot
scatterplot <- scatterplot +
  annotate("text", x = Inf, y = -Inf,
           label = paste("r =", round(correlationResult$estimate, 2),
                         "\n",
                         "p < .0001"),
           hjust = 1, vjust = -0.5)

# Display the scatterplot with correlation
print(scatterplot)

p.value <- format(correlationResult$p.value, digits = 2)
print(p.value)

ggsave("figures/recovered_blc_correlations.png")

ggplot(recovered_blc %>% filter(BLC >= -1), aes(y=BLC, x=as.factor(prior_knowledge), fill=as.factor(prior_knowledge))) +
  stat_summary(geom="bar", fun.data = "mean_se") +
  stat_summary(geom="errorbar", fun.data = "mean_se", width=0.1) +
 geom_point(position = position_jitterdodge(jitter.width = 0.2, dodge.width = 0.75), color = "black", size = 0.01) +
  scale_fill_manual(values = c("darkblue", "lightgreen"), name = "Prior Knowledge Status",
                    labels = c("no", "yes")) +
  xlab("Prior Knowledge Status") +
  theme_minimal()
```
```{r}

ggplot(recovered_blc %>% filter(flags_click.time <= 15), aes(y = flags_click.time, x = as.factor(prior_knowledge), fill = as.factor(prior_knowledge))) +
  stat_summary(geom = "bar", fun.data = "mean_se") +
  stat_summary(geom = "errorbar", fun.data = "mean_se", width = 0.1) +
    geom_point(position = position_jitterdodge(jitter.width = 0.2, dodge.width = 0.75), color = "black", size = 0.1) +
  scale_fill_manual(values = c("darkblue", "lightgreen"), name = "Prior Knowledge Status",
                    labels = c("no", "yes")) +
  xlab("Prior Knowledge Status") +
  theme_minimal()

```

##Group-level BLC for each fact
```{r}

avg_BLC <- recovered_blc %>%
  group_by(answer) %>%
  summarize(mean_BLC = mean(BLC, na.rm = TRUE)) %>% # added na.rm = TRUE to handle any missing values
  arrange(desc(mean_BLC))

# Reorder the 'answer' factor based on mean_BLC in descending order
avg_BLC$answer <- fct_reorder(avg_BLC$answer, avg_BLC$mean_BLC, .desc = TRUE)

# Create the bar graph with a gradient color from lightgreen to darkblue
ggplot(avg_BLC, aes(x = answer, y = mean_BLC, fill = mean_BLC)) +
  geom_bar(stat = "identity") +
  labs(title = "Average BLC for Each Fact",
       x = "Fact",
       y = "Average BLC") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 70, hjust = 1, vjust = 1, size = 12),
        panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank()) +
  scale_fill_gradient(low = "darkblue", high = "lightgreen")

#ggsave("figures/group-level_avgBLC.png", dpi=300)


```
##Prior knowledge across participants
```{r}
prior_knowledge_percent <- recovered_blc %>%
  group_by(answer) %>%
  summarize(percent_yes = mean(prior_knowledge) * 100) %>% # Calculate mean to get percentage
  arrange(desc(percent_yes)) # Sort by descending percentage (optional)

# Reorder the 'answer' factor based on percent_yes in descending order (if needed)
prior_knowledge_percent$answer <- fct_reorder(prior_knowledge_percent$answer, prior_knowledge_percent$percent_yes, .desc = TRUE)

# Create the bar graph with a gradient color from lightgreen to darkblue
ggplot(prior_knowledge_percent, aes(x = answer, y = percent_yes, fill = percent_yes)) +
  geom_bar(stat = "identity") +
  labs(title = "Percentage of Prior Knowledge for Each Fact",
       x = "Fact",
       y = "Percentage of Prior Knowledge") +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 70, hjust = 1, vjust = 1, size = 12), # Increase font size for x-axis labels
    panel.grid.major = element_blank(), 
    panel.grid.minor = element_blank()
  ) +
  scale_fill_gradient(low = "darkblue", high = "lightgreen")

ggsave("figures/grouplevel_priorknowledge.png", dpi=300)


```


## Is there a significant difference in BLC?

```{r}
base <- lmer(BLC ~ prior_knowledge  + (1|userId) +(0+prior_knowledge|userId), 
             recovered_blc)
tab_model(base)
```

#And what is the classification accuracy (using a single threshold for all participants)?

```{r}

recovered_blc1 <- recovered_blc %>%
  mutate(observed = if_else(prior_knowledge == 1, 1, -1))

curve = NULL
for (cutoff in seq(-1, 1.5, 0.1)) {
  subthreshold <- recovered_blc1 %>%
    mutate(prediction = ifelse(BLC <= cutoff, -1, 1)) %>%
    mutate(observed = if_else(prior_knowledge == 1, 1, -1)) %>% 
    mutate(accuracy = ifelse(prediction == observed, 1, 0)) %>%
    group_by(observed) %>%
    summarise(accuracy = mean(accuracy))
  
  tnr <- subthreshold %>% 
    filter(observed == -1) %>% 
    dplyr::select(accuracy) %>%
    as.numeric()
  
  tpr <- subthreshold %>% 
    filter(observed == 1) %>% 
    dplyr::select(accuracy) %>%
    as.numeric()
  
  partial <- tibble(Threshold = cutoff,
                    TNR = tnr,
                    TPR = tpr)
  if (is.null(curve)) {
    curve <- partial
  } else {
    curve <- rbind(curve, partial)
  }
}
```

And now, we can visualize the ROC graph. First, we can compute the global AUC

```{r}
blc_AUC <- 0
step <- 0.01
for (tnr in seq(0, 1-step, step)) {
  y <- curve %>% filter (TNR <= tnr) %>% filter(TNR == max(TNR)) %>% summarise(TPR = mean(TPR)) %>% as.numeric()
  if (!is.nan(y)) {
    blc_AUC <- blc_AUC + (y * step)
  }
}
```

The global AUC is `r blc_AUC`.

```{r, fig.width=5, fig.height=5}
ggplot(arrange(curve, TPR), aes(x=TNR, y=TPR, col=Threshold)) + 
  geom_point(size=2,  alpha=1) + 
  geom_line() + 
  geom_text_repel(aes(label=paste("BLC =", Threshold)), 
                  direction="both",
                  size=3) +
  ylab("Sensitivity (True Positive Rate)") +
  xlab("Specificity (True Negative Rate)") +
  scale_x_reverse() +
  scale_color_viridis(option="viridis") +
  labs(col="Recovered BLC") +
  ylim(0, 1) +
  xlim(1, 0) +
  coord_equal() +
  ggtitle("Classification Accuracy for BLC Estimates") +
  geom_abline(slope=1, intercept = 1, col="grey", linetype = "dashed") +
  annotate(geom="text", x=1/3, y=1/5, 
           label = paste("AUC = ", 
                         round(blc_AUC, 2))) +
  labs(col="BLC Threshold") +
  theme_minimal() +
  theme(legend.position = "bottom")

ggsave("figure8.png", dpi=300)

max_j <- curve %>%
  mutate(J = TPR - (1 - TNR)) %>%
  filter(J == max(J)) %>%
  select(Threshold)

cat("Threshold for Maximum Youden's J Statistic:", max_j$Threshold, "\n")
```
#identifying plausible correction
```{r}
known_SOFs <- cleandata_lastRep %>%
  filter(prior_knowledge == "yes")

known_SOFs <- known_SOFs %>%
  group_by(userId, lessonId) %>%
  summarize(mean_alpha = mean(alpha))

predicted_known_SOFs <- recovered_blc %>%
  filter(BLC > 0.5)

predicted_unknown_SOFs <- recovered_blc %>%
  filter(BLC <= 0.5)

avg_known <- mean(known_SOFs$mean_alpha)
avg_unknown <- mean(unknown_SOFs$mean_alpha)
avg_predicted_known <- mean(predicted_known_SOFs$alpha)
avg_predicted_unknown <- mean(predicted_unknown_SOFs$alpha)

cat("Average SOF for facts with prior knowledge:", avg_known, "\n")
cat("Average SOF for facts without prior knowledge:", avg_unknown, "\n")
cat("Average SOF for facts predicted to have prior knowledge", avg_predicted_known, "\n")
cat("Average SOF for facts predicted to not have prior knowledge", avg_predicted_unknown, "\n") 
  
calibration_factor <- mean(.346/.227)
cat("Calibration_factor:", calibration_factor, "\n")

```
#correcting facts with predicted prior knowledge
```{r}
#corrected_values <- uncorrected_values * calibration_factor
recovered_blc_corrected <- recovered_blc %>% 
  mutate(alpha = ifelse(BLC > 0.5, alpha * 1.52, alpha))

```
#comparing corrected to uncorrected data
```{r}

#after correction
ggplot(recovered_blc_corrected, aes(y = alpha, x = as.factor(userId), col = factor(prior_knowledge), fill = factor(prior_knowledge))) +
  stat_summary(geom="point", fun.data = "mean_sdl", size=2.5) +
  stat_summary(geom="ribbon", fun.data = "mean_se", 
               aes(group = prior_knowledge), 
               col = NA, 
               alpha = 0.25) +
  stat_summary(geom="line", fun = "mean", aes(group = prior_knowledge)) +
  xlab("Participant ID") +
  scale_color_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_fill_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_x_discrete() +
ylab(expression(paste(italic("SoF")))) +
  ylim(0.1, 0.5) +
  ggtitle(expression(paste ("Corrected Prior Knowledge Data"))) +
  labs(col="Prior Knowledge", fill="Prior Knowledge") +
  theme_minimal() +
  theme(legend.position = "right",
        axis.text.x = element_text (angle=90, size=5),
        panel.grid.major = element_blank())

#original plot
ggplot(cleandata_lastRep, aes(y = alpha, x = as.factor(userId), col = prior_knowledge, fill = prior_knowledge)) +
  stat_summary(geom="point", fun.data = "mean_sdl", size=2.5) +
  stat_summary(geom="ribbon", fun.data = "mean_se", 
               aes(group = prior_knowledge), 
               col = NA, 
               alpha = 0.25) +
  stat_summary(geom="line", fun = "mean", aes(group = prior_knowledge)) +
  xlab("Participant ID") +
  scale_color_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_fill_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_x_discrete() +
ylab(expression(paste(italic("SoF")))) +
  ylim(0.1, 0.5) +
  ggtitle(expression(paste ("Original Effect of Prior Knowledge Across Participants"))) +
  labs(col="Prior Knowledge", fill="Prior Knowledge") +
  theme_minimal() +
  theme(legend.position = "right",
        axis.text.x = element_text (angle=90, size=5),
        panel.grid.major = element_blank())

```

# Andy's section

## New figure Global Results

A new figure for the global results

```{r, fig.width=5, fig.height=5}
adata <- cleandata_lastRep %>%
  group_by(userId, prior_knowledge) %>%
  summarise(SoF = mean(alpha))

ggplot(adata, aes(x=prior_knowledge, y=SoF, 
                  col=prior_knowledge, fill= prior_knowledge)) +
  geom_line(aes(group=userId), color="grey", size=0.25) +
  stat_summary(geom="point", fun.data = "mean_se", size=3) +
  stat_summary(geom="errorbar", fun.data ="mean_sdl", width=0.1) +
  geom_boxplot(alpha=0.25) +
  scale_color_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_fill_manual(values=c("darkblue", "lightgreen", "orange")) +
  labs(col="Previously Known?") +
  xlab("Previously Known?") +
  ylab("Speed of Forgetting (SoF)") +
  ggtitle("Effect of Prior Knowledge on SoF Estimates") +
  theme_minimal() +
  guides(fill="none") +
  theme(legend.position = "bottom")

ggsave(filename="figure5.png", dpi=300)
```

## Correlations

```{r, fig.width=5, fig.height=5}
adata_w <- adata %>% pivot_wider(values_from = SoF, names_from = prior_knowledge)
ggplot(adata_w, aes(x = no, y = yes)) +
  scale_x_continuous() +
  scale_y_continuous() +
  coord_equal() +
  #coord_cartesian(xlim=c(0.15, 0.38), ylim=c(0.15, 0.38),) +
  geom_smooth(method = "lm", fullrange=TRUE, fill="grey") +
  geom_point(size = 4, col="blue", alpha = 0.5) +
  xlab("SoF: Previously Unknown") +
  ylab("SoF: Previously Known") +
  ggtitle("SoF by Prior Knowledge") +
  geom_abline(slope=1, intercept = 0, col="black", linetype="dashed") +
  theme_minimal() +
  annotate(geom="text", x=0.275, y=0.325, label=paste("r(70) = ", round(cor(adata_w$yes, 
                                                                            adata_w$no),
                                                                        2))) +
  theme(aspect.ratio = 1)

ggsave(filename="figure6.png", dpi = 300)
```
## BLC

```{r, fig.width=5, fig.height=5}
blcdata <-recovered_blc_corrected %>%
  mutate(prior = if_else(prior_knowledge == 0, "no", "yes")) %>%
  group_by(userId, prior) %>%
  summarise(BLC = mean(BLC))

ggplot(blcdata, aes(x=prior, y=BLC, 
                  col=prior, fill= prior)) +
  geom_line(aes(group=userId), color="grey", size=0.25) +
  stat_summary(geom="point", fun.data = "mean_se", size=3) +
  #stat_summary(geom="errorbar", fun.data ="mean_sdl", width=0.1) +
  geom_boxplot(alpha=0.3) +
  scale_color_manual(values=c("darkblue", "lightgreen", "orange")) +
  scale_fill_manual(values=c("darkblue", "lightgreen", "orange")) +
  labs(col="Previously Known?") +
  xlab("Previously Known?") +
  ylab("MLE Estimates of BLC") +
  ggtitle("MLE-Recovered BLC Values") +
  theme_minimal() +
  guides(fill="none") +
  theme(legend.position = "bottom")

ggsave("figure7.png")
```

```{r}
t.test(BLC ~ prior, paired=T, data=blcdata)
```

##

Previous knowledge can be approximated as a constant

```{r, fig.width=5, fig.height=5}
month <- 60*60*24*30
year <- month * 12
delta <- 60*60
time <- seq(1, month, delta)

gen_traces <- function(n, within=month) {
  timestep <- within / n
  seq(0, within-timestep, timestep)
}

activation <- function(t, traces) {
  timeline <- seq(1, t-delta, delta)
  activations <- c(1)
  for (time in timeline) {
    O <- 0
    d = 0.3
    for (trace in traces) {
      if (trace < time) {
        O <- O +(time - trace)**-d
        d <- 0.5 * O + 0.3
      }
    }
    activations <- append(activations, log(O))
  }
  activations
}


#plot(activation(30000, traces=c(1, 2000, 50000)), type="l")

time <- seq(1, month*12, delta)
n1 <- activation(month*12, traces=gen_traces(1))
n10 <- activation(month*12, traces=gen_traces(10))
n100 <- activation(month*12, traces=gen_traces(100))
df <- data.frame(Time=time, N1 = n1, N10 = n10, N100 = n100)

activations <- tibble(df)
lactivations <- activations %>% pivot_longer(cols = c("N1", "N10", "N100"), 
                                             values_to = "Activation", 
                                             names_to = "NEncodings") %>%
  mutate(Encodings = if_else(NEncodings == "N1", "1", if_else(NEncodings=="N10", "10", "100")))

ggplot(lactivations, aes(x=Time, y=Activation, col=Encodings)) +
  geom_line() +
  scale_x_continuous(breaks=seq(1,12)*month,
                     labels = paste(seq(1,12))) +
  xlab("Time (Months)") +
  ggtitle("Simulated Effect of Prior Knowledge Over Time") +
  scale_color_viridis(discrete=T, end=0.8) +
  theme_minimal() +
  theme(legend.position = "bottom")

ggsave("figure2.png", dpi=300)
```

# MLM Model

Random slope model.

```{r}
base <- lmer(alpha ~ prior_knowledge  
             + (1|userId)                  # Intercept
             + (0+prior_knowledge|userId), # Slope
             recovered_blc_corrected)
tab_model(base)
```