permuteMeasEq-class {semTools}

Class for the Results of Permutation Randomization Tests of Measurement Equivalence and DIF

Description

This class contains the results of tests of Measurement Equivalence and Differential Item Functioning (DIF).

Usage

## S4 method for signature 'permuteMeasEq'
show(object)

## S4 method for signature 'permuteMeasEq'
summary(object, alpha = 0.05, nd = 3, extra = FALSE)

## S4 method for signature 'permuteMeasEq'
hist(x, ..., AFI, alpha = 0.05, nd = 3,
  printLegend = TRUE, legendArgs = list(x = "topleft"))

Arguments

object, x

object of class permuteMeasEq

alpha

alpha level used to draw confidence limits in hist and flag significant statistics in summary output

nd

number of digits to display

extra

logical indicating whether the summary output should return permutation-based p values for each statistic returned by the extra function. If FALSE (default), summary will return permutation-based p values for each modification index.

...

Additional arguments to pass to hist

AFI

character indicating the fit measure whose permutation distribution should be plotted

printLegend

logical. If TRUE (default), a legend will be printed with the histogram

legendArgs

list of arguments passed to the legend function. The default argument is a list placing the legend at the top-left of the figure.

Value

• The show method prints a summary of the multiparameter omnibus test results, using the user-specified AFIs. The parametric (\Delta)\chi^2 test is also displayed.

• The summary method prints the same information from the show method, but when extra = FALSE (the default) it also provides a table summarizing any requested follow-up tests of DIF using modification indices in slot MI.obs. The user can also specify an alpha level for flagging modification indices as significant, as well as nd (the number of digits displayed). For each modification index, the p value is displayed using a central \chi^2 distribution with the df shown in that column. Additionally, a p value is displayed using the permutation distribution of the maximum index, which controls the familywise Type I error rate in a manner similar to Tukey's studentized range test. If any indices are flagged as significant using the tukey.p.value, then a message is displayed for each flagged index. The invisibly returned data.frame is the displayed table of modification indices, unless permuteMeasEq was called with param = NULL, in which case the invisibly returned object is object. If extra = TRUE, the permutation-based p values for each statistic returned by the extra function are displayed and returned in a data.frame instead of the modification indices requested in the param argument.

• The hist method returns a list of length == 2, containing the arguments for the call to hist and the arguments to the call for legend, respectively. This list may facilitate creating a customized histogram of AFI.dist, MI.dist, or extra.dist

Slots

PT

A data.frame returned by a call to parTable on the constrained model

modelType

A character indicating the specified modelType in the call to permuteMeasEq

ANOVA

A numeric vector indicating the results of the observed (\Delta)\chi^2 test, based on the central \chi^2 distribution

AFI.obs

A vector of observed (changes in) user-selected fit measures

AFI.dist

The permutation distribution(s) of user-selected fit measures. A data.frame with n.Permutations rows and one column for each AFI.obs.

AFI.pval

A vector of p values (one for each element in slot AFI.obs) calculated using slot AFI.dist, indicating the probability of observing a change at least as extreme as AFI.obs if the null hypothesis were true

MI.obs

A data.frame of observed Lagrange Multipliers (modification indices) associated with the equality constraints or fixed parameters specified in the param argument. This is a subset of the output returned by a call to lavTestScore on the constrained model.

MI.dist

The permutation distribution of the maximum modification index (among those seen in slot MI.obs$X2) at each permutation of group assignment or of covariates

extra.obs

If permuteMeasEq was called with an extra function, the output when applied to the original data is concatenated into this vector

extra.dist

A data.frame, each column of which contains the permutation distribution of the corresponding statistic in slot extra.obs

n.Permutations

An integer indicating the number of permutations requested by the user

n.Converged

An integer indicating the number of permuation iterations which yielded a converged solution

n.nonConverged

An integer vector of length n.Permutations indicating how many times group assignment was randomly permuted (at each iteration) before converging on a solution

n.Sparse

Only relevant with ordered indicators when modelType == "mgcfa". An integer vector of length n.Permutations indicating how many times group assignment was randomly permuted (at each iteration) before obtaining a sample with all categories observed in all groups.

oldSeed

An integer vector storing the value of .Random.seed before running permuteMeasEq. Only relevant when using a parallel/multicore option and the original RNGkind() != "L'Ecuyer-CMRG". This enables users to restore their previous .Random.seed state, if desired, by running: .Random.seed[-1] <- permutedResults@oldSeed[-1]

Objects from the Class

Objects can be created via the permuteMeasEq function.

Author(s)

Terrence D. Jorgensen (University of Amsterdam; [e-mail])

See Also

permuteMeasEq

Examples

# See the example from the permuteMeasEq function