Week 6 ELM

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 recreationallydepends on how much time they spent on high-quality information about the topic.

Results & Discussion

The 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 results are clear when describing the elaboration likelihood model since it shows strong, persuasive content is more likley to have a favorable response.

# Quick analysis & plot only (no code shown)
ELM <- read.csv("https://raw.githubusercontent.com/drkblake/Data/main/ELM.csv")
ELM$Minutes <- as.numeric(ELM$Minutes)
model <- glm(Favor_1 ~ Minutes, data = ELM, family = binomial)
ELM$PredictedProb <- predict(model, type="response")

plot(ELM$Minutes, ELM$PredictedProb,
     xlab="Minutes on High-Quality Info",
     ylab="Predicted Probability of Favoring Legalization",
     main="Predicted Probability from Logistic Regression",
     pch=19, col=rgb(0,0,1,0.3))

x_vals <- seq(min(ELM$Minutes), max(ELM$Minutes), length.out=100)
lines(x_vals, predict(model, newdata=data.frame(Minutes=x_vals), type="response"),
      col="red", lwd=2)

Code

# Load dataset
ELM <- read.csv("https://github.com/drkblake/Data/raw/refs/heads/main/ELM.csv")
ELM$Minutes <- as.numeric(ELM$Minutes)

# Check distribution of dependent variable
table(ELM$Favor_1)

## 
##   0   1 
## 102  98

# Logistic regression
model <- glm(Favor_1 ~ Minutes, data = ELM, family = binomial)

# Model summary
summary(model)

## 
## Call:
## glm(formula = Favor_1 ~ Minutes, family = binomial, data = ELM)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -2.3125     0.3897  -5.935 2.94e-09 ***
## Minutes       0.1545     0.0241   6.411 1.45e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 277.18  on 199  degrees of freedom
## Residual deviance: 218.46  on 198  degrees of freedom
## AIC: 222.46
## 
## Number of Fisher Scoring iterations: 4

# Odds ratios and 95% confidence intervals
exp(coef(model))

## (Intercept)     Minutes 
##  0.09900867  1.16710657

exp(confint(model))

## Waiting for profiling to be done...

##                  2.5 %    97.5 %
## (Intercept) 0.04411676 0.2045625
## Minutes     1.11612493 1.2272654

# Pseudo R-squared values
pR2(model)

## fitting null model for pseudo-r2

##          llh      llhNull           G2     McFadden         r2ML         r2CU 
## -109.2314914 -138.5894334   58.7158841    0.2118339    0.2544100    0.3392586

# Predicted probabilities
ELM$PredictedProb <- predict(model, type="response")

# Plot again (duplicate of Results graph, but with code shown)
plot(ELM$Minutes, ELM$PredictedProb,
     xlab="Minutes on High-Quality Info",
     ylab="Predicted Probability of Favoring Legalization",
     main="Predicted Probability from Logistic Regression",
     pch=19, col=rgb(0,0,1,0.3))

x_vals <- seq(min(ELM$Minutes), max(ELM$Minutes), length.out=100)
lines(x_vals, predict(model, newdata=data.frame(Minutes=x_vals), type="response"),
      col="red", lwd=2)