Permutation Test for a Local Structural Equation Model

Performs a permutation test for testing the hypothesis that model parameter are independent of a moderator variable (see Hildebrandt, Wilhelm, & Robitzsch, 2009; Hildebrandt, Luedtke, Robitzsch, Sommer, & Wilhelm, 2016).

Usage

lsem.permutationTest(lsem.object, B=1000, residualize=TRUE, verbose=TRUE,
     n.core=1, cl.type="PSOCK")

# S3 method for lsem.permutationTest
summary(object, file=NULL, digits=3, ...)

# S3 method for lsem.permutationTest
plot(x, type="global", stattype="SD",
    parindex=NULL, sig_add=TRUE, sig_level=0.05, sig_pch=17, nonsig_pch=2,
    sig_cex=1, sig_lab="p value",  stat_lab="Test statistic",
    moderator_lab=NULL, digits=3, title=NULL, parlabels=NULL,
    ask=TRUE, ...)

Arguments

lsem.object: Fitted object of class lsem with lsem.estimate
B: Number of permutation samples
residualize: Optional logical indicating whether residualization of the moderator should be performed for each permutation sample.
verbose: Optional logical printing information about computation progress.
n.core: A scalar indicating the number of cores that should be used.
cl.type: The cluster type. Default value is "PSOCK". Posix machines (Linux, Mac) generally benefit from much faster cluster computation if type is set to type="FORK".
object: Object of class lsem
file: A file name in which the summary output will be written.
digits: Number of digits.
...: Further arguments to be passed.
x: Object of class lsem
type: Type of the statistic to be plotted. If type="global", a global test will be displayed. If type="pointwise" for each value at the focal point (defined in moderator.grid) are calculated.
stattype: Type of test statistics. Can be MAD (mean absolute deviation), SD (standard deviation) or lin_slo (linear slope).
parindex: Vector of indices of selected parameters.
sig_add: Logical indicating whether significance values (p values) should be displayed.
sig_level: Significance level.
sig_pch: Point symbol for significant values.
nonsig_pch: Point symbol for non-significant values.
sig_cex: Point size for graphic displaying p values
sig_lab: Label for significance value (p value).
stat_lab: Label of y axis for graphic with pointwise test statistic
moderator_lab: Label of the moderator.
title: Title of the plot. Can be a vector.
parlabels: Labels of the parameters. Can be a vector.
ask: A logical which asks for changing the graphic for each parameter.

Value

List with following entries

teststat: Data frame with global test statistics. The statistics are SD, MAD and lin_slo with their corresponding p values.
parameters_pointwise_test: Data frame with pointwise test statistics.
parameters: Original parameters.
parameters: Parameters in permutation samples.
parameters_summary: Original parameter summary.
parameters_summary_M: Mean of each parameter in permutation sample.
parameters_summary_SD: Standard deviation (SD) statistic in permutation slope.
parameters_summary_MAD: Mean absolute deviation (MAD) statistic in permutation sample.
parameters_summary_MAD: Linear slope parameter in permutation sample.
nonconverged_rate: Percentage of permuted dataset in which a LSEM model did not converge

References

Hildebrandt, A., Luedtke, O., Robitzsch, A., Sommer, C., & Wilhelm, O. (2016). Exploring factor model parameters across continuous variables with local structural equation models. Multivariate Behavioral Research, 51(2-3), 257-278. doi:10.1080/00273171.2016.1142856

Hildebrandt, A., Wilhelm, O., & Robitzsch, A. (2009). Complementary and competing factor analytic approaches for the investigation of measurement invariance. Review of Psychology, 16, 87-102.

Author