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

# The Theory

# 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*= 0.60Initial 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 0.6610948 0.7047776 0.7244349 0.7332807 0.7372613`

# The Intention ~ Norms Regression Coefficients Across Time:

`bIN`

`## [1] 0.0000000 0.4465540 0.4938549 0.5151404 0.5247188 0.5290291`

Bo^{2}m.