Rationale

The Elaboration Likelihood Model says that when people focus on strong persuasive information it is more likely to change their attitudes in a lasting way. In this study, people who had no strong opinion on recreational marijuana would be more likely to support legalization if they spent more time reading high quality arguments in favor of it. The website they viewed included both strong arguments and weaker surface level cues. Eye tracking measured how much time each person spent on each type of content. The theory suggests that the more time someone spent on high quality information the more likely they were to support legalization in the long term.

Hypothesis

Participants are more likely to support the legalization of recreational marijuana in the long term if they spend more time viewing high quality information on a website promoting legalization.

Variables & method

The dependent variable in this study was whether or not participants supported or opposed legalization of recreational marijuana in Tennessee, one month after viewing the advocacy website,and since all participants had initially indicated no strong opinion, the independent variable was how long each person spent viewing strong quality persuasive information on the website. The hypothesis was that participants who spent more time with this type of material, in comparison to peripheral quality cues like celebrity status, would be more likely to support legalization.

In total, 200 participants were asked to spend a total of 30 minutes browsing a website created for a fictional group seeking to legalize recreational marijuana in Tennessee. An eye tracker was used to record the amount of time each participant spent viewing strong arguments (e.g., expert quotes, medical studies, incarceration rates, tax revenue projections, etc.), as a point of comparison with time spent viewing peripheral quality cues (e.g., celebrity status, images). One month later, participants were surveyed again to determine if they now supported or opposed legalization.

Results & discussion

Logistic regression was used for the data analysis. The results aligned with the hypothesis that the longer participants engaged with high quality information, the more likely they were to agree to legalize recreational marijuana in Tennessee. The logistic regression curve in chart one depicts a positive trend; chart two indicates a p-value of 0.0000 for the independent variable in the regression results, which implies the findings were statistically significant. The Box-Tidwell test illustrates a p-value of 0.6869, which just passed for logistic regression. Participants that spent at least around 15 minutes on high quality information are likely to have been in favor of legalization, as indicated in chart three.

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