# Mixed ANOVA Analysis for Domain Means - EOHI2
# EOHI Experiment Data Analysis - Domain Level Analysis with INTERVAL factor
# Variables: NPast_5_pref_MEAN, NPast_5_pers_MEAN, NPast_5_val_MEAN, etc.
#           NFut_5_pref_MEAN, NFut_5_pers_MEAN, NFut_5_val_MEAN, etc.
#           NPast_10_pref_MEAN, NPast_10_pers_MEAN, NPast_10_val_MEAN, etc.
#           NFut_10_pref_MEAN, NFut_10_pers_MEAN, NFut_10_val_MEAN, etc.
#           5.10past_pref_MEAN, 5.10past_pers_MEAN, 5.10past_val_MEAN
#           5.10fut_pref_MEAN, 5.10fut_pers_MEAN, 5.10fut_val_MEAN

# Load required libraries
library(tidyverse)
library(ez)
library(car)
library(afex)         # For aov_ez (cleaner ANOVA output)
library(nortest)      # For normality tests
library(emmeans)      # For post-hoc comparisons
library(purrr)        # For map functions
library(effsize)      # For Cohen's d calculations
library(effectsize)   # For effect size calculations

# Global options to remove scientific notation
options(scipen = 999)

# Set contrasts to sum for mixed ANOVA (necessary for proper interpretation)
options(contrasts = c("contr.sum", "contr.poly"))

setwd("C:/Users/irina/Documents/DND/EOHI/eohi2")

# Read the data
data <- read.csv("eohi2.csv")

# Display basic information about the dataset
print(paste("Dataset dimensions:", paste(dim(data), collapse = " x")))
print(paste("Number of participants:", length(unique(data$ResponseId))))

# Verify the specific variables we need
required_vars <- c("NPast_5_pref_MEAN", "NPast_5_pers_MEAN", "NPast_5_val_MEAN",
                   "NPast_10_pref_MEAN", "NPast_10_pers_MEAN", "NPast_10_val_MEAN",
                   "NFut_5_pref_MEAN", "NFut_5_pers_MEAN", "NFut_5_val_MEAN",
                   "NFut_10_pref_MEAN", "NFut_10_pers_MEAN", "NFut_10_val_MEAN",
                   "5.10past_pref_MEAN", "5.10past_pers_MEAN", "5.10past_val_MEAN",
                   "5.10fut_pref_MEAN", "5.10fut_pers_MEAN", "5.10fut_val_MEAN")

missing_vars <- required_vars[!required_vars %in% colnames(data)]
if (length(missing_vars) > 0) {
  print(paste("Warning: Missing variables:", paste(missing_vars, collapse = ", ")))
} else {
  print("All required domain mean variables found!")
}

# Define domain mapping with TIME, DOMAIN, and INTERVAL factors
domain_mapping <- data.frame(
  variable = required_vars,
  time = c(rep("Past", 3), rep("Past", 3), rep("Future", 3), rep("Future", 3), 
           rep("Past", 3), rep("Future", 3)),
  domain = rep(c("Preferences", "Personality", "Values"), 6),
  interval = c(rep("5", 3), rep("10", 3), rep("5", 3), rep("10", 3), 
               rep("5_10", 3), rep("5_10", 3)),
  stringsAsFactors = FALSE
)

print("Domain mapping created:")
print(domain_mapping)

# Efficient data pivoting using pivot_longer
long_data <- data %>%
  select(ResponseId, TEMPORAL_DO, INTERVAL_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
  mutate(
    TIME = factor(time, levels = c("Past", "Future")),
    DOMAIN = factor(domain, levels = c("Preferences", "Personality", "Values")),
    INTERVAL = factor(interval, levels = c("5", "10", "5_10")),
    ResponseId = as.factor(ResponseId),
    TEMPORAL_DO = as.factor(TEMPORAL_DO),
    INTERVAL_DO = as.factor(INTERVAL_DO)
  ) %>%
  # Select final columns and remove any rows with missing values
  select(ResponseId, TEMPORAL_DO, INTERVAL_DO, TIME, DOMAIN, INTERVAL, MEAN_DIFFERENCE) %>%
  filter(!is.na(MEAN_DIFFERENCE))

print(paste("Long data dimensions:", paste(dim(long_data), collapse = " x")))
print(paste("Number of participants:", length(unique(long_data$ResponseId))))

# =============================================================================
# DESCRIPTIVE STATISTICS
# =============================================================================

# Overall descriptive statistics by TIME, DOMAIN, and INTERVAL
desc_stats <- long_data %>%
  group_by(TIME, DOMAIN, INTERVAL) %>%
  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("Descriptive statistics by TIME, DOMAIN, and INTERVAL:")
print(desc_stats)

# Descriptive statistics by between-subjects factors
desc_stats_by_between <- long_data %>%
  group_by(TEMPORAL_DO, INTERVAL_DO, TIME, DOMAIN, INTERVAL) %>%
  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("Descriptive statistics by between-subjects factors:")
print(desc_stats_by_between)

# Summary by between-subjects factors only
desc_stats_between_only <- long_data %>%
  group_by(TEMPORAL_DO, INTERVAL_DO) %>%
  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("Descriptive statistics by between-subjects factors only:")
print(desc_stats_between_only)

# =============================================================================
# ASSUMPTION TESTING
# =============================================================================

# Remove missing values for assumption testing
long_data_clean <- long_data[!is.na(long_data$MEAN_DIFFERENCE), ]
print(paste("Data after removing missing values:", paste(dim(long_data_clean), collapse = " x")))

# 1. Missing values check
missing_summary <- long_data %>%
  group_by(TIME, DOMAIN, INTERVAL) %>%
  summarise(
    n_total = n(),
    n_missing = sum(is.na(MEAN_DIFFERENCE)),
    pct_missing = round(100 * n_missing / n_total, 2),
    .groups = 'drop'
  )

print("Missing values by TIME, DOMAIN, and INTERVAL:")
print(missing_summary)

# 2. Outlier detection
outlier_summary <- long_data_clean %>%
  group_by(TIME, DOMAIN, INTERVAL) %>%
  summarise(
    n = n(),
    mean = mean(MEAN_DIFFERENCE),
    sd = sd(MEAN_DIFFERENCE),
    q1 = quantile(MEAN_DIFFERENCE, 0.25),
    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 (IQR method):")
print(outlier_summary)

# 3. Anderson-Darling normality test
normality_results <- long_data_clean %>%
  group_by(TIME, DOMAIN, INTERVAL) %>%
  summarise(
    n = n(),
    ad_statistic = ad.test(.data$MEAN_DIFFERENCE)$statistic,
    ad_p_value = ad.test(.data$MEAN_DIFFERENCE)$p.value,
    .groups = 'drop'
  )

print("Anderson-Darling normality test results:")
# Round only the numeric columns
normality_results_rounded <- normality_results %>%
  mutate(across(where(is.numeric), ~ round(.x, 5)))
print(normality_results_rounded)

# 4. Homogeneity of variance (Levene's test)
# Test homogeneity across TIME within each DOMAIN × INTERVAL combination
homogeneity_time <- long_data_clean %>%
  group_by(DOMAIN, INTERVAL) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ TIME)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ TIME)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print("Homogeneity of variance across TIME within each DOMAIN × INTERVAL combination:")
print(homogeneity_time)

# Test homogeneity across DOMAIN within each TIME × INTERVAL combination
homogeneity_domain <- long_data_clean %>%
  group_by(TIME, INTERVAL) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print("Homogeneity of variance across DOMAIN within each TIME × INTERVAL combination:")
print(homogeneity_domain)

# Test homogeneity across INTERVAL within each TIME × DOMAIN combination
homogeneity_interval <- long_data_clean %>%
  group_by(TIME, DOMAIN) %>%
  summarise(
    levene_F = leveneTest(MEAN_DIFFERENCE ~ INTERVAL)$`F value`[1],
    levene_p = leveneTest(MEAN_DIFFERENCE ~ INTERVAL)$`Pr(>F)`[1],
    .groups = 'drop'
  )

print("Homogeneity of variance across INTERVAL within each TIME × DOMAIN combination:")
print(homogeneity_interval)

# 5. Hartley's F-max test for between-subjects factors
print("\n=== HARTLEY'S F-MAX TEST FOR BETWEEN-SUBJECTS FACTORS ===")

# Check what values the between-subjects factors actually have
print("Unique TEMPORAL_DO values:")
print(unique(long_data_clean$TEMPORAL_DO))
print("Unique INTERVAL_DO values:")
print(unique(long_data_clean$INTERVAL_DO))

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

# Hartley's F-max test across TEMPORAL_DO within each TIME × DOMAIN × INTERVAL combination
print("\n=== HARTLEY'S F-MAX TEST: TEMPORAL_DO within each TIME × DOMAIN × INTERVAL combination ===")

observed_temporal_ratios <- long_data_clean %>%
  group_by(TIME, DOMAIN, INTERVAL) %>%
  summarise(
    # Calculate variances for each TEMPORAL_DO level within this 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, INTERVAL, past_var, fut_var, f_max_ratio)

print(observed_temporal_ratios)

# Hartley's F-max test across INTERVAL_DO within each TIME × DOMAIN × TEMPORAL_DO combination
print("\n=== HARTLEY'S F-MAX TEST: INTERVAL_DO within each TIME × DOMAIN × TEMPORAL_DO combination ===")

observed_interval_ratios <- long_data_clean %>%
  group_by(TIME, DOMAIN, TEMPORAL_DO) %>%
  summarise(
    # Calculate variances for each INTERVAL_DO level within this combination
    int5_var = var(MEAN_DIFFERENCE[INTERVAL_DO == "5"], na.rm = TRUE),
    int10_var = var(MEAN_DIFFERENCE[INTERVAL_DO == "10"], na.rm = TRUE),
    # Calculate F-max ratio
    f_max_ratio = max(int5_var, int10_var) / min(int5_var, int10_var),
    .groups = 'drop'
  ) %>%
  select(TIME, DOMAIN, TEMPORAL_DO, int5_var, int10_var, f_max_ratio)

print(observed_interval_ratios)

# =============================================================================
# MIXED ANOVA ANALYSIS
# =============================================================================

# Check data dimensions and structure
print(paste("Data size for ANOVA:", nrow(long_data_clean), "rows"))
print(paste("Number of participants:", length(unique(long_data_clean$ResponseId))))
print(paste("Design factors: TIME (", length(levels(long_data_clean$TIME)), "), DOMAIN (", 
            length(levels(long_data_clean$DOMAIN)), "), INTERVAL (", 
            length(levels(long_data_clean$INTERVAL)), "), TEMPORAL_DO (", 
            length(levels(long_data_clean$TEMPORAL_DO)), "), INTERVAL_DO (", 
            length(levels(long_data_clean$INTERVAL_DO)), ")", sep = ""))

# Check for complete cases
complete_cases <- sum(complete.cases(long_data_clean))
print(paste("Complete cases:", complete_cases, "out of", nrow(long_data_clean)))

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

# =============================================================================
# MIXED ANOVA WITH SPHERICITY CORRECTIONS
# =============================================================================

print("\n=== MIXED ANOVA RESULTS (with sphericity corrections) ===")

# Mixed ANOVA using ezANOVA with automatic sphericity corrections
# Between-subjects: TEMPORAL_DO (2 levels: 01PAST, 02FUT) × INTERVAL_DO (2 levels: 5, 10)
# Within-subjects: TIME (2 levels: Past, Future) × DOMAIN (3 levels: Preferences, Personality, Values) × INTERVAL (3 levels: 5, 10, 5_10)

mixed_anova_model <- ezANOVA(data = long_data_clean, 
                             dv = MEAN_DIFFERENCE, 
                             wid = ResponseId, 
                             between = .(TEMPORAL_DO, INTERVAL_DO), 
                             within = .(TIME, DOMAIN, INTERVAL),
                             type = 3,
                             detailed = TRUE)

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

# Show Mauchly's test for sphericity
print("\nMauchly's Test of Sphericity:")
print(mixed_anova_model$Mauchly)

# Show sphericity-corrected results (Greenhouse-Geisser and Huynh-Feldt)
if(!is.null(mixed_anova_model$`Sphericity Corrections`)) {
  print("\nGreenhouse-Geisser and Huynh-Feldt Corrections:")
  print(mixed_anova_model$`Sphericity Corrections`)
  
  # Extract and display corrected degrees of freedom
  cat("\n=== CORRECTED DEGREES OF FREEDOM ===\n")
  
  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)
  
  cat("\n=== CORRECTED F-TESTS ===\n")
  
  # Between-subjects effects (no sphericity corrections needed)
  cat("\nBETWEEN-SUBJECTS EFFECTS:\n")
  between_effects <- c("TEMPORAL_DO", "INTERVAL_DO", "TEMPORAL_DO:INTERVAL_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)
  cat("\nWITHIN-SUBJECTS EFFECTS:\n")
  
  # 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 (3 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))
  }
  
  # INTERVAL main effect (3 levels, needs sphericity correction)
  if("INTERVAL" %in% anova_table$Effect) {
    f_value <- anova_table$F[anova_table$Effect == "INTERVAL"]
    dfn <- anova_table$DFn[anova_table$Effect == "INTERVAL"]
    dfd <- anova_table$DFd[anova_table$Effect == "INTERVAL"]
    p_value <- anova_table$p[anova_table$Effect == "INTERVAL"]
    cat(sprintf("INTERVAL: F(%d, %d) = %.3f, p = %.6f\n", dfn, dfd, f_value, p_value))
  }
  
  # Interactions with sphericity corrections
  cat("\nINTERACTIONS WITH SPHERICITY CORRECTIONS:\n")
  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 (GENERALIZED ETA SQUARED)
# =============================================================================

print("\n=== EFFECT SIZES (GENERALIZED ETA SQUARED) ===")

# Extract generalized eta squared from ezANOVA (already calculated)
effect_sizes <- mixed_anova_model$ANOVA[, c("Effect", "ges")]
effect_sizes$ges <- round(effect_sizes$ges, 5)
print("Generalized Eta Squared:")
print(effect_sizes)