Data: Summers
A (18 x 18) indicator correlation matrix.
Sigma_Summers_composites
An object of class matrix (inherits from array) with 18 rows and 18 columns.
The indicator correlation matrix for a modified version of Summers (1965) model. All constructs are modeled as composites.
Own calculation based on Dijkstra and Henseler (2015).
Dijkstra TK, Henseler J (2015).
“Consistent and Asymptotically Normal PLS Estimators for Linear Structural Equations.”
Computational Statistics & Data Analysis, 81, 10–23.
Summers R (1965).
“A Capital Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimators.”
Econometrica, 33(1), 1–41.
require(cSEM)
model <- "
ETA1 ~ ETA2 + XI1 + XI2
ETA2 ~ ETA1 + XI3 +XI4
ETA1 ~~ ETA2
XI1 <~ x1 + x2 + x3
XI2 <~ x4 + x5 + x6
XI3 <~ x7 + x8 + x9
XI4 <~ x10 + x11 + x12
ETA1 <~ y1 + y2 + y3
ETA2 <~ y4 + y5 + y6
"
## Generate data
summers_dat <- MASS::mvrnorm(n = 300, mu = rep(0, 18),
Sigma = Sigma_Summers_composites, empirical = TRUE)
## Estimate
res <- csem(.data = summers_dat, .model = model) # inconsistent
##
# 2SLS
res_2SLS <- csem(.data = summers_dat, .model = model, .approach_paths = "2SLS",
.instruments = list(ETA1 = c('XI1', 'XI2', 'XI3', 'XI4'),
ETA2 = c('XI1', 'XI2', 'XI3', 'XI4'))
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