psycModel (version 0.5.0)

measurement_invariance: Measurement Invariance

Description

Compute the measurement invariance model (i.e., measurement equivalence model) using multi-group confirmatory factor analysis (MGCFA; Jöreskog, 1971). This function uses the lavaan::cfa() in the backend. Users can run the configural-metric or the configural-metric-scalar comparisons (see below for detail instruction). All arguments (except the CFA items) must be explicitly named (like model = your-model; see example for inappropriate behavior).

Usage

measurement_invariance(
  data,
  ...,
  model = NULL,
  group,
  ordered = FALSE,
  group_partial = NULL,
  invariance_level = "scalar",
  estimator = "ML",
  digits = 3,
  quite = FALSE,
  streamline = FALSE,
  return_result = FALSE
)

Value

a data.frame of the fit measure summary

Arguments

data

data.frame

...

CFA items. Multi-factor CFA items should be separated by comma (as different argument). See below for examples. Support dplyr::select() syntax.

model

explicit lavaan model. Must be specify with model = lavaan_model_syntax.

group

the nested variable for multilevel dataset (e.g., Country). Support dplyr::select() syntax.

ordered

Default is FALSE. If it is set to TRUE, lavaan will treat it as a ordinal variable and use DWLS instead of ML

group_partial

items for partial equivalence. The form should be c('DV =~ item1', 'DV =~ item2'). See details for recommended practice.

invariance_level

"metric" or "scalar". Default is 'metric'. Set as 'metric' for configural-metric comparison, and set as 'scalar' for configural-metric-scalar comparison.

estimator

estimator for lavaan. Default is ML

digits

number of digits to round to

quite

suppress printing output except the model summary.

streamline

print streamlined output

return_result

If it is set to TRUE, it will return a data frame of the fit measure summary

Details

Chen (2007) suggested that change in CFI <= |-0.010| supplemented by RMSEA <= 0.015 indicate non-invariance when sample sizes were equal across groups and larger than 300 in each group (Chen, 2007). And, Chen (2007) suggested that change in CFI <= |-0.005| and change in RMSEA <= 0.010 for unequal sample size with each group smaller than 300. For SRMR, Chen (2007) recommend change in SRMR < 0.030 for metric-invariance and change in SRMR < 0.015 for scalar-invariance. For large group size, Rutowski & Svetina (2014) recommended a more liberal cut-off for metric non-invariance for CFI (change in CFI <= |-0.020|) and RMSEA (RMSEA <= 0.030). However, this more liberal cut-off DOES NOT apply to testing scalar non-invariance. If measurement-invariance is not achieved, some researchers suggesting partial invariance is acceptable (by releasing the constraints on some factors). For example, Steenkamp and Baumgartner (1998) suggested that ideally more than half of items on a factor should be invariant. However, it is important to note that no empirical studies were cited to support the partial invariance guideline (Putnick & Bornstein, 2016).

References

Chen, F. F. (2007). Sensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464–504. https://doi.org/10.1080/10705510701301834

Jöreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika, 36(4), 409-426.

Putnick, D. L., & Bornstein, M. H. (2016). Measurement Invariance Conventions and Reporting: The State of the Art and Future Directions for Psychological Research. Developmental Review: DR, 41, 71–90. https://doi.org/10.1016/j.dr.2016.06.004

Rutkowski, L., & Svetina, D. (2014). Assessing the Hypothesis of Measurement Invariance in the Context of Large-Scale International Surveys. Educational and Psychological Measurement, 74(1), 31–57. https://doi.org/10.1177/0013164413498257

Steenkamp, J.-B. E. M., & Baumgartner, H. (n.d.). Assessing Measurement Invariance in Cross-National Consumer Research. JOURNAL OF CONSUMER RESEARCH, 13.

Examples

# REMEMBER, YOU MUST NAMED ALL ARGUMENT EXCEPT THE CFA ITEMS ARGUMENT
# Fitting a multiple-factor measurement invariance model by passing items.
measurement_invariance(
  x1:x3,
  x4:x6,
  x7:x9,
  data = lavaan::HolzingerSwineford1939,
  group = "school",
  invariance_level = "scalar" # you can change this to metric
)

# Fitting measurement invariance model by passing explicit lavaan model
# I am also going to only test for metric invariance instead of the default scalar invariance
# \donttest{
measurement_invariance(
  model = "visual  =~ x1 + x2 + x3;
           textual =~ x4 + x5 + x6;
           speed   =~ x7 + x8 + x9",
  data = lavaan::HolzingerSwineford1939,
  group = "school",
  invariance_level = "metric"
)
# }

if (FALSE) {
# This will fail because I did not add `model = ` in front of the lavaan model.
# Therefore,you must add the tag in front of all arguments
# For example, `return_result = 'model'` instaed of `model`
measurement_invariance(
  "visual  =~ x1 + x2 + x3;
             textual =~ x4 + x5 + x6;
             speed   =~ x7 + x8 + x9",
  data = lavaan::HolzingerSwineford1939
)
}