Rationale

The Elaboration Likelihood Model explains how people interprate persuasive messages. When people process high-quality persuasive information, they are more likely to develop opinions that are more more likely to stick with them longterm. This study examines whether the amount of time participants spent looking at high-quality persuasive information was related to their later opinions toward marijuana legalization in Tennessee.

Hypothesis

Participants who spend more time looking at high-quality persuasive information will be more likely to agree with legalizing marijuana in Tennessee one month later.

Methods

The study included 200 participants who, prior to the study, had no strong opinion for or against legalizing recreational marijuana in Tennessee. Participants spent 30 minutes browsing a realistic-looking website for a made-up organization, while an eye-tracking device recorded how much time they spent looking at high-quality persuasive information and peripheral cues. One month later, participants reported whether they were for or against the legalization of marijuana in Tennessee.

The independent variable was Minutes, which measured the number of minutes participants spent looking at high-quality persuasive information. The dependent variable was Favor 1, which indicated whether participants favored legalization (1) or opposed legalization (0).

## `geom_smooth()` using formula = 'y ~ x'
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

Results

A logistic regression was conducted to determine whether the amount of time participants spent looking at high-quality persuasive information predicted whether they favored marijuana legalization. The analysis found that there was a correlation between minutes spent viewing high-quality persuasive information and favoring legalization. The odds ratio for “Minutes,” was 1.170, with a 95% confidence interval of 1.120 to 1.230, p < .001. This indicates that each additional minute spent looking at high-quality persuasive information was associated with around a 17% increase in the odds of favoring legalization.

The Box-Tidwell test did not show a break of the linearity-of-the-logit assumption, p = .687. The inflection point of the logistic curve was 14.965 minutes, meaning the model predicted a 50% probability of favoring legalization at approximately 15 minutes of viewing high-quality persuasive information.

Overall, the results support the hypothesis. Participants who spent more time looking at high-quality persuasive information were more likely to favor legalization of marijuana one month later.

Conclusion

The results of the study provide support for the Elaboration Likelihood Model. Participants who spent more time viewing high-quality persuasive information were more likely to favor marijuana legalization one month later. These results show a consistent correlation that continued exposure to high-quality persuasive information can effect attitude change long time for partcipants.

Code Chunk

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)

options(scipen = 999)

mydata <- read.csv("ELM.csv")

mydata$DV <- mydata$Favor_1
mydata$IV <- mydata$Minutes

mydata$DV <- as.numeric(as.character(mydata$DV))

logit_plot <- ggplot(mydata, aes(x = IV, y = DV)) +
  geom_point(alpha = 0.5) +
  geom_smooth(
    method = "glm",
    method.args = list(family = "binomial"),
    se = FALSE,
    color = "#1f78b4"
  ) +
  labs(
    title = "Logistic Regression Curve",
    x = "Minutes Spent Looking at High-Quality Persuasive Information",
    y = "Favoring Legalization"
  )

logit_plotly <- ggplotly(logit_plot)

log.ed <- glm(
  DV ~ IV,
  data = mydata,
  family = "binomial"
)

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
  )

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"
  )

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"
  )

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"
  )

logit_plotly
summary(log.ed)
results_table
linearity_table
inflection_table