Rationale

The Elaboration Likelihood Model (ELM) explains that persuasion happens through two routes. The central route is characterized by rational arguments that require relatively intense cognitive processing to understand but tend to cause enduring attitude change. The peripheral route is characterized by messages that require relatively little cognitive processing to understand and tend to produce comparatively temporary attitude change. Which route is used depends on an individual’s motivation and ability to process the message.

ELM predicts that people high in elaboration will be persuaded more by strong arguments on the Marijuana Policy Project (MPP) website, while those low in elaboration will be influenced more by peripheral cues such as testimonials or endorsements.

Hypothesis

The odds of supporting legalized marijuana will increase as time spent viewing content on the MPP website increases.

Variables & method

The dependent variable in this study was a categorical measure of opposition (0) or support (1) of legalizing marijuana after six months have passed. The independent variable was a continuous number of minutes, out of 30, spent reading dense persuasive information on the website. A sample of 200 individuals who were undecided about legalization completed the study. Their exposure time was recorded during the initial session and their legalization attitude was measured again after six months.

Results & discussion

The logistic regression results show that time spent reading persuasive content on the MPP website significantly predicted support for marijuana legalization after six months. As shown in the table, the independent variable was statistically significant with the odds ratio = 1.167. This indicates that for each additional minute participants spent reading, the odds of supporting legalization increased.

The Box–Tidwell test confirmed the assumptions (p=0.686). The inflection point analysis further indicated that the predicted probability of support reached 0.5 when participants spent roughly 15 minutes on the site. This suggests that sustained exposure was needed before undecided individuals became more likely than not to favor legalization.

Overall, these results support the hypothesis: greater time spent engaging with persuasive content increased the likelihood of supporting marijuana legalization. The strong statistical significance shows that this relationship is reliable and unlikely due to chance.

Logistic Regression Results
Odds Ratios with 95% Confidence Intervals
term Odds_Ratio CI_Lower CI_Upper P_Value
(Intercept) 0.099 0.044 0.205 0.0000
IV 1.167 1.116 1.227 0.0000
Linearity of the Logit Test (Box-Tidwell)
Interaction term indicates violation if significant
term Estimate Std_Error P_Value
(Intercept) −2.566 1.100 0.0196
IV 0.262 0.290 0.3657
IV_log −0.032 0.078 0.6869
Inflection Point of Logistic Curve
Value of IV where predicted probability = 0.50
Probability Inflection_Point
0.5 14.965

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

# ################################################
# # (Optional) Remove specific case(es)s by row number
# ################################################
# # Example: remove rows 10 and 25
# rows_to_remove <- c(10, 25) # Edit and uncomment this line
# mydata <- mydata[-rows_to_remove, ] # Uncomment this line

# 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