causal_decompose: Estimation and decomposition of simultaneous equation model
In SIRE: Finding Feedback Effects in SEM and Testing for Their Significance

Description Usage Arguments Value Examples

Estimate and/or decompose a Simultaneous Equation Model into its recursive and Interdependent sub-systems

1 2	causal_decompose(data, eq.system, resid.est = "noDfCor", instruments, sigma.in = NULL)

`data`	the data frame containing the data
`eq.system`	the system of equations (a list of formula objects, e.g. as in pkg `systemfit`)
`resid.est`	the estimation methods for the residual covariance matrix (as in `systemfit`)
`instruments`	the intruments used to estimate the model via 3-SLS (as in `systemfit`)
`sigma.in`	the Σ matrix, if the user wants to simulate a particular structure at stochastic level. Overrides 3SLS estimation if specified.

A list with components

eq.system: the system of equations given as input
Gamma: the 3-SLS estimate of Γ'
C: the matrix highlighting the interdependent mechanisms at deterministic level.
Psi1: the matrix highlighting the interdependent mechanisms at stochastic level.
Psi0: the matrix highlighting the causal mechanisms.
A: the 3-SLS estimate of A
Sigma: the 3-SLS estimate of Sigma
systemfit: the output from the systemfit function used to estimate the model
all.graph: the path diagram of the model, using the package igraph
dec.graph: the path diagram of the decomposed model, with color coding for each vertex
type.out: the type of analysis performed, either 'simulation' or 'empirical'

data("macroIT")
eq.system = list(
               eq1 = C ~  CP  + I + CP_1,
               eq2 = I ~ K + CP_1,
               eq3 = WP ~ I + GDP + GDP_1,
               eq4 = GDP ~ C + I + GDP_1,
               eq5 = CP ~ WP + T,
               eq6 = K ~ I + K_1)

instruments = ~ T + CP_1 + GDP_1 + K_1

causal_decompose(data = macroIT,
               eq.system = eq.system,
               resid.est = "noDfCor",
               instruments = instruments,
               sigma.in = NULL)