bootstrapD {restriktor}

Bootstrapping a Lavaan Model

Description

Bootstrap the D statistic.

Usage

  bootstrapD(h0 = NULL, h1 = NULL, constraints, type = "A", 
             bootstrap.type = "bollen.stine", R = 1000L,  
             return.D = FALSE, double.bootstrap = "no", 
             double.bootstrap.R = 500L, double.bootstrap.alpha = 0.05, 
             verbose = FALSE, warn = -1L, 
             parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, 
             seed = NULL)
             
  ## S3 method for class 'conTestLavaan'
print(x, digits = max(3, getOption("digits") - 2), ...)

Arguments

h0

An object of class lavaan. The restricted model.

h1

An object of class lavaan. The unrestricted model.

x

an object of class conTestLavaan.

constraints

The imposed (in)equality constraints on the model.

type

hypothesis test type "A", "B".

bootstrap.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".

R

Integer. The number of bootstrap draws.

return.D

Logical; if TRUE, the function returns bootstrapped D-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.

verbose

If TRUE, show information for each bootstrap draw.

warn

Sets the handling of warning messages. See options.

parallel

The type of parallel operation to be used (if any). If missing, the default is "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 bootstrapLavaan or bootstrapLRT call.

digits

the number of significant digits to use when printing.

...

no additional arguments for now.

seed

An integer to set the seed. Or NULL if no reproducible seeds are needed.

Value

A bootstrap p value, calculated as the proportion of bootstrap samples with a D statistic at least as large as the D statistic for the original data.

Author(s)

Leonard Vanbrabant

References

Bollen, K. and Stine, R. (1992) Bootstrapping Goodness of Fit Measures in Structural Equation Models. Sociological Methods and Research, 21, 205–229.

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

Yuan, K.-H., Hayashi, K., and Yanagihara, H. (2007). A class of population covariance matrices in the bootstrap approach to covariance structure analysis. Multivariate Behavioral Research, 42, 261–281.

Examples

#########################
### 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 <- conTestD(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 <- lavaan::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 <- conTestD(model = model, data = Data.new, 
                     start = lavaan::parTable(fit),
                     R = 10L, double.bootstrap = "no",
                     constraints = constraints)
example2