# Bootstrapping a Lavaan Model Bootstrap the D statistic. ```r 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. ## 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. ## Returns 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. ## Examples ```r ######################### ### 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 ```

bootstrapD function