Comparing Regression Parameters of Different lavaan Models Fitted to the Same Dataset

The function dmlavaan compares model parameters from different lavaan models fitted to the same dataset. This leads to dependent coefficients. Statistical inference is either conducted by M-estimation (i.e., robust sandwich method; method="bootstrap") or bootstrap (method="bootstrap"). See Mize et al. (2019) or Weesie (1999) for more details.

Usage

dmlavaan(fun1, args1, fun2, args2, method="sandwich", R=50)

Arguments

fun1: lavaan function of the first model (e.g., "lavaan", "cfa", or "sem")
args1: arguments for lavaan function in the first model
fun2: lavaan function of the second model (e.g., "lavaan", "cfa", or "sem")
args2: arguments for lavaan function in the second model
method: estimation method for standard errors
R: Number of bootstrap samples

Details

In bootstrap estimation, a normal approximation is applied in the computation of confidence intervals. Hence, R could be chosen relatively small.

TO DO (not yet implemented):

1)	inclusion of sampling weights
2)	cluster robust standard errors in hierarchical sampling
3)	stratification

Value

A list with following entries

coef: Model parameters of both models
vcov: Covariance matrix of model parameters of both models
partable: Parameter table containing all univariate model parameters
...: More entries

References

Mize, T.D., Doan, L., & Long, J.S. (2019). A general framework for comparing predictions and marginal effects across models. Sociological Methodology, 49(1), 152-189. doi:10.1177/0081175019852763

Weesie, J. (1999) Seemingly unrelated estimation and the cluster-adjusted sandwich estimator. Stata Technical Bulletin, 9, 231-248.

Examples

if (FALSE) {
############################################################################
# EXAMPLE 1: Confirmatory factor analysis with and without fourth item
#############################################################################

#**** simulate data
N <- 200  # number of persons
I <- 4    # number of items

# loadings and error correlations
lam <- seq(.7,.4, len=I)
PSI <- diag( 1-lam^2 )

# define some model misspecification
sd_error <- .1
S1 <- matrix( c( -1.84, 0.39,-0.68, 0.13,
  0.39,-1.31,-0.07,-0.27,
 -0.68,-0.07, 0.90, 1.91,
  0.13,-0.27, 1.91,-0.56 ), nrow=4, ncol=4, byrow=TRUE)
S1 <- ( S1 - mean(S1) ) / sd(S1) * sd_error

Sigma <- lam %*% t(lam) + PSI + S1
dat <- MASS::mvrnorm(n=N, mu=rep(0,I), Sigma=Sigma)
colnames(dat) <- paste0("X",1:4)
dat <- as.data.frame(dat)
rownames(Sigma) <- colnames(Sigma) <- colnames(dat)


#*** define two lavaan models
lavmodel1 <- "F=~ X1 + X2 + X3 + X4"
lavmodel2 <- "F=~ X1 + X2 + X3"

#*** define lavaan estimation arguments and functions
fun2 <- fun1 <- "cfa"
args1 <- list( model=lavmodel1, data=dat, std.lv=TRUE, estimator="MLR")
args2 <- args1
args2$model <- lavmodel2

#* run model comparison
res1 <- sirt::dmlavaan( fun1=fun1, args1=args1, fun2=fun2, args2=args2)

# inspect results
sirt:::print_digits(res1$partable, digits=3)
}