Rationale

We know that the Elaboration Likelihood Model is a theory used to understand how persuasive messaging works or why it doesn’t work. Assuming the participants in this made-up study regarding legalizing marijuana for recreational purposes in Tennessee, all have the mental energy to spend on processing the information presented to them. According to ELM, attitudes and opinions of a topic that are formed through the central route processing are more resistant to change. Central route processing emphasizes high-quality arguements and presents lots of information and facts.

In the made-up study, we will determine if the amount of time each of the participants spent looking at strong, high-quality information will show a greater or lesser amount of support for legalizing marijuana for recreational use in Tennessee.

Hypothesis

Participants who spend more time reviewing high-quality persuasive information will be more likely to be in favor of legalizing marijuana for recreational use in the state of Tennessee.

Variables & Method

The dependent variable in the study is whether or not a participant favors legalizing marijuana for recreational use. 1 = In Favor and 0 = Opposed or undecided.

The independent variable is minutes in this study and it shows how much time participants spent consuming high-quality persuasive information.

A regression analysis was used in this assessment since the dependent variable was binary.The graph showed the likelihood that a participant favors the legalization of marijuana recreationally depends on how much time they spent on high-quality information about the topic. Once the participant spent at least 15 minutes or more, the likelihood of them favoring legalizing the use of marijuana recreationally increased.

Results & Discussion

The logistic regression graph indicates a positive relationship between the time spent watching high-quality persuasive information for legalizing marijuana in Tennessee. The graph predicts a trend that if the participant spent more surrounding themselves with high-quality information, the chances of them supporting legalizing marijuana increased. The logistic regression curve estimates probabilities between 0 and 1 and shows that as time increases, the probability of favoring legalization in this made-up study increases.

The results are clear when describing the elaboration likelihood model since it shows strong, persuasive content is more likely to have a favorable response. The analysis shows for each additional minute spent reviewing the made-up information, the odds of supporting the cause increased significantly. Participants who spent less time viewing the content were less likely to not favor legalization of marijuana recreationally in Tennessee.

The elaboration likelihood model says participants must have the mental energy on processing the information. The results of this fake study show central route processing, which includes high-quality information complete with strong facts.

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

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

Updated ELM report

DeAnn Hays

2025-10-03

Rationale

Hypothesis

Variables & Method

Results & Discussion

Code: