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Sequential chi square model tests, RMSEA lower bound, and AIC

Source: R/efa_smt.R
efa_smt.Rd

Sequential chi square model tests (SMT) are a factor retention method where multiple EFAs with increasing numbers of factors are fitted and the number of factors for which the Chi Square value first becomes non-significant is taken as the suggested number of factors. Preacher, Zhang, Kim, & Mels (2013) suggested a similar approach with the lower bound of the 90% confidence interval of the Root Mean Square Error of Approximation (RMSEA; Browne & Cudeck, 1992; Steiger & Lind, 1980), and with the Akaike Information Criterion (AIC). For the RMSEA, the number of factors for which this lower bound first falls below .05 is the suggested number of factors to retain. For the AIC, it is the number of factors where the AIC is lowest.

Usage

efa_smt(
  x,
  N = NA,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  estimate_control = NULL
)

Source

Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods, 24(4), 468–491. https://doi.org/10.1037/met0000200

Browne, M.W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods and Research, 21, 230–258.

Preacher, K. J., Zhang G., Kim, C., & Mels, G. (2013). Choosing the Optimal Number of Factors in Exploratory Factor Analysis: A Model Selection Perspective, Multivariate Behavioral Research, 48(1), 28-56, doi:10.1080/00273171.2012.710386

Steiger, J. H., & Lind, J. C. (1980, May). Statistically based tests for the number of common factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.

Arguments

x

data.frame or matrix. Dataframe or matrix of raw data or matrix with correlations.

N

numeric. The number of observations. Needs only be specified if a correlation matrix is used.

use

character. Passed to stats::cor() if raw data is given as input. Default is "pairwise.complete.obs".

cor_method

character. One of "pearson", "spearman", or "kendall", passed to stats::cor(). "poly" and "tetra" are not supported because SMT rests on a normal-theory chi-square test that is not valid for polychoric / tetrachoric correlations. Default is "pearson".

estimate_control

an estimate_control() object with the estimation settings for the sequential efa_fit() fits. NULL (default) uses the efa_fit() defaults. The sequential models are fitted with maximum likelihood (the chi-square, RMSEA, and AIC the SMT is built on are defined for it), so of the estimation knobs only start_method takes effect; the ones governing principal axis factoring do not apply. The models are unrotated, so no rotation settings apply either.

Value

An object of class efa_retention (see print.efa_retention() for the print method). Its main fields are:

n_factors

A named numeric vector ("chi", "RMSEA", "AIC") with the suggested number of factors from the sequential chi-square model tests, the RMSEA lower bound, and the AIC.

results

A list with one record per criterion, each holding the criterion values for the null model (zero factors) through the maximum number of factors.

settings

A list of the settings used.

Details

As a first step in the procedure, a maximum number of factors to extract is determined for which the model is still over-identified (df > 0).

Then, EFAs with increasing numbers of factors from 1 to the maximum number are fitted with maximum likelihood estimation.

For the SMT, first the significance of the chi square value for a model with 0 factors is determined. If this value is not significant, 0 factors are suggested to retain. If it is significant, a model with 1 factor is estimated and the significance of its chi square value is determined, and so on, until a non-significant result is obtained. The suggested number of factors is the number of factors for the model where the chi square value first becomes non-significant.

Regarding the RMSEA, the suggested number of factors is the number of factors for the model where the lower bound of the 90% confidence interval of the RMSEA first falls below the .05 threshold.

Regarding the AIC, the suggested number of factors is the number of factors for the model with the lowest AIC.

In comparison with other prominent factor retention criteria, SMT performed well at determining the number of factors to extract in EFA (Auerswald & Moshagen, 2019). The RMSEA lower bound also performed well at determining the true number of factors, while the AIC performed well at determining the most generalizable model (Preacher, Zhang, Kim, & Mels, 2013).

See also

efa_retain() as a wrapper function for this and the other factor retention criteria.

Other factor retention criteria: efa_cd(), efa_ekc(), efa_hull(), efa_kgc(), efa_map(), efa_nest(), efa_parallel(), efa_retain(), efa_scree()

Examples

SMT_base <- efa_smt(test_models$baseline$cormat, N = 500)
SMT_base
#> ── Sequential model tests ──────────────────────────────────────────────────────
#> 
#> • Sequential chi-square model tests: 3
#> • Lower bound of RMSEA 90% CI: 2
#> • Akaike Information Criterion: 3