InformativeTesting: Testing order/inequality Constrained Hypotheses in SEM

Description

Testing order/inequality constrained Hypotheses in SEM

Usage

InformativeTesting(model = NULL, data, constraints = NULL, 
                   R = 1000L, type = "bollen.stine",
                   return.LRT = TRUE, 
                   double.bootstrap = "standard",
                   double.bootstrap.R = 249L, 
                   double.bootstrap.alpha = 0.05,
                   parallel = c("no", "multicore", "snow"), 
                   ncpus = 1L, cl = NULL, verbose = FALSE, ...)

Value

An object of class InformativeTesting for which a print and a plot method is available.

Arguments

model: Model syntax specifying the model. See model.syntax for more information.
data: The data frame containing the observed variables being used to fit the model.
constraints: The imposed inequality constraints on the model.
R: Integer; number of bootstrap draws. The default value is set to 1000.
type: If "parametric", the parametric bootstrap is used. If "bollen.stine", the semi-nonparametric Bollen-Stine bootstrap is used. The default is set to "bollen.stine".
return.LRT: Logical; if TRUE, the function returns bootstrapped LRT-values.
double.bootstrap: If "standard" (default) the genuine double bootstrap is used to compute an additional set of plug-in p-values for each bootstrap sample. If "no", no double bootstrap is used. If "FDB", the fast double bootstrap is used to compute second level LRT-values for each bootstrap sample. Note that the "FDB" is experimental and should not be used by inexperienced users.
double.bootstrap.R: Integer; number of double bootstrap draws. The default value is set to 249.
double.bootstrap.alpha: The significance level to compute the adjusted alpha based on the plugin p-values. Only used if double.bootstrap = "standard". The default value is set to 0.05.
parallel: The type of parallel operation to be used (if any). If missing, the default is set "no".
ncpus: Integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs.
cl: An optional parallel or snow cluster for use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the InformativeTesting call.
verbose: Logical; if TRUE, information is shown at each bootstrap draw.
...: Other named arguments from the lavaan package which are passed to the function. For example "group" in a multiple group model.

Author

Leonard Vanbrabant lgf.vanbrabant@gmail.com

Details

The following hypothesis tests are available:

Type A: Test H0: all restriktions with equalities ("=") active against HA: at least one inequality restriktion (">") strictly true.
Type B: Test H0: all restriktions with inequalities (">") (including some equalities ("=")) active against HA: at least one restriktion false (some equality restriktions may be maintained).

References

Van de Schoot, R., Hoijtink, H., & Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Structural Equation Modeling, 17, 443-463.

Van de Schoot, R., Strohmeier, D. (2011). Testing informative hypotheses in SEM increases power: An illustration contrasting classical. International Journal of Behavioral Development, 35, 180-190.

Silvapulle, M.J. and Sen, P.K. (2005). Constrained Statistical Inference. Wiley, New York.

Examples

Run this code

if (FALSE) {
#########################
### real data example ###
#########################
# Multiple group path model for facial burns example.

# model syntax with starting values.
  burns.model <- 'Selfesteem ~ Age + c(m1, f1)*TBSA + HADS +
                             start(-.10, -.20)*TBSA  
                 HADS ~ Age + c(m2, f2)*TBSA + RUM +
                        start(.10, .20)*TBSA '
 
 
# constraints syntax
 burns.constraints <- 'f2 > 0  ; m1 < 0
                       m2 > 0  ; f1 < 0
                       f2 > m2 ; f1 < m1'
 
# we only generate 2 bootstrap samples in this example; in practice
# you may wish to use a much higher number. 
# the double bootstrap was switched off; in practice you probably 
# want to set it to "standard".
example1 <- InformativeTesting(model = burns.model, data = FacialBurns,
                               R = 2, constraints = burns.constraints,
                               double.bootstrap = "no", group = "Sex")

example1

##########################
### artificial example ###
##########################
# Simple ANOVA model with 3 groups (N = 20 per group)
set.seed(1234)
Y <- cbind(c(rnorm(20,0,1), rnorm(20,0.5,1), rnorm(20,1,1)))
grp <- c(rep("1", 20), rep("2", 20), rep("3", 20))
Data <- data.frame(Y, grp)

#create model matrix
fit.lm <- lm(Y ~ grp, data = Data)
mfit <- fit.lm$model
mm <- model.matrix(mfit)

Y <- model.response(mfit)
X <- data.frame(mm[,2:3])
names(X) <- c("d1", "d2")
Data.new <- data.frame(Y, X)

# model
model <- 'Y ~ 1 + a1*d1 + a2*d2'

# fit without constraints
fit <- sem(model, data = Data.new)

# constraints syntax: mu1 < mu2 < mu3
constraints <- ' a1 > 0
                 a1 < a2 '

# we only generate 10 bootstrap samples in this example; in practice
# you may wish to use a much higher number, say > 1000. The double 
# bootstrap is not necessary in case of an univariate ANOVA model.
example2 <- InformativeTesting(model = model, data = Data.new, 
                               start = parTable(fit),
                               R = 10L, double.bootstrap = "no",
                               constraints = constraints)
example2
}

Run the code above in your browser using DataLab

Last chance! 50% off unlimited learning