# Dynamic Theory of Reasoned Action

## 2017/09/05

A replicated dynamic theory of reasoned action, inspired by Boster, Shaw, Carpenter, and Lindsey (2015; link HERE).

# The Theory In A Difference Equation:

I(t) = b1*Norms(t-1) + b2*Attitudes(t-1) + b3*Intention(t-1)

# Simulation

• b1 = 0.15

• b2 = 0.25

• b3 = 0.60

• Initial Distributions:

• 1,600 cases with a mean of 3 and a standard deviation of 1.

Here, we will generate initial data consistent with the initial distribution description above and a correlation matrix shown in the “Sigma” code below. We will then simulate the process (for 6 time steps) consistent with our description of a dynamic theory of reasoned action and the parameters shown above. At each time step we will save the beta regression coefficient from “attitudes” to “intention” and “norms” to “intention.”

library(MASS)

k = 6
A = matrix(,nrow = 1600, ncol = 6)
N = matrix(,nrow = 1600, ncol = 6)
I = matrix(,nrow = 1600, ncol = 6)
bIA = numeric(k)
bIN = numeric(k)

Sigma = matrix(c(1.0, 0.25, 0.56, 0.25,
0.25, 1.0, 0.31, 0.13,
0.56, 0.31, 1.0, 0.50,
0.25, 0.13, 0.50, 1.0), 4, 4, byrow = T)

Mu = c(3,3,3,3)

Xne = mvrnorm(1600, Mu, Sigma)

A[,1] = Xne[,1]
N[,1] = Xne[,2]
I[,1] = Xne[,3]

for (i in 2:k){
A[,i] = A[,(i-1)]
N[,i] = N[,(i-1)]
I[,i] = 0.20*N[,(i-1)] + 0.35*A[,(i-1)] + 0.45*I[,(i-1)]
fit_IA = lm(I[,i]~A[,i])
bIA[i] = coef(fit_IA)[2]
fit_IN = lm(I[,i]~N[,i])
bIN[i] = coef(fit_IN)[2]
}

# The Intention ~ Attitudes Regression Coefficients Across Time:

bIA
## [1] 0.0000000 0.6497525 0.6962329 0.7171491 0.7265614 0.7307969

# The Intention ~ Norms Regression Coefficients Across Time:

bIN
## [1] 0.0000000 0.4302162 0.4864031 0.5116873 0.5230651 0.5281852

Bo2m.