Rationale

According to the elaboration likelihood model of persuasion (ELM), humans’ have their attitudes decided through either a central or peripheral processing route. The central processing route means that rational, persuasive arguments are used, which require intense cognitive processing to change a someone’s attitude for a long-term. On the other hand, the peripheral processing route uses messages that require less cognitive processing, and cause a more temporary attitude change.

In this case, we will look at the central processing route to determine if “high-quality” persuasive information about legalizing recreational marijuana in Tennessee can produce long-term attitude change in research participants.

Hypothesis

The amount of time spent consuming “high-quality” persuasive information (“Minutes”) is associated with the likelihood of favoring the legalization of recreational marijuana in Tennessee (“Favor_1”).

Variables & Method

A total of 200 research participants spent 30 minutes with an eye tracker watching them look through a realistic-looking website for a fake organization advocating to legalize recreational marijuana in Tennessee. All 200 had no strong opinions for or against recreational marijuana before the research.

The eye tracker recorded how much of the 30 minutes participants spent looking at persuasive information in favor of legalizing recreational marijuana rather than peripheral cues (“Minutes”).

A month later, the research participants were asked whether they favored or opposed legalizing recreational marijuana. Participants either favored or opposed (“Favor_1”).

Results & Discussion

The graph below shows the distribution of the dependent variable (“Favor_1”) and the independent variable (“Minutes”). The results table, linearity table, and inflection table are also shown.

term	Odds_Ratio	CI_Lower	CI_Upper	P_Value
Logistic Regression Results
Odds Ratios with 95% Confidence Intervals
(Intercept)	0.099	0.044	0.205	0.0000
IV	1.167	1.116	1.227	0.0000

term	Estimate	Std_Error	P_Value
Linearity of the Logit Test (Box-Tidwell)
Interaction term indicates violation if significant
(Intercept)	−2.566	1.100	0.0196
IV	0.262	0.290	0.3657
IV_log	−0.032	0.078	0.6869

Probability	Inflection_Point
Inflection Point of Logistic Curve
Value of IV where predicted probability = 0.50
0.5	14.965

The results supported the hypothesis. As participants spent more time looking at the persuasive information, they were more likely to side in favor of legalizing recreational marijuana. The inflection point shows us that when participants spent about 14.97 minutes interacting with the persuasive content, they had a 50% probability of siding with legalizing recreational marijuana. The logistic regression analysis found the association to be statistically significant.

Code

# ------------------------------
# Install and load required packages
# ------------------------------
if (!require("tidyverse")) install.packages("tidyverse")
if (!require("gt")) install.packages("gt")
if (!require("gtExtras")) install.packages("gtExtras")
if (!require("plotly")) install.packages("plotly")

library(ggplot2)
library(dplyr)
library(gt)
library(gtExtras)
library(plotly)


# ------------------------------
# Read the data
# ------------------------------
mydata <- read.csv("ELM.csv") # <-- EDIT filename

# Specify dependent (DV) and independent (IV) variables
mydata$DV <- mydata$Favor_1   # <-- EDIT DV column
mydata$IV <- mydata$Minutes   # <-- EDIT IV column

# Ensure DV is binary numeric (0/1)
mydata$DV <- as.numeric(as.character(mydata$DV))


# ------------------------------
# Logistic regression plot 
# ------------------------------
logit_plot <- ggplot(mydata, aes(x = IV, y = DV)) +
  geom_point(alpha = 0.5) +   # scatterplot of observed data
  geom_smooth(method = "glm",
              method.args = list(family = "binomial"),
              se = FALSE,
              color = "#1f78b4") +
  labs(title = "Logistic Regression Curve",
       x = "Independent Variable (IV)",
       y = "Dependent Variable (DV)")

logit_plotly <- ggplotly(logit_plot)


# ------------------------------
# Run logistic regression
# ------------------------------
options(scipen = 999)
log.ed <- glm(DV ~ IV, data = mydata, family = "binomial")

# Extract coefficients and odds ratios
results <- broom::tidy(log.ed, conf.int = TRUE, exponentiate = TRUE) %>%
  select(term, estimate, conf.low, conf.high, p.value) %>%
  rename(Odds_Ratio = estimate,
         CI_Lower = conf.low,
         CI_Upper = conf.high,
         P_Value = p.value)

# Display results as a nice gt table
results_table <- results %>%
  gt() %>%
  fmt_number(columns = c(Odds_Ratio, CI_Lower, CI_Upper), decimals = 3) %>%
  fmt_number(columns = P_Value, decimals = 4) %>%
  tab_header(
    title = "Logistic Regression Results",
    subtitle = "Odds Ratios with 95% Confidence Intervals"
  )


# ------------------------------
# Check linearity of the logit (Box-Tidwell test)
# ------------------------------
# (Assumes IV > 0; shift IV if needed)
mydata$IV_log <- mydata$IV * log(mydata$IV)
linearity_test <- glm(DV ~ IV + IV_log, data = mydata, family = "binomial")

linearity_results <- broom::tidy(linearity_test) %>%
  select(term, estimate, std.error, p.value) %>%
  rename(Estimate = estimate,
         Std_Error = std.error,
         P_Value = p.value)

linearity_table <- linearity_results %>%
  gt() %>%
  fmt_number(columns = c(Estimate, Std_Error), decimals = 3) %>%
  fmt_number(columns = P_Value, decimals = 4) %>%
  tab_header(
    title = "Linearity of the Logit Test (Box-Tidwell)",
    subtitle = "Interaction term indicates violation if significant"
  )


# ------------------------------
# Calculate the inflection point (p = .50)
# ------------------------------
p <- 0.50
Inflection_point <- (log(p/(1-p)) - coef(log.ed)[1]) / coef(log.ed)[2]

inflection_table <- tibble(
  Probability = 0.5,
  Inflection_Point = Inflection_point
) %>%
  gt() %>%
  fmt_number(columns = Inflection_Point, decimals = 3) %>%
  tab_header(
    title = "Inflection Point of Logistic Curve",
    subtitle = "Value of IV where predicted probability = 0.50"
  )


# ------------------------------
# Outputs
# ------------------------------
# Interactive plot
logit_plotly

# Tables
results_table
linearity_table
inflection_table

Elaboration Likelihood Analysis

Bradley Krpejs

2026-09-28

Rationale

Hypothesis

Variables & Method

Results & Discussion

Code