---
title: "Mixed ANOVA Analysis for Domain Means"
author: "Irina"
date: "`r Sys.Date()`"
output: 
  html_document:
    toc: true
    toc_float: true
    code_folding: hide
    theme: flatly
    highlight: tango
    fig_width: 10
    fig_height: 6
---

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

# Introduction

This analysis examines domain-level differences in mean scores across time periods using a mixed ANOVA design. The analysis focuses on four domains (Preferences, Personality, Values, Life) across two time periods (Past, Future) with a between-subjects factor (TEMPORAL_DO).

# Data Preparation and Setup

```{r libraries}
library(tidyverse)
library(ez)
library(car)
library(nortest)      # For normality tests
library(emmeans)      # For post-hoc comparisons
library(purrr)        # For map functions
library(effsize)      # For Cohen's d calculations
library(ggplot2)      # For plotting

options(scipen = 999)
options(contrasts = c("contr.sum", "contr.poly"))

setwd("C:/Users/irina/Documents/DND/EOHI/eohi1")
```

```{r data-loading}
# Read the data
data <- read.csv("exp1.csv")

required_vars <- c("NPast_mean_pref", "NPast_mean_pers", "NPast_mean_val", "NPast_mean_life",
                   "NFut_mean_pref", "NFut_mean_pers", "NFut_mean_val", "NFut_mean_life")

# Define domain mapping
domain_mapping <- data.frame(
  variable = c("NPast_mean_pref", "NPast_mean_pers", "NPast_mean_val", "NPast_mean_life",
               "NFut_mean_pref", "NFut_mean_pers", "NFut_mean_val", "NFut_mean_life"),
  time = c(rep("Past", 4), rep("Future", 4)),
  domain = rep(c("Preferences", "Personality", "Values", "Life"), 2),
  stringsAsFactors = FALSE
)
```

```{r data-reshaping}
long_data <- data %>%
  select(pID, ResponseId, TEMPORAL_DO, all_of(required_vars)) %>%
  pivot_longer(
    cols = all_of(required_vars),
    names_to = "variable",
    values_to = "MEAN_DIFFERENCE"
  ) %>%
  left_join(domain_mapping, by = "variable") %>%
  # Convert to factors with proper levels (note: columns are 'time' and 'domain' from mapping)
  mutate(
    TIME = factor(time, levels = c("Past", "Future")),
    DOMAIN = factor(domain, levels = c("Preferences", "Personality", "Values", "Life")),
    pID = as.factor(pID),
    TEMPORAL_DO = as.factor(TEMPORAL_DO)
  ) %>%
  # Select final columns and remove any rows with missing values
  select(pID, ResponseId, TEMPORAL_DO, TIME, DOMAIN, MEAN_DIFFERENCE) %>%
  filter(!is.na(MEAN_DIFFERENCE))

# Create clean dataset for analysis (fixing the reference issue)
long_data_clean <- long_data
```

# Descriptive Statistics

## Overall Descriptive Statistics by TIME and DOMAIN

```{r descriptive-stats}
desc_stats <- long_data %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n = n(),
    mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    median = round(median(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    q1 = round(quantile(MEAN_DIFFERENCE, 0.25, na.rm = TRUE), 5),
    q3 = round(quantile(MEAN_DIFFERENCE, 0.75, na.rm = TRUE), 5),
    min = round(min(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    max = round(max(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    .groups = 'drop'
  )

print(desc_stats)
```

## Descriptive Statistics by Between-Subjects Factors

```{r descriptive-stats-temporal}
desc_stats_by_temporal <- long_data %>%
  group_by(TEMPORAL_DO, TIME, DOMAIN) %>%
  summarise(
    n = n(),
    mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
    .groups = 'drop'
  )

print(desc_stats_by_temporal)
```

# Assumption Testing

## Missing Values Check

```{r missing-values}
missing_summary <- long_data %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n_total = n(),
    n_missing = sum(is.na(MEAN_DIFFERENCE)),
    pct_missing = round(100 * n_missing / n_total, 2),
    .groups = 'drop'
  )

print(missing_summary)
```

## Outlier Detection

```{r outlier-detection}
outlier_summary <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n = n(),
    mean = mean(MEAN_DIFFERENCE),
    sd = sd(MEAN_DIFFERENCE),
    q1 = quantile(MEAN_DIFFERENCE, 0.25),
    median = median(MEAN_DIFFERENCE),
    q3 = quantile(MEAN_DIFFERENCE, 0.75),
    iqr = q3 - q1,
    lower_bound = q1 - 1.5 * iqr,
    upper_bound = q3 + 1.5 * iqr,
    n_outliers = sum(MEAN_DIFFERENCE < lower_bound | MEAN_DIFFERENCE > upper_bound),
    .groups = 'drop'
  )

print(outlier_summary)
```

## Anderson-Darling Normality Test

```{r normality-test}
normality_results <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    n = n(),
    ad_statistic = ad.test(.data$MEAN_DIFFERENCE)$statistic,
    ad_p_value = ad.test(.data$MEAN_DIFFERENCE)$p.value,
    .groups = 'drop'
  )

print(normality_results)
```

## Homogeneity of Variance (Levene's Test)

### Test homogeneity across TIME within each DOMAIN

```{r homogeneity-time}
homogeneity_time <- long_data_clean %>%
  group_by(DOMAIN) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ TIME)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ TIME)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print(homogeneity_time)
```

### Test homogeneity across DOMAIN within each TIME

```{r homogeneity-domain}
homogeneity_domain <- long_data_clean %>%
  group_by(TIME) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print(homogeneity_domain)
```

## Hartley's F-Max Test with Bootstrap Critical Values

```{r hartley-function}
# Function to calculate Hartley's F-max ratio
calculate_hartley_ratio <- function(variances) {
  max(variances, na.rm = TRUE) / min(variances, na.rm = TRUE)
}

# More efficient bootstrap function for Hartley's F-max test
bootstrap_hartley_critical <- function(data, group_var, response_var, n_iter = 1000) {
  # Get unique groups and their sample sizes
  groups <- unique(data[[group_var]])
  
  # Calculate observed variances for each group
  observed_vars <- data %>%
    dplyr::group_by(!!rlang::sym(group_var)) %>%
    dplyr::summarise(var = var(!!rlang::sym(response_var), na.rm = TRUE), .groups = 'drop') %>%
    dplyr::pull(var)
  
  # Handle invalid variances
  if(any(observed_vars <= 0 | is.na(observed_vars))) {
    observed_vars[observed_vars <= 0 | is.na(observed_vars)] <- 1e-10
  }
  
  # Calculate observed F-max ratio
  observed_ratio <- max(observed_vars) / min(observed_vars)
  
  # Pre-allocate storage for bootstrap ratios
  bootstrap_ratios <- numeric(n_iter)
  
  # Get group data once
  group_data_list <- map(groups, ~ {
    group_data <- data[data[[group_var]] == .x, response_var]
    group_data[!is.na(group_data)]
  })
  
  # Bootstrap with pre-allocated storage
  for(i in 1:n_iter) {
    # Bootstrap sample from each group independently
    sample_vars <- map_dbl(group_data_list, ~ {
      bootstrap_sample <- sample(.x, size = length(.x), replace = TRUE)
      var(bootstrap_sample, na.rm = TRUE)
    })
    bootstrap_ratios[i] <- max(sample_vars) / min(sample_vars)
  }
  
  # Remove invalid ratios
  valid_ratios <- bootstrap_ratios[is.finite(bootstrap_ratios) & !is.na(bootstrap_ratios)]
  
  if(length(valid_ratios) == 0) {
    stop("No valid bootstrap ratios generated")
  }
  
  # Calculate critical value (95th percentile)
  critical_95 <- quantile(valid_ratios, 0.95, na.rm = TRUE)
  
  # Return only essential information
  return(list(
    observed_ratio = observed_ratio,
    critical_95 = critical_95,
    n_valid_iterations = length(valid_ratios)
  ))
}
```

```{r hartley-results}
# For mixed ANOVA: Test homogeneity across BETWEEN-SUBJECTS factor (TEMPORAL_DO)
# within each combination of within-subjects factors (TIME × DOMAIN)

print(unique(long_data_clean$TEMPORAL_DO))
print(table(long_data_clean$TEMPORAL_DO))

observed_temporal_ratios <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    # Calculate variances for each TEMPORAL_DO level within this TIME × DOMAIN combination
    past_var = var(MEAN_DIFFERENCE[TEMPORAL_DO == "01PAST"], na.rm = TRUE),
    fut_var = var(MEAN_DIFFERENCE[TEMPORAL_DO == "02FUT"], na.rm = TRUE),
    # Calculate F-max ratio
    f_max_ratio = max(past_var, fut_var) / min(past_var, fut_var),
    .groups = 'drop'
  ) %>%
  select(TIME, DOMAIN, past_var, fut_var, f_max_ratio)

print(observed_temporal_ratios)

# Hartley's F-max test across TEMPORAL_DO within each TIME × DOMAIN combination
set.seed(123)  # For reproducibility

hartley_temporal_results <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    hartley_result = list(bootstrap_hartley_critical(pick(TEMPORAL_DO, MEAN_DIFFERENCE), "TEMPORAL_DO", "MEAN_DIFFERENCE")),
    .groups = 'drop'
  ) %>%
  mutate(
    observed_ratio = map_dbl(hartley_result, ~ .x$observed_ratio),
    critical_95 = map_dbl(hartley_result, ~ .x$critical_95),
    significant = observed_ratio > critical_95
  ) %>%
  select(TIME, DOMAIN, observed_ratio, critical_95, significant)

print(hartley_temporal_results)
```

# Mixed ANOVA Analysis

## Design Balance Check

```{r design-check}
# Check for complete cases
complete_cases <- sum(complete.cases(long_data_clean))
print(complete_cases)

# Check if design is balanced
design_balance <- table(long_data_clean$pID, long_data_clean$TIME, long_data_clean$DOMAIN)
if(all(design_balance %in% c(0, 1))) {
  print("Design is balanced: each participant has data for all TIME × DOMAIN combinations")
} else {
  print("Warning: Design is unbalanced")
  print(summary(as.vector(design_balance)))
}
```

## Mixed ANOVA with Sphericity Corrections

```{r mixed-anova}
# Mixed ANOVA using ezANOVA with automatic sphericity corrections
# Between-subjects: TEMPORAL_DO (2 levels: 01PAST, 02FUT)
# Within-subjects: TIME (2 levels: Past, Future) × DOMAIN (4 levels: Preferences, Personality, Values, Life)
mixed_anova_model <- ezANOVA(data = long_data_clean, 
                             dv = MEAN_DIFFERENCE, 
                             wid = pID, 
                             between = TEMPORAL_DO, 
                             within = .(TIME, DOMAIN),
                             type = 3,
                             detailed = TRUE)

anova_output <- mixed_anova_model$ANOVA
rownames(anova_output) <- NULL  # Reset row numbers to be sequential
print(anova_output)
```

## Mauchly's Test for Sphericity

```{r mauchly-test}
print(mixed_anova_model$Mauchly)
```

## Sphericity-Corrected Results

```{r sphericity-corrections}
# Show sphericity-corrected results (Greenhouse-Geisser and Huynh-Feldt)
if(!is.null(mixed_anova_model$`Sphericity Corrections`)) {
  print(mixed_anova_model$`Sphericity Corrections`)
  
  # Extract and display corrected degrees of freedom
  sphericity_corr <- mixed_anova_model$`Sphericity Corrections`
  anova_table <- mixed_anova_model$ANOVA
  
  corrected_df <- data.frame(
    Effect = sphericity_corr$Effect,
    Original_DFn = anova_table$DFn[match(sphericity_corr$Effect, anova_table$Effect)],
    Original_DFd = anova_table$DFd[match(sphericity_corr$Effect, anova_table$Effect)],
    GG_DFn = anova_table$DFn[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$GGe,
    GG_DFd = anova_table$DFd[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$GGe,
    HF_DFn = anova_table$DFn[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$HFe,
    HF_DFd = anova_table$DFd[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$HFe,
    GG_epsilon = sphericity_corr$GGe,
    HF_epsilon = sphericity_corr$HFe
  )
  
  print(corrected_df)
  
  # Between-subjects effects (no sphericity corrections needed)
  between_effects <- c("TEMPORAL_DO")
  for(effect in between_effects) {
    if(effect %in% anova_table$Effect) {
      f_value <- anova_table$F[anova_table$Effect == effect]
      dfn <- anova_table$DFn[anova_table$Effect == effect]
      dfd <- anova_table$DFd[anova_table$Effect == effect]
      p_value <- anova_table$p[anova_table$Effect == effect]
      
      cat(sprintf("%s: F(%d, %d) = %.3f, p = %.6f\n", effect, dfn, dfd, f_value, p_value))
    }
  }
  
  # Within-subjects effects (sphericity corrections where applicable)
  
  # TIME main effect (2 levels, sphericity automatically satisfied)
  if("TIME" %in% anova_table$Effect) {
    f_value <- anova_table$F[anova_table$Effect == "TIME"]
    dfn <- anova_table$DFn[anova_table$Effect == "TIME"]
    dfd <- anova_table$DFd[anova_table$Effect == "TIME"]
    p_value <- anova_table$p[anova_table$Effect == "TIME"]
    cat(sprintf("TIME: F(%d, %d) = %.3f, p = %.6f (2 levels, sphericity satisfied)\n", dfn, dfd, f_value, p_value))
  }
  
  # DOMAIN main effect (4 levels, needs sphericity correction)
  if("DOMAIN" %in% anova_table$Effect) {
    f_value <- anova_table$F[anova_table$Effect == "DOMAIN"]
    dfn <- anova_table$DFn[anova_table$Effect == "DOMAIN"]
    dfd <- anova_table$DFd[anova_table$Effect == "DOMAIN"]
    p_value <- anova_table$p[anova_table$Effect == "DOMAIN"]
    cat(sprintf("DOMAIN: F(%d, %d) = %.3f, p = %.6f\n", dfn, dfd, f_value, p_value))
  }
  
  # Interactions with sphericity corrections
  for(i in seq_len(nrow(corrected_df))) {
    effect <- corrected_df$Effect[i]
    f_value <- anova_table$F[match(effect, anova_table$Effect)]
    
    cat(sprintf("\n%s:\n", effect))
    cat(sprintf("  Original: F(%d, %d) = %.3f\n", 
                corrected_df$Original_DFn[i], corrected_df$Original_DFd[i], f_value))
    cat(sprintf("  GG-corrected: F(%.2f, %.2f) = %.3f, p = %.6f\n", 
                corrected_df$GG_DFn[i], corrected_df$GG_DFd[i], f_value, sphericity_corr$`p[GG]`[i]))
    cat(sprintf("  HF-corrected: F(%.2f, %.2f) = %.3f, p = %.6f\n", 
                corrected_df$HF_DFn[i], corrected_df$HF_DFd[i], f_value, sphericity_corr$`p[HF]`[i]))
  }
} else {
  print("\nNote: Sphericity corrections not needed (sphericity assumption met)")
}
```

# Effect Sizes (Cohen's d)

## Main Effects

```{r cohens-d-main}
# Create aov model for emmeans 
aov_model <- aov(MEAN_DIFFERENCE ~ TEMPORAL_DO * TIME * DOMAIN + Error(pID/(TIME * DOMAIN)), 
                 data = long_data_clean)

# Main Effect of TIME
time_emmeans <- emmeans(aov_model, ~ TIME)
print(time_emmeans)

time_main_contrast <- pairs(time_emmeans, adjust = "Bonferroni")
time_main_df <- as.data.frame(time_main_contrast)
print(time_main_df)

# Calculate Cohen's d for TIME main effect
if(nrow(time_main_df) > 0) {
  cat("\nCohen's d for TIME main effect:\n")
  time_past_data <- long_data_clean$MEAN_DIFFERENCE[long_data_clean$TIME == "Past"]
  time_future_data <- long_data_clean$MEAN_DIFFERENCE[long_data_clean$TIME == "Future"]
  
  time_cohens_d <- cohen.d(time_past_data, time_future_data)
  cat(sprintf("Past vs Future: n1 = %d, n2 = %d\n", length(time_past_data), length(time_future_data)))
  cat(sprintf("Cohen's d: %.5f\n", time_cohens_d$estimate))
  cat(sprintf("Effect size interpretation: %s\n", time_cohens_d$magnitude))
  cat(sprintf("p-value: %.5f\n", time_main_df$p.value[1]))
}
```

```{r cohens-d-domain}
# Main Effect of DOMAIN (significant: p < 0.001)
domain_emmeans <- emmeans(aov_model, ~ DOMAIN)
print(domain_emmeans)
domain_main_contrast <- pairs(domain_emmeans, adjust = "bonferroni")
domain_main_df <- as.data.frame(domain_main_contrast)
print(domain_main_df)

# Calculate Cohen's d for significant DOMAIN contrasts
significant_domain <- domain_main_df[domain_main_df$p.value < 0.05, ]
if(nrow(significant_domain) > 0) {
  cat("\nCohen's d for significant DOMAIN contrasts:\n")
  for(i in seq_len(nrow(significant_domain))) {
    contrast_name <- as.character(significant_domain$contrast[i])
    contrast_parts <- strsplit(contrast_name, " - ")[[1]]
    if(length(contrast_parts) == 2) {
      level1 <- trimws(contrast_parts[1])
      level2 <- trimws(contrast_parts[2])
      
      data1 <- long_data_clean$MEAN_DIFFERENCE[long_data_clean$DOMAIN == level1]
      data2 <- long_data_clean$MEAN_DIFFERENCE[long_data_clean$DOMAIN == level2]
      
      if(length(data1) > 0 && length(data2) > 0) {
        domain_cohens_d <- cohen.d(data1, data2)
        cat(sprintf("Comparison: %s\n", contrast_name))
        cat(sprintf("  n1 = %d, n2 = %d\n", length(data1), length(data2)))
        cat(sprintf("  Cohen's d: %.5f\n", domain_cohens_d$estimate))
        cat(sprintf("  Effect size interpretation: %s\n", domain_cohens_d$magnitude))
        cat(sprintf("  p-value: %.5f\n", significant_domain$p.value[i]))
        cat("\n")
      }
    }
  }
}
```