1 Giriş

Bu bölmədə CAT simulyasiya nəticələrinin vizual təhlili üçün hərtərəfli qrafik funksiyalar sistemi yaradacağıq. Vizual analiz CAT sistemlərinin performansını anlamaq və nəticələri effektiv şəkildə təqdim etmək üçün əsasdır.

Vizual analiz aşağıdakı məqsədlərə xidmət edir:

Pattern Detection: Məlumatdakı nümunələrin və trendlərin aşkarlanması
Performance Assessment: Sistemin performansının qrafik yolla qiymətləndirilməsi
Quality Control: Problemlərin və anomaliyaların vizual identifikasiyası
Communication: Nəticələrin effektiv və aydın təqdimatı
Decision Support: Qərar qəbul etmə prosesində vizual dəstək

1.1 Vizual Analiz Prinsipləri

1.1.1 Məlumat Vizuallaşdırma Əsasları

Clarity: Aydın və anlaşılan qrafiklər
Accuracy: Məlumatın dəqiq təqdimatı
Efficiency: Məlumatın sürətli qavranılması
Aesthetics: Cəlbedici və professional görünüş

1.1.2 CAT-specific Vizualizasiya Tələbləri

Multi-dimensional Analysis: Çoxölçülü məlumatların təqdimatı
Temporal Patterns: Vaxt ərzində dəyişimlərin göstərilməsi
Group Comparisons: Qruplar arası müqayisələr
Interactive Elements: İnteraktiv elementlərin daxil edilməsi

2 Test Məlumatlarının Hazırlanması

# Test məlumatları yaratmaq üçün funksiya
generate_sample_data <- function(n_subjects = 100, seed = 12345) {
    
    set.seed(seed)
    
    # Simulate CAT results
    true_theta <- rnorm(n_subjects, 0, 1)
    estimation_error <- abs(rnorm(n_subjects, 0, 0.3))
    estimated_theta <- true_theta + rnorm(n_subjects, 0, estimation_error)
    standard_error <- runif(n_subjects, 0.2, 0.5)
    items_administered <- sample(5:30, n_subjects, replace = TRUE)
    bias <- estimated_theta - true_theta
    
    # Derived variables
    ability_group <- cut(true_theta, 
                        breaks = c(-Inf, -1, 0, 1, Inf),
                        labels = c("Aşağı", "Orta-Aşağı", "Orta-Yuxarı", "Yuxarı"))
    
    precision_met <- standard_error <= 0.3
    efficiency <- 1 / (standard_error * items_administered)
    
    results_df <- data.frame(
        examinee_id = 1:n_subjects,
        true_theta = true_theta,
        estimated_theta = estimated_theta,
        estimation_error = estimation_error,
        standard_error = standard_error,
        items_administered = items_administered,
        bias = bias,
        ability_group = ability_group,
        precision_met = precision_met,
        efficiency = efficiency
    )
    
    return(results_df)
}

# Sample data yaratmaq
results_summary <- generate_sample_data(100)

cat("=== TEST MƏLUMATLARI HAZIRLANDI ===\n")

## === TEST MƏLUMATLARI HAZIRLANDI ===

cat("Test alıcı sayı:", nrow(results_summary), "\n")

## Test alıcı sayı: 100

cat("Dəyişən sayı:", ncol(results_summary), "\n")

## Dəyişən sayı: 10

cat("Həqiqi θ aralığı:", round(range(results_summary$true_theta), 2), "\n")

## Həqiqi θ aralığı: -2.38 2.48

cat("Qiymətləndirmə xətası aralığı:", round(range(results_summary$estimation_error), 3), "\n")

## Qiymətləndirmə xətası aralığı: 0.004 0.797

cat("Test uzunluğu aralığı:", range(results_summary$items_administered), "\n\n")

## Test uzunluğu aralığı: 5 30

3 Əsas Vizual Analiz Funksiyaları

# 1. Həqiqi vs Qiymətləndirilmiş qabiliyyət scatter plot
plot_accuracy <- function(results_df, interactive = FALSE) {
    
    # Correlation hesablama
    correlation <- cor(results_df$true_theta, results_df$estimated_theta)
    r_squared <- correlation^2
    
    p <- ggplot(results_df, aes(x = true_theta, y = estimated_theta)) +
        geom_point(aes(color = ability_group), alpha = 0.7, size = 2.5) +
        geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed", size = 1.2) +
        geom_smooth(method = "lm", se = TRUE, color = "blue", alpha = 0.3) +
        labs(title = "Həqiqi vs Qiymətləndirilmiş Qabiliyyət",
             subtitle = paste("r =", round(correlation, 3), " | R² =", round(r_squared, 3)),
             x = "Həqiqi Qabiliyyət (θ)",
             y = "Qiymətləndirilmiş Qabiliyyət (θ̂)",
             color = "Qabiliyyət Qrupu") +
        theme_minimal() +
        theme(legend.position = "bottom") +
        coord_equal() +
        scale_color_viridis_d() +
        annotate("text", x = min(results_df$true_theta), y = max(results_df$estimated_theta), 
                label = "Mükəmməl xətt", color = "red", hjust = 0, vjust = 1)
    
    if (interactive) {
        return(ggplotly(p))
    } else {
        return(p)
    }
}

# 2. Qiymətləndirmə xətasının paylanması
plot_error_distribution <- function(results_df, by_group = FALSE) {
    
    mae <- mean(results_df$estimation_error)
    rmse <- sqrt(mean(results_df$estimation_error^2))
    
    if (by_group) {
        p <- ggplot(results_df, aes(x = estimation_error, fill = ability_group)) +
            geom_histogram(bins = 20, alpha = 0.7, color = "black", position = "identity") +
            facet_wrap(~ ability_group, scales = "free_y") +
            scale_fill_viridis_d()
    } else {
        p <- ggplot(results_df, aes(x = estimation_error)) +
            geom_histogram(bins = 25, fill = "lightcoral", alpha = 0.8, color = "black") +
            geom_density(aes(y = ..scaled..*max(..count..)), alpha = 0.3, fill = "blue")
    }
    
    p <- p +
        labs(title = "Qiymətləndirmə Xətasının Paylanması",
             subtitle = paste("MAE =", round(mae, 3), " | RMSE =", round(rmse, 3)),
             x = "Mütləq Qiymətləndirmə Xətası",
             y = "Tezlik") +
        theme_minimal() +
        geom_vline(xintercept = mae, color = "red", linetype = "dashed", size = 1.2) +
        annotate("text", x = mae + 0.05, y = Inf, 
                label = paste("MAE =", round(mae, 3)), 
                color = "red", hjust = 0, vjust = 1.2)
    
    if (!by_group) {
        p <- p + theme(legend.position = "none")
    }
    
    return(p)
}

# 3. Tapşırıq sayının paylanması
plot_items_distribution <- function(results_df, overlay_stats = TRUE) {
    
    mean_items <- mean(results_df$items_administered)
    median_items <- median(results_df$items_administered)
    
    p <- ggplot(results_df, aes(x = items_administered)) +
        geom_histogram(bins = 20, fill = "lightgreen", alpha = 0.8, color = "black") +
        labs(title = "İstifadə Edilən Tapşırıq Sayının Paylanması",
             subtitle = paste("Orta =", round(mean_items, 1), " | Median =", median_items),
             x = "Tapşırıq Sayı",
             y = "Tezlik") +
        theme_minimal()
    
    if (overlay_stats) {
        p <- p +
            geom_vline(xintercept = mean_items, color = "red", linetype = "dashed", size = 1.2) +
            geom_vline(xintercept = median_items, color = "blue", linetype = "dotted", size = 1.2) +
            annotate("text", x = mean_items + 1, y = Inf, 
                    label = "Orta", color = "red", hjust = 0, vjust = 1.2) +
            annotate("text", x = median_items + 1, y = Inf, 
                    label = "Median", color = "blue", hjust = 0, vjust = 2.4)
    }
    
    return(p)
}

# 4. SE vs Tapşırıq sayı əlaqəsi
plot_se_vs_items <- function(results_df, add_threshold = TRUE) {
    
    correlation <- cor(results_df$items_administered, results_df$standard_error)
    
    p <- ggplot(results_df, aes(x = items_administered, y = standard_error)) +
        geom_point(aes(color = ability_group), alpha = 0.7, size = 2.5) +
        geom_smooth(method = "loess", se = TRUE, color = "red", alpha = 0.3) +
        labs(title = "Standart Xəta vs Tapşırıq Sayı",
             subtitle = paste("Korrelyasiya r =", round(correlation, 3)),
             x = "Tapşırıq Sayı",
             y = "Standart Xəta",
             color = "Qabiliyyət Qrupu") +
        theme_minimal() +
        theme(legend.position = "bottom") +
        scale_color_viridis_d()
    
    if (add_threshold) {
        p <- p +
            geom_hline(yintercept = 0.3, color = "orange", linetype = "dashed", size = 1.2) +
            annotate("text", x = max(results_df$items_administered), y = 0.32, 
                    label = "SE Threshold = 0.3", color = "orange", hjust = 1, vjust = 0)
    }
    
    return(p)
}

# Əsas qrafiklərın göstərilməsi
cat("=== ƏSAS VİZUAL ANALİZ QRAFİKLƏRİ ===\n\n")

## === ƏSAS VİZUAL ANALİZ QRAFİKLƏRİ ===

# Basic plots
p1 <- plot_accuracy(results_summary)
p2 <- plot_error_distribution(results_summary)
p3 <- plot_items_distribution(results_summary)
p4 <- plot_se_vs_items(results_summary)

# İlk dəst qrafiklər
grid.arrange(p1, p2, ncol = 2)

# İkinci dəst qrafiklər
grid.arrange(p3, p4, ncol = 2)

# Group-wise error distribution
p2_group <- plot_error_distribution(results_summary, by_group = TRUE)
print(p2_group)

4 İrəliləmiş Vizualizasiya Funksiyaları

# 5. Comprehensive performance dashboard
create_performance_dashboard <- function(results_df) {
    
    # Calculate summary statistics
    summary_stats <- results_df %>%
        summarise(
            n = n(),
            mean_items = round(mean(items_administered), 1),
            rmse = round(sqrt(mean(estimation_error^2)), 3),
            correlation = round(cor(true_theta, estimated_theta), 3),
            precision_rate = round(mean(precision_met) * 100, 1)
        )
    
    # Main scatter plot
    p1 <- ggplot(results_df, aes(x = true_theta, y = estimated_theta)) +
        geom_point(aes(color = standard_error, size = items_administered), alpha = 0.7) +
        geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
        scale_color_gradient2(low = "green", mid = "yellow", high = "red", 
                             midpoint = 0.3, name = "SE") +
        scale_size_continuous(range = c(1, 4), name = "Items") +
        labs(title = "CAT Performance Dashboard",
             subtitle = paste("n =", summary_stats$n, "| RMSE =", summary_stats$rmse, 
                             "| r =", summary_stats$correlation),
             x = "Həqiqi θ", y = "Qiymətləndirilmiş θ") +
        theme_minimal() +
        coord_equal()
    
    # Error by ability
    p2 <- ggplot(results_df, aes(x = ability_group, y = estimation_error, fill = ability_group)) +
        geom_boxplot(alpha = 0.7) +
        geom_jitter(width = 0.2, alpha = 0.4) +
        scale_fill_viridis_d() +
        labs(title = "Xəta vs Qabiliyyət Qrupu", x = "Qrup", y = "Xəta") +
        theme_minimal() +
        theme(legend.position = "none")
    
    # Precision achievement
    precision_summary <- results_df %>%
        group_by(ability_group) %>%
        summarise(precision_rate = mean(precision_met) * 100, .groups = 'drop')
    
    p3 <- ggplot(precision_summary, aes(x = ability_group, y = precision_rate, fill = ability_group)) +
        geom_col(alpha = 0.8) +
        geom_text(aes(label = paste0(round(precision_rate, 1), "%")), 
                  vjust = -0.5, size = 3) +
        scale_fill_viridis_d() +
        labs(title = "Precision Achievement", x = "Qrup", y = "Rate (%)") +
        theme_minimal() +
        theme(legend.position = "none") +
        ylim(0, 110)
    
    # Test length distribution
    p4 <- ggplot(results_df, aes(x = items_administered, fill = precision_met)) +
        geom_histogram(bins = 15, alpha = 0.7, position = "stack") +
        scale_fill_manual(values = c("red", "green"), 
                         labels = c("SE > 0.3", "SE ≤ 0.3"),
                         name = "Precision") +
        labs(title = "Test Uzunluğu vs Precision", x = "Items", y = "Count") +
        theme_minimal()
    
    return(list(p1 = p1, p2 = p2, p3 = p3, p4 = p4))
}

# 6. Bias analysis visualization
plot_bias_analysis <- function(results_df) {
    
    # Bias by true theta
    p1 <- ggplot(results_df, aes(x = true_theta, y = bias)) +
        geom_point(alpha = 0.6, color = "darkred") +
        geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
        geom_smooth(method = "loess", se = TRUE, color = "blue") +
        labs(title = "Bias Pattern Analysis",
             subtitle = paste("Orta Bias =", round(mean(results_df$bias), 3)),
             x = "Həqiqi θ", y = "Bias (θ̂ - θ)") +
        theme_minimal()
    
    # Bias distribution
    p2 <- ggplot(results_df, aes(x = bias)) +
        geom_histogram(bins = 25, fill = "lightblue", alpha = 0.7, color = "black") +
        geom_vline(xintercept = 0, color = "red", linetype = "dashed") +
        geom_vline(xintercept = mean(results_df$bias), color = "blue", linetype = "dashed") +
        labs(title = "Bias Paylanması", x = "Bias", y = "Tezlik") +
        theme_minimal()
    
    return(list(bias_pattern = p1, bias_distribution = p2))
}

# 7. Efficiency analysis
plot_efficiency_analysis <- function(results_df) {
    
    # Efficiency vs ability
    p1 <- ggplot(results_df, aes(x = true_theta, y = efficiency)) +
        geom_point(aes(color = ability_group), alpha = 0.7, size = 2) +
        geom_smooth(method = "loess", se = TRUE, color = "red") +
        scale_color_viridis_d() +
        labs(title = "Test Effektivliyi vs Qabiliyyət",
             x = "Həqiqi θ", y = "Effektivlik (1/SE×Items)",
             color = "Qrup") +
        theme_minimal()
    
    # Efficiency distribution by group
    p2 <- ggplot(results_df, aes(x = ability_group, y = efficiency, fill = ability_group)) +
        geom_violin(alpha = 0.7) +
        geom_boxplot(width = 0.2, alpha = 0.5) +
        scale_fill_viridis_d() +
        labs(title = "Effektivlik Paylanması", x = "Qrup", y = "Effektivlik") +
        theme_minimal() +
        theme(legend.position = "none")
    
    return(list(efficiency_trend = p1, efficiency_distribution = p2))
}

# İrəliləmiş qrafiklər
dashboard <- create_performance_dashboard(results_summary)
bias_plots <- plot_bias_analysis(results_summary)
efficiency_plots <- plot_efficiency_analysis(results_summary)

# Dashboard göstərimi
grid.arrange(dashboard$p1, dashboard$p2, dashboard$p3, dashboard$p4, ncol = 2)

# Bias və efficiency analizi
grid.arrange(bias_plots$bias_pattern, bias_plots$bias_distribution, ncol = 2)

grid.arrange(efficiency_plots$efficiency_trend, efficiency_plots$efficiency_distribution, ncol = 2)

5 İnteraktiv Vizualizasiya

# 8. Interactive scatter plot
create_interactive_scatter <- function(results_df, save_html = FALSE) {
    
    # Əlavə məlumat tooltips üçün
    results_df$tooltip_text <- paste(
        "ID:", results_df$examinee_id,
        "<br>Həqiqi θ:", round(results_df$true_theta, 3),
        "<br>Qiymətləndirilmiş θ:", round(results_df$estimated_theta, 3),
        "<br>Xəta:", round(results_df$estimation_error, 3),
        "<br>SE:", round(results_df$standard_error, 3),
        "<br>Items:", results_df$items_administered
    )
    
    p <- ggplot(results_df, aes(x = true_theta, y = estimated_theta, 
                               text = tooltip_text, color = ability_group)) +
        geom_point(alpha = 0.7, size = 2) +
        geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
        labs(title = "İnteraktiv CAT Performans Analizi",
             x = "Həqiqi θ", y = "Qiymətləndirilmiş θ",
             color = "Qabiliyyət Qrupu") +
        theme_minimal() +
        scale_color_viridis_d()
    
    interactive_plot <- ggplotly(p, tooltip = "text")
    
    if (save_html) {
        # Faylı saxlamaq üçün (real implementasiyada)
        cat("İnteraktiv qrafik 'interactive_cat_analysis.html' faylında saxlanacaq\n")
    }
    
    return(interactive_plot)
}

# 9. Correlation matrix visualization
plot_correlation_matrix <- function(results_df) {
    
    # Numeric dəyişənləri seçmək
    numeric_vars <- results_df %>%
        select(true_theta, estimated_theta, estimation_error, 
               standard_error, items_administered, efficiency) %>%
        rename(
            "Həqiqi θ" = true_theta,
            "Qiymətləndirməli θ" = estimated_theta,
            "Xəta" = estimation_error,
            "SE" = standard_error,
            "Items" = items_administered,
            "Effektivlik" = efficiency
        )
    
    # Correlation matrix
    cor_matrix <- cor(numeric_vars)
    
    # Custom correlation plot
    corrplot(cor_matrix, 
             method = "circle",
             type = "upper",
             order = "hclust",
             tl.cex = 0.8,
             tl.col = "black",
             cl.ratio = 0.2,
             addCoef.col = "black",
             number.cex = 0.7,
             title = "Dəyişənlər Arasında Korrelyasiya",
             mar = c(0,0,1,0))
    
    return(cor_matrix)
}

# 10. Multi-panel summary plot
create_summary_multipanel <- function(results_df) {
    
    # Hazırlıq
    results_long <- results_df %>%
        select(examinee_id, true_theta, estimated_theta, estimation_error, 
               standard_error, items_administered) %>%
        pivot_longer(cols = c(estimation_error, standard_error, items_administered),
                     names_to = "metric", values_to = "value")
    
    results_long$metric <- factor(results_long$metric,
                                 levels = c("estimation_error", "standard_error", "items_administered"),
                                 labels = c("Qiymətləndirmə Xətası", "Standart Xəta", "Test Uzunluğu"))
    
    # Multi-panel plot
    p <- ggplot(results_long, aes(x = true_theta, y = value)) +
        geom_point(alpha = 0.6, color = "steelblue") +
        geom_smooth(method = "loess", se = TRUE, color = "red") +
        facet_wrap(~ metric, scales = "free_y", ncol = 3) +
        labs(title = "CAT Metrics vs Həqiqi Qabiliyyət",
             x = "Həqiqi θ", y = "Dəyər") +
        theme_minimal() +
        theme(strip.text = element_text(size = 10, face = "bold"))
    
    return(p)
}

# İnteraktiv və multipanel qrafiklər
cat("İnteraktiv və ətraflı qrafiklər yaradılır...\n\n")

## İnteraktiv və ətraflı qrafiklər yaradılır...

# Interactive scatter (static version for demo)
# interactive_scatter <- create_interactive_scatter(results_summary)
# print(interactive_scatter)

# Correlation matrix
correlation_matrix <- plot_correlation_matrix(results_summary)

# Multi-panel summary
multipanel_plot <- create_summary_multipanel(results_summary)
print(multipanel_plot)

6 Specialized Təhlil Qrafiklər

# 11. Convergence analysis visualization (simulated)
plot_convergence_analysis <- function(results_df, n_subjects = 5) {
    
    # Simulated convergence data
    convergence_data <- data.frame()
    
    for (i in 1:n_subjects) {
        subject_data <- results_df[i, ]
        n_steps <- subject_data$items_administered
        
        # Simulate theta progression
        theta_progression <- cumsum(rnorm(n_steps, 0, 0.1)) + subject_data$true_theta
        se_progression <- 1 / sqrt(1:n_steps)
        
        temp_data <- data.frame(
            Subject = paste("Test alıcısı", i),
            Step = 1:n_steps,
            Theta_Est = theta_progression,
            SE = se_progression,
            True_Theta = subject_data$true_theta
        )
        
        convergence_data <- rbind(convergence_data, temp_data)
    }
    
    # Theta convergence
    p1 <- ggplot(convergence_data, aes(x = Step, y = Theta_Est, color = Subject)) +
        geom_line(size = 1.2, alpha = 0.8) +
        geom_point(size = 2, alpha = 0.6) +
        facet_wrap(~ Subject, scales = "free_y") +
        geom_hline(aes(yintercept = True_Theta), linetype = "dashed", color = "red") +
        labs(title = "Theta Konvergensiyası",
             x = "Test Addımı", y = "Qiymətləndirilmiş θ") +
        theme_minimal() +
        theme(legend.position = "none")
    
    # SE progression
    p2 <- ggplot(convergence_data, aes(x = Step, y = SE, color = Subject)) +
        geom_line(size = 1.2, alpha = 0.8) +
        geom_point(size = 2, alpha = 0.6) +
        geom_hline(yintercept = 0.3, linetype = "dashed", color = "orange") +
        labs(title = "Standart Xəta Azalması",
             x = "Test Addımı", y = "SE") +
        theme_minimal() +
        scale_color_viridis_d()
    
    return(list(theta_convergence = p1, se_progression = p2))
}

# 12. Item usage heatmap (simulated)
plot_item_usage_heatmap <- function(results_df, n_items = 50) {
    
    # Simulate item usage data
    set.seed(123)
    item_usage_matrix <- matrix(0, nrow = nrow(results_df), ncol = n_items)
    
    for (i in 1:nrow(results_df)) {
        n_used <- results_df$items_administered[i]
        used_items <- sample(1:n_items, n_used)
        item_usage_matrix[i, used_items] <- 1
    }
    
    # Convert to long format
    item_usage_long <- expand.grid(
        Subject = 1:nrow(results_df),
        Item = 1:n_items
    )
    item_usage_long$Used <- as.vector(item_usage_matrix)
    
    # Calculate item usage frequency
    item_freq <- colSums(item_usage_matrix)
    top_items <- order(item_freq, decreasing = TRUE)[1:20]
    
    # Filter for top used items and subset of subjects
    subset_data <- item_usage_long %>%
        filter(Item %in% top_items, Subject <= 20)
    
    p <- ggplot(subset_data, aes(x = factor(Item), y = factor(Subject), fill = factor(Used))) +
        geom_tile(color = "white") +
        scale_fill_manual(values = c("0" = "white", "1" = "steelblue"),
                         labels = c("İstifadə edilməyib", "İstifadə edilib"),
                         name = "Status") +
        labs(title = "Item İstifadə Pattern (İlk 20 test alıcısı, Ən çox istifadə edilən items)",
             x = "Item ID", y = "Test Alıcısı ID") +
        theme_minimal() +
        theme(axis.text.x = element_text(angle = 45, hjust = 1))
    
    return(p)
}

# 13. Quality control charts
create_quality_control_charts <- function(results_df) {
    
    # Moving average for monitoring
    results_df$order <- 1:nrow(results_df)
    window_size <- 10
    
    # Calculate moving averages
    moving_avg_error <- rep(NA, nrow(results_df))
    moving_avg_se <- rep(NA, nrow(results_df))
    
    for (i in window_size:nrow(results_df)) {
        start_idx <- max(1, i - window_size + 1)
        moving_avg_error[i] <- mean(results_df$estimation_error[start_idx:i])
        moving_avg_se[i] <- mean(results_df$standard_error[start_idx:i])
    }
    
    results_df$moving_avg_error <- moving_avg_error
    results_df$moving_avg_se <- moving_avg_se
    
    # Error control chart
    p1 <- ggplot(results_df, aes(x = order)) +
        geom_point(aes(y = estimation_error), alpha = 0.5, color = "gray") +
        geom_line(aes(y = moving_avg_error), color = "blue", size = 1.2) +
        geom_hline(yintercept = mean(results_df$estimation_error, na.rm = TRUE), 
                   color = "red", linetype = "dashed") +
        geom_hline(yintercept = mean(results_df$estimation_error, na.rm = TRUE) + 
                   2*sd(results_df$estimation_error, na.rm = TRUE), 
                   color = "orange", linetype = "dotted") +
        labs(title = "Qiymətləndirmə Xətası Nəzarət Qrafiki",
             subtitle = paste("Hərəkətli orta (", window_size, "sınaq)"),
             x = "Test Alıcısı Sıra Nömrəsi", y = "Qiymətləndirmə Xətası") +
        theme_minimal()
    
    # SE control chart
    p2 <- ggplot(results_df, aes(x = order)) +
        geom_point(aes(y = standard_error), alpha = 0.5, color = "gray") +
        geom_line(aes(y = moving_avg_se), color = "green", size = 1.2) +
        geom_hline(yintercept = 0.3, color = "red", linetype = "dashed") +
        geom_hline(yintercept = mean(results_df$standard_error, na.rm = TRUE), 
                   color = "blue", linetype = "dashed") +
        labs(title = "Standart Xəta Nəzarət Qrafiki",
             x = "Test Alıcısı Sıra Nömrəsi", y = "Standart Xəta") +
        theme_minimal()
    
    return(list(error_control = p1, se_control = p2))
}

# Specialized qrafiklər
convergence_plots <- plot_convergence_analysis(results_summary)
item_heatmap <- plot_item_usage_heatmap(results_summary)
qc_charts <- create_quality_control_charts(results_summary)

# Convergence analysis
grid.arrange(convergence_plots$theta_convergence, convergence_plots$se_progression, ncol = 1)

# Item usage heatmap
print(item_heatmap)

# Quality control charts
grid.arrange(qc_charts$error_control, qc_charts$se_control, ncol = 1)

7 Comprehensive Reporting Dashboard

# 14. Executive dashboard
create_executive_dashboard <- function(results_df) {
    
    # Calculate key metrics
    key_metrics <- list(
        n_subjects = nrow(results_df),
        mean_items = round(mean(results_df$items_administered), 1),
        rmse = round(sqrt(mean(results_df$estimation_error^2)), 3),
        correlation = round(cor(results_df$true_theta, results_df$estimated_theta), 3),
        precision_rate = round(mean(results_df$precision_met) * 100, 1),
        efficiency = round(30 / mean(results_df$items_administered), 2)
    )
    
    # Create summary text plot
    summary_text <- paste(
        "CAT SİSTEMİ PERFORMANS XÜLASƏSİ\n\n",
        "Test alıcı sayı: ", key_metrics$n_subjects, "\n",
        "Orta test uzunluğu: ", key_metrics$mean_items, " item\n",
        "RMSE: ", key_metrics$rmse, "\n",
        "Validity (r): ", key_metrics$correlation, "\n",
        "Precision rate: ", key_metrics$precision_rate, "%\n",
        "Efficiency ratio: ", key_metrics$efficiency, "\n\n",
        "STATUS: ", 
        ifelse(key_metrics$rmse < 0.4 & key_metrics$correlation > 0.8, 
               "✅ ƏLA PERFORMANS", "⚠️ TƏKMİLLƏŞDİRMƏ LAZIM")
    )
    
    # Text plot
    p_text <- ggplot() + 
        annotate("text", x = 0.5, y = 0.5, label = summary_text, 
                size = 4, hjust = 0.5, vjust = 0.5, family = "mono") +
        theme_void() +
        labs(title = "İcra Xülasəsi")
    
    # Performance gauge (simulated with bar chart)
    performance_data <- data.frame(
        Metric = c("Validity", "Precision", "Efficiency", "Overall"),
        Score = c(
            min(key_metrics$correlation * 100, 100),
            key_metrics$precision_rate,
            min(key_metrics$efficiency * 50, 100),
            NA
        )
    )
    performance_data$Score[4] <- mean(performance_data$Score[1:3], na.rm = TRUE)
    
    p_gauge <- ggplot(performance_data, aes(x = Metric, y = Score, fill = Metric)) +
        geom_col(alpha = 0.8) +
        geom_text(aes(label = paste0(round(Score, 1), "%")), 
                  vjust = -0.5, size = 3) +
        coord_cartesian(ylim = c(0, 110)) +
        scale_fill_viridis_d() +
        labs(title = "Performans Skorları", y = "Skor (%)", x = "") +
        theme_minimal() +
        theme(legend.position = "none")
    
    # Trend analysis
    results_df$batch <- cut(1:nrow(results_df), breaks = 5, labels = 1:5)
    trend_data <- results_df %>%
        group_by(batch) %>%
        summarise(
            Mean_Error = mean(estimation_error),
            Mean_SE = mean(standard_error),
            Mean_Items = mean(items_administered),
            .groups = 'drop'
        )
    
    trend_long <- trend_data %>%
        pivot_longer(cols = c(Mean_Error, Mean_SE, Mean_Items),
                     names_to = "Metric", values_to = "Value") %>%
        mutate(Metric = recode(Metric,
                              "Mean_Error" = "Orta Xəta",
                              "Mean_SE" = "Orta SE", 
                              "Mean_Items" = "Orta Items"))
    
    p_trend <- ggplot(trend_long, aes(x = batch, y = Value, color = Metric, group = Metric)) +
        geom_line(size = 1.2) +
        geom_point(size = 3) +
        facet_wrap(~ Metric, scales = "free_y") +
        scale_color_viridis_d() +
        labs(title = "Performans Trendi", x = "Batch", y = "Dəyər") +
        theme_minimal() +
        theme(legend.position = "none")
    
    return(list(
        summary = p_text,
        performance = p_gauge,
        trend = p_trend,
        metrics = key_metrics
    ))
}

# 15. Comprehensive comparison plot
create_comparison_plot <- function(results_df, scenarios = NULL) {
    
    if (is.null(scenarios)) {
        # Create simulated comparison scenarios
        scenarios <- list(
            "Current" = results_df,
            "Scenario A" = results_df %>% 
                mutate(standard_error = standard_error * 0.9,
                       items_administered = items_administered + 2),
            "Scenario B" = results_df %>% 
                mutate(standard_error = standard_error * 1.1,
                       items_administered = items_administered - 1)
        )
    }
    
    # Combine scenarios
    comparison_data <- data.frame()
    for (i in 1:length(scenarios)) {
        scenario_name <- names(scenarios)[i]
        scenario_data <- scenarios[[i]]
        scenario_data$Scenario <- scenario_name
        comparison_data <- rbind(comparison_data, scenario_data)
    }
    
    # Summary comparison
    scenario_summary <- comparison_data %>%
        group_by(Scenario) %>%
        summarise(
            Mean_Items = mean(items_administered),
            Mean_SE = mean(standard_error),
            RMSE = sqrt(mean(estimation_error^2)),
            Precision_Rate = mean(precision_met) * 100,
            .groups = 'drop'
        )
    
    # Comparison plots
    p1 <- ggplot(scenario_summary, aes(x = Scenario, y = Mean_Items, fill = Scenario)) +
        geom_col(alpha = 0.8) +
        geom_text(aes(label = round(Mean_Items, 1)), vjust = -0.5) +
        scale_fill_viridis_d() +
        labs(title = "Orta Test Uzunluğu", y = "Items") +
        theme_minimal() +
        theme(legend.position = "none")
    
    p2 <- ggplot(scenario_summary, aes(x = Scenario, y = Mean_SE, fill = Scenario)) +
        geom_col(alpha = 0.8) +
        geom_text(aes(label = round(Mean_SE, 3)), vjust = -0.5) +
        geom_hline(yintercept = 0.3, color = "red", linetype = "dashed") +
        scale_fill_viridis_d() +
        labs(title = "Orta SE", y = "Standard Error") +
        theme_minimal() +
        theme(legend.position = "none")
    
    p3 <- ggplot(scenario_summary, aes(x = Scenario, y = RMSE, fill = Scenario)) +
        geom_col(alpha = 0.8) +
        geom_text(aes(label = round(RMSE, 3)), vjust = -0.5) +
        scale_fill_viridis_d() +
        labs(title = "RMSE", y = "Root Mean Square Error") +
        theme_minimal() +
        theme(legend.position = "none")
    
    p4 <- ggplot(scenario_summary, aes(x = Scenario, y = Precision_Rate, fill = Scenario)) +
        geom_col(alpha = 0.8) +
        geom_text(aes(label = paste0(round(Precision_Rate, 1), "%")), vjust = -0.5) +
        scale_fill_viridis_d() +
        labs(title = "Precision Rate", y = "Rate (%)") +
        theme_minimal() +
        theme(legend.position = "none")
    
    return(list(p1 = p1, p2 = p2, p3 = p3, p4 = p4, summary = scenario_summary))
}

# Executive dashboard
executive_dash <- create_executive_dashboard(results_summary)
comparison_plots <- create_comparison_plot(results_summary)

# Executive dashboard göstərimi
grid.arrange(executive_dash$summary, executive_dash$performance, ncol = 2)

print(executive_dash$trend)

# Comparison plots
grid.arrange(comparison_plots$p1, comparison_plots$p2, 
             comparison_plots$p3, comparison_plots$p4, ncol = 2)

8 Export və Sharing Funksiyaları

# 16. Export functions for different formats
export_visualizations <- function(plot_list, output_dir = "cat_visualizations", 
                                 formats = c("png", "pdf", "svg")) {
    
    cat("=== VİZUALLAşDIRMA EKSPORTu ===\n\n")
    cat("Export directory:", output_dir, "\n")
    cat("Export formatları:", paste(formats, collapse = ", "), "\n\n")
    
    # Create directory (simulated)
    cat("📁 Directory yaradılır...\n")
    
    # Export each plot (simulated)
    plot_names <- names(plot_list)
    
    for (i in 1:length(plot_list)) {
        plot_name <- ifelse(is.null(plot_names) || plot_names[i] == "", 
                           paste0("plot_", i), plot_names[i])
        
        for (format in formats) {
            filename <- paste0(plot_name, ".", format)
            cat("📊 Export edilir:", filename, "\n")
            
            # Real implementasiyada:
            # ggsave(filename = file.path(output_dir, filename), 
            #        plot = plot_list[[i]], 
            #        width = 10, height = 6, dpi = 300)
        }
    }
    
    cat("\n✅ Bütün qrafiklər uğurla export edildi!\n\n")
    
    # Create index file info
    cat("📋 Index faylı yaradılır: visualization_index.html\n")
    cat("🔗 Sharing link yaradılır: cat_analysis_report.html\n\n")
    
    return(paste0(output_dir, "/visualization_index.html"))
}

# 17. Create presentation-ready plots
create_presentation_plots <- function(results_df, theme_type = "professional") {
    
    cat("=== PRESENTASİYA QRAFİKLƏRİ ===\n\n")
    
    # Custom theme
    if (theme_type == "professional") {
        custom_theme <- theme_minimal() +
            theme(
                plot.title = element_text(size = 14, face = "bold", hjust = 0.5),
                plot.subtitle = element_text(size = 12, hjust = 0.5),
                axis.title = element_text(size = 12, face = "bold"),
                axis.text = element_text(size = 10),
                legend.title = element_text(size = 11, face = "bold"),
                legend.text = element_text(size = 10),
                panel.grid.minor = element_blank(),
                plot.background = element_rect(fill = "white", color = NA),
                panel.background = element_rect(fill = "white", color = NA)
            )
    } else {
        custom_theme <- theme_light()
    }
    
    # Key slides
    slide1 <- ggplot(results_df, aes(x = true_theta, y = estimated_theta)) +
        geom_point(aes(color = ability_group), alpha = 0.7, size = 3) +
        geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed", size = 1.5) +
        scale_color_viridis_d() +
        labs(title = "CAT Sistem Performansı",
             subtitle = paste("Validity: r =", round(cor(results_df$true_theta, results_df$estimated_theta), 3)),
             x = "Həqiqi Qabiliyyət", y = "Qiymətləndirilmiş Qabiliyyət",
             color = "Qabiliyyət Qrupu") +
        custom_theme +
        coord_equal()
    
    slide2 <- results_df %>%
        group_by(ability_group) %>%
        summarise(
            Mean_Items = mean(items_administered),
            Mean_SE = mean(standard_error),
            Precision_Rate = mean(precision_met) * 100,
            .groups = 'drop'
        ) %>%
        pivot_longer(cols = c(Mean_Items, Mean_SE, Precision_Rate),
                     names_to = "Metric", values_to = "Value") %>%
        mutate(Metric = recode(Metric,
                              "Mean_Items" = "Orta Test Uzunluğu",
                              "Mean_SE" = "Orta SE",
                              "Precision_Rate" = "Precision Rate (%)")) %>%
        ggplot(aes(x = ability_group, y = Value, fill = ability_group)) +
        geom_col(alpha = 0.8) +
        facet_wrap(~ Metric, scales = "free_y") +
        scale_fill_viridis_d() +
        labs(title = "Qabiliyyət Qruplarına Görə Performans",
             x = "Qabiliyyət Qrupu", y = "Dəyər",
             fill = "Qrup") +
        custom_theme +
        theme(legend.position = "none")
    
    slide3 <- ggplot(results_df, aes(x = items_administered, y = standard_error, color = precision_met)) +
        geom_point(alpha = 0.7, size = 3) +
        geom_hline(yintercept = 0.3, color = "red", linetype = "dashed", size = 1.2) +
        scale_color_manual(values = c("red", "green"), 
                          labels = c("SE > 0.3", "SE ≤ 0.3"),
                          name = "Precision Status") +
        labs(title = "Effektivlik vs Precision",
             subtitle = "Test uzunluğu və dəqiqlik arasında əlaqə",
             x = "Test Uzunluğu", y = "Standart Xəta") +
        custom_theme
    
    cat("📊 Slide 1: Ana performans qrafiki\n")
    cat("📊 Slide 2: Qrup müqayisə qrafiki\n") 
    cat("📊 Slide 3: Effektivlik analizi\n\n")
    
    return(list(
        slide1 = slide1,
        slide2 = slide2, 
        slide3 = slide3
    ))
}

# 18. Generate automated report
generate_visual_report <- function(results_df, output_format = "html") {
    
    cat("=== AVTOMATİK VİZUAL HESABAT ===\n\n")
    
    # Report metadata
    report_info <- list(
        title = "CAT Sistem Analizi Hesabatı",
        date = Sys.Date(),
        n_subjects = nrow(results_df),
        analysis_type = "Comprehensive Visual Analysis"
    )
    
    # Key findings
    key_findings <- list(
        validity = round(cor(results_df$true_theta, results_df$estimated_theta), 3),
        rmse = round(sqrt(mean(results_df$estimation_error^2)), 3),
        precision_rate = round(mean(results_df$precision_met) * 100, 1),
        efficiency = round(30 / mean(results_df$items_administered), 2)
    )
    
    # Report sections
    cat("📋 HESABAT KOMPONENTLƏRİ:\n")
    cat("1. Executive Summary\n")
    cat("2. Performance Overview\n") 
    cat("3. Detailed Analysis\n")
    cat("4. Quality Control\n")
    cat("5. Recommendations\n\n")
    
    # Recommendations based on findings
    recommendations <- c()
    
    if (key_findings$validity < 0.8) {
        recommendations <- c(recommendations, "• Validity yaxşılaşdırılması lazımdır")
    }
    
    if (key_findings$rmse > 0.4) {
        recommendations <- c(recommendations, "• Qiymətləndirmə dəqiqliyinin artırılması")
    }
    
    if (key_findings$precision_rate < 70) {
        recommendations <- c(recommendations, "• Precision rate artırılması")
    }
    
    if (key_findings$efficiency < 1.5) {
        recommendations <- c(recommendations, "• Test səmərəliliyinin optimallaşdırılması")
    }
    
    if (length(recommendations) == 0) {
        recommendations <- "✅ Sistem əla performans göstərir"
    }
    
    cat("💡 ƏSaS TOVSİYƏLƏR:\n")
    cat(paste(recommendations, collapse = "\n"), "\n\n")
    
    cat("📁 Hesabat faylları (", output_format, " formatında):\n")
    cat("• cat_visual_report.", output_format, "\n")
    cat("• interactive_dashboard.html\n")
    cat("• presentation_slides.pptx\n")
    cat("• technical_appendix.pdf\n\n")
    
    return(list(
        report_info = report_info,
        key_findings = key_findings,
        recommendations = recommendations
    ))
}

# Export və reporting
all_plots <- list(
    accuracy = plot_accuracy(results_summary),
    error_dist = plot_error_distribution(results_summary),
    items_dist = plot_items_distribution(results_summary),
    se_vs_items = plot_se_vs_items(results_summary)
)

export_info <- export_visualizations(all_plots)

## === VİZUALLAşDIRMA EKSPORTu ===
## 
## Export directory: cat_visualizations 
## Export formatları: png, pdf, svg 
## 
## 📁 Directory yaradılır...
## 📊 Export edilir: accuracy.png 
## 📊 Export edilir: accuracy.pdf 
## 📊 Export edilir: accuracy.svg 
## 📊 Export edilir: error_dist.png 
## 📊 Export edilir: error_dist.pdf 
## 📊 Export edilir: error_dist.svg 
## 📊 Export edilir: items_dist.png 
## 📊 Export edilir: items_dist.pdf 
## 📊 Export edilir: items_dist.svg 
## 📊 Export edilir: se_vs_items.png 
## 📊 Export edilir: se_vs_items.pdf 
## 📊 Export edilir: se_vs_items.svg 
## 
## ✅ Bütün qrafiklər uğurla export edildi!
## 
## 📋 Index faylı yaradılır: visualization_index.html
## 🔗 Sharing link yaradılır: cat_analysis_report.html

presentation_slides <- create_presentation_plots(results_summary)

## === PRESENTASİYA QRAFİKLƏRİ ===
## 
## 📊 Slide 1: Ana performans qrafiki
## 📊 Slide 2: Qrup müqayisə qrafiki
## 📊 Slide 3: Effektivlik analizi

visual_report <- generate_visual_report(results_summary)

## === AVTOMATİK VİZUAL HESABAT ===
## 
## 📋 HESABAT KOMPONENTLƏRİ:
## 1. Executive Summary
## 2. Performance Overview
## 3. Detailed Analysis
## 4. Quality Control
## 5. Recommendations
## 
## 💡 ƏSaS TOVSİYƏLƏR:
## • Precision rate artırılması 
## 
## 📁 Hesabat faylları ( html  formatında):
## • cat_visual_report. html 
## • interactive_dashboard.html
## • presentation_slides.pptx
## • technical_appendix.pdf

# Presentation slides göstərimi
grid.arrange(presentation_slides$slide1, presentation_slides$slide2, ncol = 2)

print(presentation_slides$slide3)

9 Nəticə və Tövsiyələr

Bu bölmədə CAT simulyasiya nəticələrinin hərtərəfli vizual təhlili üçün professional visualizasiya sistemi yaratdıq.

9.1 Əsas Nəticələr

9.1.1 1. Vizual Analiz Arsenalı

Basic Plots: Fundamental performance indicators
Advanced Dashboards: Multi-dimensional analysis tools
Interactive Elements: Dynamic exploration capabilities
Specialized Charts: Domain-specific visualizations

9.1.2 2. Presentation Solutions

Executive Dashboards: High-level summary views
Technical Analysis: Detailed diagnostic plots
Comparative Views: Scenario comparison tools
Quality Control: Process monitoring charts

9.2 Praktiki Dəyər

9.2.1 1. Decision Support

Visual Evidence: Data-driven decision making
Trend Detection: Pattern recognition və early warning
Performance Monitoring: Real-time quality control
Stakeholder Communication: Clear və compelling presentation

9.2.2 2. Research Applications

Exploratory Analysis: Data pattern discovery
Hypothesis Testing: Visual validation tools
Publication Ready: Journal-quality graphics
Reproducible Research: Automated visualization pipelines

9.2.3 3. Operational Excellence

Quality Assurance: Visual QC protocols
Process Improvement: Performance optimization guides
Training Materials: Educational visualization tools
Documentation: Comprehensive visual records

9.3 Best Practices

9.3.1 1. Design Principles

Clarity over Complexity: Simple və clear messaging
Consistency: Unified visual language
Accessibility: Color-blind friendly palettes
Professional Aesthetics: Publication-quality standards

9.3.2 2. Technical Excellence

Scalability: Efficient rendering for large datasets
Interactivity: User-friendly exploration tools
Responsiveness: Multi-device compatibility
Performance: Fast loading və smooth interaction

9.3.3 3. Communication Effectiveness

Audience Awareness: Tailored to viewer expertise
Story Telling: Narrative-driven presentation
Action Orientation: Clear recommendations
Evidence Based: Data-supported conclusions

9.4 Gələcək İnkişaf

9.4.1 1. Advanced Technologies

AI-Powered Insights: Automated pattern detection
Real-time Analytics: Live data visualization
AR/VR Integration: Immersive data exploration
Voice Interaction: Natural language queries

9.4.2 2. Enhanced Functionality

Custom Themes: Brand-specific styling
Advanced Interactions: Drill-down capabilities
Integration APIs: Third-party tool connection
Cloud Deployment: Scalable hosting solutions

9.4.3 3. User Experience

Personalization: User-specific dashboards
Mobile Optimization: Touch-friendly interfaces
Collaborative Features: Team-based analysis tools
Learning Paths: Progressive skill development

Qeyd: Bu vizual analiz sistemi CAT tədqiqatları və praktiki tətbiqlər üçün professional səviyyədə visualization toolkit təqdim edir. Sistem modular struktura malikdir və müxtəlif tələblərə uyğunlaşdırıla bilər.

Bölmə 17: Vizual Analiz Funksiyaları

Kompüter Adaptiv Testləşmə (CAT) Tədrisi

CAT Tədrisi

2025-07-12

1 Giriş

1.1 Vizual Analiz Prinsipləri

1.1.1 Məlumat Vizuallaşdırma Əsasları

1.1.2 CAT-specific Vizualizasiya Tələbləri

2 Test Məlumatlarının Hazırlanması

3 Əsas Vizual Analiz Funksiyaları

4 İrəliləmiş Vizualizasiya Funksiyaları

5 İnteraktiv Vizualizasiya

6 Specialized Təhlil Qrafiklər

7 Comprehensive Reporting Dashboard

9 Nəticə və Tövsiyələr

9.1 Əsas Nəticələr

9.1.1 1. Vizual Analiz Arsenalı

9.1.2 2. Presentation Solutions

9.2 Praktiki Dəyər

9.2.1 1. Decision Support

9.2.2 2. Research Applications

9.2.3 3. Operational Excellence

9.3 Best Practices

9.3.1 1. Design Principles

9.3.2 2. Technical Excellence

9.3.3 3. Communication Effectiveness

9.4 Gələcək İnkişaf

9.4.1 1. Advanced Technologies

9.4.2 2. Enhanced Functionality

9.4.3 3. User Experience

Bölmə 17: Vizual Analiz Funksiyaları

Kompüter Adaptiv Testləşmə (CAT) Tədrisi

CAT Tədrisi

2025-07-12

1 Giriş

1.1 Vizual Analiz Prinsipləri

1.1.1 Məlumat Vizuallaşdırma Əsasları

1.1.2 CAT-specific Vizualizasiya Tələbləri

2 Test Məlumatlarının Hazırlanması

3 Əsas Vizual Analiz Funksiyaları

4 İrəliləmiş Vizualizasiya Funksiyaları

5 İnteraktiv Vizualizasiya

6 Specialized Təhlil Qrafiklər

7 Comprehensive Reporting Dashboard

8 Export və Sharing Funksiyaları

9 Nəticə və Tövsiyələr

9.1 Əsas Nəticələr

9.1.1 1. Vizual Analiz Arsenalı

9.1.2 2. Presentation Solutions

9.1.3 3. Export və Sharing

9.2 Praktiki Dəyər

9.2.1 1. Decision Support

9.2.2 2. Research Applications

9.2.3 3. Operational Excellence

9.3 Best Practices

9.3.1 1. Design Principles

9.3.2 2. Technical Excellence

9.3.3 3. Communication Effectiveness

9.4 Gələcək İnkişaf

9.4.1 1. Advanced Technologies

9.4.2 2. Enhanced Functionality

9.4.3 3. User Experience