486 lines
19 KiB
Plaintext
486 lines
19 KiB
Plaintext
---
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title: "Regression Analysis - Assumption Checking"
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subtitle: "IVs: demo_sex, demo_age, demo_edu | DVs: eohiDGEN_mean, ehi_global_mean"
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author: "Irina"
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date: today
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format:
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html:
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theme: cosmo
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toc: true
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toc-depth: 3
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code-fold: false
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code-tools: true
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execute:
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echo: true
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warning: false
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message: false
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---
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## Setup and Data Preparation
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```{r setup}
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#| label: setup
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#| echo: true
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# Load required libraries
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library(dplyr) # Must load first for %>% operator
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library(car)
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library(performance)
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library(see)
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library(ggplot2)
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library(gridExtra)
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library(lmtest) # For bptest and durbinWatsonTest
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# Set options
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options(scipen = 999)
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# Set working directory and load data
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setwd("C:/Users/irina/Documents/DND/EOHI/eohi1")
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data <- read.csv("ehi1.csv")
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```
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```{r data-prep}
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#| label: data-prep
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#| echo: true
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# Check for missing values
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missing_summary <- data %>%
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select(demo_sex, demo_age_1, demo_edu, eohiDGEN_mean, ehi_global_mean) %>%
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summarise_all(~sum(is.na(.)))
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print("Missing values check:")
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print(missing_summary)
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# Remove rows with missing values
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data_clean <- data %>%
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select(pID, demo_sex, demo_age_1, demo_edu, eohiDGEN_mean, ehi_global_mean) %>%
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filter(complete.cases(.))
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print(paste("Clean data dimensions:", paste(dim(data_clean), collapse = " x ")))
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# Recode demo_sex as numeric for regression (0 = Female, 1 = Male)
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data_clean$demo_sex_numeric <- ifelse(data_clean$demo_sex == "Male", 1, 0)
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# Check demo_edu levels and create dummy variables
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print("Education levels:")
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edu_table <- table(data_clean$demo_edu)
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print(edu_table)
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print(paste("Number of education levels:", length(unique(data_clean$demo_edu))))
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# Create dummy variables for education (k-1 coding: 7 levels = 6 dummy variables)
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# Using High School as reference category (excluded dummy)
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data_clean$edu_college <- ifelse(data_clean$demo_edu == "College Diploma/Certificate", 1, 0)
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data_clean$edu_undergrad <- ifelse(data_clean$demo_edu == "University - Undergraduate", 1, 0)
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data_clean$edu_grad <- ifelse(data_clean$demo_edu == "University - Graduate", 1, 0)
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# Check what other education levels exist and create additional dummies
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edu_levels <- unique(data_clean$demo_edu)
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print("All education levels found:")
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for(i in 1:length(edu_levels)) {
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print(paste(i, ":", edu_levels[i]))
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}
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# Create additional dummy variables for other education levels
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# (You'll need to adjust these based on your actual data)
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# Example for additional levels - adjust names and conditions as needed:
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# data_clean$edu_other1 <- ifelse(data_clean$demo_edu == "Other Level 1", 1, 0)
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# data_clean$edu_other2 <- ifelse(data_clean$demo_edu == "Other Level 2", 1, 0)
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# data_clean$edu_other3 <- ifelse(data_clean$demo_edu == "Other Level 3", 1, 0)
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# Note: Once you identify all 7 levels, create 6 dummy variables total (k-1)
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# Verify dummy coding
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print("Sex recoding (0=Female, 1=Male):")
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print(table(data_clean$demo_sex_numeric))
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print("Education dummy variables (k-1 coding with High School as reference):")
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print("High School (reference):", sum(data_clean$demo_edu == "High School (or equivalent)"))
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print("College:", sum(data_clean$edu_college))
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print("Undergraduate:", sum(data_clean$edu_undergrad))
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print("Graduate:", sum(data_clean$edu_grad))
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```
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## Regression Models
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```{r models}
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#| label: models
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#| echo: true
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# Define the 6 regression models
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models <- list()
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# Model 1: demo_sex → eohiDGEN_mean
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models$sex_eohiDGEN <- lm(eohiDGEN_mean ~ demo_sex_numeric, data = data_clean)
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# Model 2: demo_age → eohiDGEN_mean
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models$age_eohiDGEN <- lm(eohiDGEN_mean ~ demo_age, data = data_clean)
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# Model 3: education dummies → eohiDGEN_mean (k-1 coding, HS as reference)
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models$edu_eohiDGEN <- lm(eohiDGEN_mean ~ edu_college + edu_undergrad + edu_grad, data = data_clean)
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# Model 4: demo_sex → ehi_global_mean
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models$sex_ehi_global <- lm(ehi_global_mean ~ demo_sex_numeric, data = data_clean)
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# Model 5: demo_age → ehi_global_mean
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models$age_ehi_global <- lm(ehi_global_mean ~ demo_age, data = data_clean)
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# Model 6: education dummies → ehi_global_mean (k-1 coding, HS as reference)
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models$edu_ehi_global <- lm(ehi_global_mean ~ edu_college + edu_undergrad + edu_grad, data = data_clean)
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```
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## Assumption Checking Functions
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```{r functions}
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#| label: functions
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#| echo: true
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# Function to check linearity assumption
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check_linearity <- function(model, model_name) {
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print(paste("=== LINEARITY CHECK:", model_name, "==="))
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# Residuals vs Fitted plot
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plot(model, which = 1, main = paste("Linearity:", model_name))
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# Component + residual plot (partial residual plot)
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crPlots(model, main = paste("Component+Residual Plot:", model_name))
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return(NULL)
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}
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# Function to check normality of residuals
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check_normality <- function(model, model_name) {
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print(paste("=== NORMALITY CHECK:", model_name, "==="))
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# Q-Q plot
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plot(model, which = 2, main = paste("Q-Q Plot:", model_name))
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# Shapiro-Wilk test
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residuals <- residuals(model)
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shapiro_test <- shapiro.test(residuals)
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print(paste("Shapiro-Wilk test p-value:", format(shapiro_test$p.value, digits = 5)))
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# Kolmogorov-Smirnov test
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ks_test <- ks.test(residuals, "pnorm", mean(residuals), sd(residuals))
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print(paste("Kolmogorov-Smirnov test p-value:", format(ks_test$p.value, digits = 5)))
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# Histogram of residuals
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hist_plot <- ggplot(data.frame(residuals = residuals), aes(x = residuals)) +
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geom_histogram(bins = 30, fill = "lightblue", color = "black") +
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ggtitle(paste("Residuals Histogram:", model_name)) +
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theme_minimal()
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print(hist_plot)
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return(list(shapiro_p = shapiro_test$p.value, ks_p = ks_test$p.value))
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}
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# Function to check homoscedasticity (constant variance)
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check_homoscedasticity <- function(model, model_name) {
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print(paste("=== HOMOSCEDASTICITY CHECK:", model_name, "==="))
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# Scale-Location plot
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plot(model, which = 3, main = paste("Scale-Location Plot:", model_name))
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# Breusch-Pagan test
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bp_test <- bptest(model)
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print(paste("Breusch-Pagan test p-value:", format(bp_test$p.value, digits = 5)))
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# White test (if available)
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tryCatch({
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white_test <- bptest(model, ~ fitted(model) + I(fitted(model)^2))
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print(paste("White test p-value:", format(white_test$p.value, digits = 5)))
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}, error = function(e) {
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print("White test not available for this model")
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})
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return(list(bp_p = bp_test$p.value))
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}
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# Function to check independence (no autocorrelation)
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check_independence <- function(model, model_name) {
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print(paste("=== INDEPENDENCE CHECK:", model_name, "==="))
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# Durbin-Watson test
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dw_test <- durbinWatsonTest(model)
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print(paste("Durbin-Watson statistic:", format(dw_test$dw, digits = 5)))
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print(paste("Durbin-Watson p-value:", format(dw_test$p, digits = 5)))
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# Residuals vs Order plot
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residuals_vs_order <- ggplot(data.frame(
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residuals = residuals(model),
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order = seq_along(residuals(model))
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), aes(x = order, y = residuals)) +
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geom_point(color = "black") +
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geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
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ggtitle(paste("Residuals vs Order:", model_name)) +
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theme_minimal()
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print(residuals_vs_order)
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return(list(dw_stat = dw_test$dw, dw_p = dw_test$p))
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}
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# Function to check for influential observations
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check_influence <- function(model, model_name) {
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print(paste("=== INFLUENCE CHECK:", model_name, "==="))
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# Cook's Distance plot
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plot(model, which = 4, main = paste("Cook's Distance:", model_name))
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# Calculate influence measures
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cooks_d <- cooks.distance(model)
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leverage <- hatvalues(model)
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dffits_val <- dffits(model)
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# Identify influential observations
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cooks_threshold <- 4/length(cooks_d) # Cook's D threshold
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leverage_threshold <- 2 * (length(coef(model))/nobs(model)) # Leverage threshold
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dffits_threshold <- 2 * sqrt(length(coef(model))/nobs(model)) # DFFITS threshold
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influential_cooks <- which(cooks_d > cooks_threshold)
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influential_leverage <- which(leverage > leverage_threshold)
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influential_dffits <- which(abs(dffits_val) > dffits_threshold)
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print(paste("Cook's Distance threshold:", format(cooks_threshold, digits = 5)))
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print(paste("Influential observations (Cook's D):", length(influential_cooks)))
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print(paste("Leverage threshold:", format(leverage_threshold, digits = 5)))
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print(paste("High leverage observations:", length(influential_leverage)))
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print(paste("DFFITS threshold:", format(dffits_threshold, digits = 5)))
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print(paste("Influential observations (DFFITS):", length(influential_dffits)))
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if (length(influential_cooks) > 0) {
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print(paste("Cook's D influential cases:", paste(influential_cooks, collapse = ", ")))
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}
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if (length(influential_leverage) > 0) {
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print(paste("High leverage cases:", paste(influential_leverage, collapse = ", ")))
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}
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if (length(influential_dffits) > 0) {
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print(paste("DFFITS influential cases:", paste(influential_dffits, collapse = ", ")))
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}
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return(list(influential_cooks = influential_cooks,
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influential_leverage = influential_leverage,
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influential_dffits = influential_dffits))
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}
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# Function to get comprehensive model summary
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get_model_summary <- function(model, model_name) {
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print(paste("=== MODEL SUMMARY:", model_name, "==="))
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# Basic model summary
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summary_model <- summary(model)
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print(summary_model)
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# R-squared and adjusted R-squared
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print(paste("R-squared:", format(summary_model$r.squared, digits = 5)))
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print(paste("Adjusted R-squared:", format(summary_model$adj.r.squared, digits = 5)))
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# AIC and BIC
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aic_val <- AIC(model)
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bic_val <- BIC(model)
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print(paste("AIC:", format(aic_val, digits = 5)))
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print(paste("BIC:", format(bic_val, digits = 5)))
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return(list(summary = summary_model, r_squared = summary_model$r.squared,
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adj_r_squared = summary_model$adj.r.squared, aic = aic_val, bic = bic_val))
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}
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```
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## Model 1: Sex → EOHI-DGEN Mean
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```{r model1}
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#| label: model1
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#| echo: true
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model1_summary <- get_model_summary(models$sex_eohiDGEN, "Sex → EOHI-DGEN")
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model1_normality <- check_normality(models$sex_eohiDGEN, "Sex → EOHI-DGEN")
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model1_homosced <- check_homoscedasticity(models$sex_eohiDGEN, "Sex → EOHI-DGEN")
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model1_independence <- check_independence(models$sex_eohiDGEN, "Sex → EOHI-DGEN")
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model1_influence <- check_influence(models$sex_eohiDGEN, "Sex → EOHI-DGEN")
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model1_linearity <- check_linearity(models$sex_eohiDGEN, "Sex → EOHI-DGEN")
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```
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## Model 2: Age → EOHI-DGEN Mean
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```{r model2}
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#| label: model2
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#| echo: true
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model2_summary <- get_model_summary(models$age_eohiDGEN, "Age → EOHI-DGEN")
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model2_normality <- check_normality(models$age_eohiDGEN, "Age → EOHI-DGEN")
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model2_homosced <- check_homoscedasticity(models$age_eohiDGEN, "Age → EOHI-DGEN")
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model2_independence <- check_independence(models$age_eohiDGEN, "Age → EOHI-DGEN")
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model2_influence <- check_influence(models$age_eohiDGEN, "Age → EOHI-DGEN")
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model2_linearity <- check_linearity(models$age_eohiDGEN, "Age → EOHI-DGEN")
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```
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## Model 3: Education → EOHI-DGEN Mean
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```{r model3}
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#| label: model3
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#| echo: true
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model3_summary <- get_model_summary(models$edu_eohiDGEN, "Education → EOHI-DGEN")
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model3_normality <- check_normality(models$edu_eohiDGEN, "Education → EOHI-DGEN")
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model3_homosced <- check_homoscedasticity(models$edu_eohiDGEN, "Education → EOHI-DGEN")
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model3_independence <- check_independence(models$edu_eohiDGEN, "Education → EOHI-DGEN")
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model3_influence <- check_influence(models$edu_eohiDGEN, "Education → EOHI-DGEN")
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model3_linearity <- check_linearity(models$edu_eohiDGEN, "Education → EOHI-DGEN")
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```
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## Model 4: Sex → EHI-Global Mean
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```{r model4}
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#| label: model4
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#| echo: true
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model4_summary <- get_model_summary(models$sex_ehi_global, "Sex → EHI-Global")
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model4_normality <- check_normality(models$sex_ehi_global, "Sex → EHI-Global")
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model4_homosced <- check_homoscedasticity(models$sex_ehi_global, "Sex → EHI-Global")
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model4_independence <- check_independence(models$sex_ehi_global, "Sex → EHI-Global")
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model4_influence <- check_influence(models$sex_ehi_global, "Sex → EHI-Global")
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model4_linearity <- check_linearity(models$sex_ehi_global, "Sex → EHI-Global")
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```
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## Model 5: Age → EHI-Global Mean
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```{r model5}
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#| label: model5
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#| echo: true
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model5_summary <- get_model_summary(models$age_ehi_global, "Age → EHI-Global")
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model5_normality <- check_normality(models$age_ehi_global, "Age → EHI-Global")
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model5_homosced <- check_homoscedasticity(models$age_ehi_global, "Age → EHI-Global")
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model5_independence <- check_independence(models$age_ehi_global, "Age → EHI-Global")
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model5_influence <- check_influence(models$age_ehi_global, "Age → EHI-Global")
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model5_linearity <- check_linearity(models$age_ehi_global, "Age → EHI-Global")
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```
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## Model 6: Education → EHI-Global Mean
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```{r model6}
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#| label: model6
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#| echo: true
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model6_summary <- get_model_summary(models$edu_ehi_global, "Education → EHI-Global")
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model6_normality <- check_normality(models$edu_ehi_global, "Education → EHI-Global")
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model6_homosced <- check_homoscedasticity(models$edu_ehi_global, "Education → EHI-Global")
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model6_independence <- check_independence(models$edu_ehi_global, "Education → EHI-Global")
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model6_influence <- check_influence(models$edu_ehi_global, "Education → EHI-Global")
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model6_linearity <- check_linearity(models$edu_ehi_global, "Education → EHI-Global")
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```
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## Summary Tables
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### Assumption Violation Summary
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```{r violation-summary}
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#| label: violation-summary
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#| echo: true
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# Create summary table
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violation_summary <- data.frame(
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Model = c("Sex → EOHI-DGEN", "Age → EOHI-DGEN", "Education → EOHI-DGEN",
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"Sex → EHI-Global", "Age → EHI-Global", "Education → EHI-Global"),
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Normality = c(
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ifelse(model1_normality$shapiro_p < 0.05, "VIOLATED", "OK"),
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ifelse(model2_normality$shapiro_p < 0.05, "VIOLATED", "OK"),
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ifelse(model3_normality$shapiro_p < 0.05, "VIOLATED", "OK"),
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ifelse(model4_normality$shapiro_p < 0.05, "VIOLATED", "OK"),
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ifelse(model5_normality$shapiro_p < 0.05, "VIOLATED", "OK"),
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ifelse(model6_normality$shapiro_p < 0.05, "VIOLATED", "OK")
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),
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Homoscedasticity = c(
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ifelse(model1_homosced$bp_p < 0.05, "VIOLATED", "OK"),
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ifelse(model2_homosced$bp_p < 0.05, "VIOLATED", "OK"),
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ifelse(model3_homosced$bp_p < 0.05, "VIOLATED", "OK"),
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ifelse(model4_homosced$bp_p < 0.05, "VIOLATED", "OK"),
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ifelse(model5_homosced$bp_p < 0.05, "VIOLATED", "OK"),
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ifelse(model6_homosced$bp_p < 0.05, "VIOLATED", "OK")
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),
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Independence = c(
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ifelse(model1_independence$dw_p < 0.05, "VIOLATED", "OK"),
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ifelse(model2_independence$dw_p < 0.05, "VIOLATED", "OK"),
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ifelse(model3_independence$dw_p < 0.05, "VIOLATED", "OK"),
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ifelse(model4_independence$dw_p < 0.05, "VIOLATED", "OK"),
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ifelse(model5_independence$dw_p < 0.05, "VIOLATED", "OK"),
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ifelse(model6_independence$dw_p < 0.05, "VIOLATED", "OK")
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),
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Influential_Obs = c(
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ifelse(length(model1_influence$influential_cooks) > 0,
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paste("YES (", length(model1_influence$influential_cooks), ")", sep = ""), "NO"),
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ifelse(length(model2_influence$influential_cooks) > 0,
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paste("YES (", length(model2_influence$influential_cooks), ")", sep = ""), "NO"),
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ifelse(length(model3_influence$influential_cooks) > 0,
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paste("YES (", length(model3_influence$influential_cooks), ")", sep = ""), "NO"),
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ifelse(length(model4_influence$influential_cooks) > 0,
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paste("YES (", length(model4_influence$influential_cooks), ")", sep = ""), "NO"),
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ifelse(length(model5_influence$influential_cooks) > 0,
|
|
paste("YES (", length(model5_influence$influential_cooks), ")", sep = ""), "NO"),
|
|
ifelse(length(model6_influence$influential_cooks) > 0,
|
|
paste("YES (", length(model6_influence$influential_cooks), ")", sep = ""), "NO")
|
|
),
|
|
stringsAsFactors = FALSE
|
|
)
|
|
|
|
print(violation_summary)
|
|
```
|
|
|
|
### Model Comparison Summary
|
|
|
|
```{r comparison-summary}
|
|
#| label: comparison-summary
|
|
#| echo: true
|
|
|
|
# Create model comparison table
|
|
comparison_table <- data.frame(
|
|
Model = c("Sex → EOHI-DGEN", "Age → EOHI-DGEN", "Education → EOHI-DGEN",
|
|
"Sex → EHI-Global", "Age → EHI-Global", "Education → EHI-Global"),
|
|
R_Squared = c(model1_summary$r_squared, model2_summary$r_squared, model3_summary$r_squared,
|
|
model4_summary$r_squared, model5_summary$r_squared, model6_summary$r_squared),
|
|
Adj_R_Squared = c(model1_summary$adj_r_squared, model2_summary$adj_r_squared, model3_summary$adj_r_squared,
|
|
model4_summary$adj_r_squared, model5_summary$adj_r_squared, model6_summary$adj_r_squared),
|
|
AIC = c(model1_summary$aic, model2_summary$aic, model3_summary$aic,
|
|
model4_summary$aic, model5_summary$aic, model6_summary$aic),
|
|
BIC = c(model1_summary$bic, model2_summary$bic, model3_summary$bic,
|
|
model4_summary$bic, model5_summary$bic, model6_summary$bic),
|
|
Significant = c(
|
|
ifelse(model1_summary$summary$coefficients[2, 4] < 0.05, "YES", "NO"),
|
|
ifelse(model2_summary$summary$coefficients[2, 4] < 0.05, "YES", "NO"),
|
|
ifelse(model3_summary$summary$coefficients[2, 4] < 0.05, "YES", "NO"),
|
|
ifelse(model4_summary$summary$coefficients[2, 4] < 0.05, "YES", "NO"),
|
|
ifelse(model5_summary$summary$coefficients[2, 4] < 0.05, "YES", "NO"),
|
|
ifelse(model6_summary$summary$coefficients[2, 4] < 0.05, "YES", "NO")
|
|
),
|
|
stringsAsFactors = FALSE
|
|
)
|
|
|
|
print(comparison_table)
|
|
```
|
|
|
|
## Recommendations
|
|
|
|
### For Assumption Violations:
|
|
|
|
**1. Normality Violations:**
|
|
- If violated: Consider transforming the dependent variable (log, sqrt, Box-Cox)
|
|
- Alternative: Use robust regression methods or bootstrapping
|
|
|
|
**2. Homoscedasticity Violations:**
|
|
- If violated: Use weighted least squares or robust standard errors
|
|
- Alternative: Transform the dependent variable or use heteroscedasticity-consistent standard errors
|
|
|
|
**3. Independence Violations:**
|
|
- If violated: Check for clustering or repeated measures structure
|
|
- Alternative: Use mixed-effects models or clustered standard errors
|
|
|
|
**4. Influential Observations:**
|
|
- If present: Examine these cases for data entry errors
|
|
- Consider: Running analysis with and without influential cases
|
|
- Alternative: Use robust regression methods
|
|
|
|
**5. Linearity Violations:**
|
|
- If violated: Add polynomial terms or use splines
|
|
- Alternative: Transform predictors or use non-parametric methods
|
|
|
|
---
|
|
|
|
*Analysis completed for 6 regression models examining the relationship between demographic variables (sex, age, education) and EOHI measures.*
|