neg.semfit {negligible}

Equivalence Tests for Fit Indices

Description

Function performs equivalence tests for RMSEA, CFI, and SRMR.

Usage

neg.semfit(
  mod,
  alpha = 0.05,
  round = 3,
  rmsea.eq.bound = 0.05,
  rmsea.modif.eq.bound = FALSE,
  rmsea.ci.method = "not.close",
  rmsea.nboot = 250L,
  cfi.eq.bound = 0.95,
  cfi.modif.eq.bound = FALSE,
  cfi.ci.method = "yhy.boot",
  cfi.nboot = 250L,
  srmr.eq.bound = 0.08,
  srmr.modif.eq.bound = FALSE,
  srmr.ci.method = "MO",
  usrmr = TRUE,
  srmr.nboot = 250L
)

Arguments

mod

lavaan model object

alpha

desired alpha level (default = .05)

round

number of digits to round equivalence bound and confidence interval bounds (default = 3)

rmsea.eq.bound

upper bound of the equivalence interval for RMSEA for comparison; must be .01, .05, .08, or .10 if rmsea.modif.eq.bound = TRUE

rmsea.modif.eq.bound

should the upper bound of the equivalence interval for RMSEA be modified (default = FALSE)

rmsea.ci.method

method used to calculate confidence interval for RMSEA; options are "not.close" or "yhy.boot"; "not.close" corresponds to (1-2alpha) percent CI, "yhy.boot" corresponds to (1-2alpha) percent boot CI (default = "not.close")

rmsea.nboot

number of bootstrap samples if "yhy.boot" is selected as rmsea.ci.method (default = 250L)

cfi.eq.bound

lower bound of equivalence interval for CFI for comparison; must be .99, .95, .92 or .90 if cfi.modif.eq.bound = TRUE

cfi.modif.eq.bound

should the lower bound of the equivalence interval for CFI be modified (default = FALSE)

cfi.ci.method

method used to calculate confidence interval for CFI; options are "yuan", "equiv" or "yhy.boot"; "yuan" corresponds to (1-alpha) percent CI, "equiv" corresponds to (1-2alpha) percent CI, "yhy.boot" corresponds to (1-2alpha) percent boot CI (default = "equiv")

cfi.nboot

number of bootstrap samples if "yhy.boot" is selected as cfi.ci.method (default = 250L)

srmr.eq.bound

upper bound of equivalence interval for SRMR for comparison; must be .05 or .10 if modif.eq.bound = TRUE

srmr.modif.eq.bound

should the upper bound of the equivalence interval for SRMR be modified? (default = FALSE)

srmr.ci.method

method used to calculate confidence interval for SRMR; options are "MO" or "yhy.boot"; "MO" corresponds to (1-2alpha) percent CI, "yhy.boot" corresponds to (1-2alpha) percent boot CI (default = "MO")

usrmr

fit index around which equivalence test should be structured (usrmr = TRUE which is the default states that usrmr from Maydeu-Olivares, 2017 will be used, otherwise srmr from fitmeasures() output in lavaan will be used)

srmr.nboot

number of bootstrap samples if "yhy.boot" is selected as srmr.ci.method (default = 250L)

Details

#' The user specifies the lavaan fitted model object, the desired equivalence bound, and method of confidence interval computation for RMSEA, CFI, and SRMR. By default, the function does not modify the equivalence bounds according to Yuan et al. (2016) or according to Shi et al. (2018). The user can also choose to instead run an equivalence test using a modified equivalence bound if the equivalence bound to be modified is .01, .05, .08, or .10 for RMSEA,.99, .95, .92 or .90 for CFI, .05 or .10 for SRMR. Alpha level can also be modified.

For information on modified equivalence bounds for CFI and RMSEA see Yuan, K. H., Chan, W., Marcoulides, G. A., & Bentler, P. M. (2016). Assessing structural equation models by equivalence testing with adjusted fit indexes. Structural Equation Modeling: A Multidisciplinary Journal, 23(3), 319-330. doi: https://doi.org/10.1080/10705511.2015.1065414. For information on uSRMR and modified cut-offs for SRMR see: Maydeu-Olivares, A. (2017). Maximum likelihood estimation of structural equation models for continuous data: Standard errors and goodness of fit. Structural Equation Modeling: A Multidisciplinary Journal, 24(3), 383-394. Shi, D., Maydeu-Olivares, A., & DiStefano, C. (2018). The relationship between the standardized root mean square residual and model misspecification in factor analysis models. Multivariate Behavioral Research, 53(5), 676-694.

Value

returns a list containing analysis and respective statistics and decision.

• title1 The appropriate title of the test will be displayed depending on the ci.method chosen and whether modif.eq.bound is TRUE or FALSE.

• cfi_index The CFI index.

• ci.method The method for confidence interval calculation.

• cfi_eq The lower end of the confidence interval for the CFI index.

• eq.bound The equivalence bound.

Author(s)

Rob Cribbie [e-mail] and Nataly Beribisky [e-mail]

Examples

d <- lavaan::HolzingerSwineford1939
hs.mod <- 'visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9'
fit1 <- lavaan::cfa(hs.mod, data = d)
neg.cfi(mod = fit1, alpha = .05, eq.bound = .95,  modif.eq.bound = FALSE, ci.method = "equiv",
round = 3, plot = TRUE)