GitHub - mdsteiner/EFAtools (original) (raw)

EFAtools

The EFAtools package provides functions to perform exploratory factor analysis (EFA) procedures and compare their solutions. The goal is to provide state-of-the-art factor retention methods and a high degree of flexibility in the EFA procedures. This way, implementations from R psych and SPSS can be compared. Moreover, functions for Schmid-Leiman transformation, and computation of omegas are provided. To speed up the analyses, some of the iterative procedures like principal axis factoring (PAF) are implemented in C++.

Installation

You can install the release version fromCRAN with:

install.packages("EFAtools")

You can install the development version fromGitHub with:

install.packages("devtools") devtools::install_github("mdsteiner/EFAtools")

To also build the vignette when installing the development version, use:

install.packages("devtools") devtools::install_github("mdsteiner/EFAtools", build_vignettes = TRUE)

Example

Here are a few examples on how to perform the analyses with the different types and how to compare the results using the COMPAREfunction. For more details, see the vignette by runningvignette("EFAtools", package = "EFAtools"). The vignette provides a high-level introduction into the functionalities of the package.

load the package

library(EFAtools)

Run all possible factor retention methods

N_FACTORS(test_models$baseline$cormat, N = 500, method = "ML") #> Warning in N_FACTORS(test_models$baseline$cormat, N = 500, method = "ML"): ! 'x' was a correlation matrix but CD needs raw data. Skipping CD. #> ◉ 🏃 ◯ ◯ ◯ ◯ ◯ Running EKC ◉ ◉ 🏃 ◯ ◯ ◯ ◯ Running HULL ◉ ◉ ◉ 🏃 ◯ ◯ ◯ Running KGC ◉ ◉ ◉ ◉ 🏃 ◯ ◯ Running PARALLEL ◉ ◉ ◉ ◉ ◉ 🏃 ◯ Running SCREE ◉ ◉ ◉ ◉ ◉ ◉ 🏃 Running SMT ◉ ◉ ◉ ◉ ◉ ◉ ◉ Done! #> #> ── Tests for the suitability of the data for factor analysis ─────────────────── #> #> Bartlett's test of sphericity #> #> ✔ The Bartlett's test of sphericity was significant at an alpha level of .05. #> These data are probably suitable for factor analysis. #> #> 𝜒²(153) = 2173.28, p < .001 #> #> Kaiser-Meyer-Olkin criterion (KMO) #> #> ✔ The overall KMO value for your data is marvellous with 0.916. #> These data are probably suitable for factor analysis. #> #> ── Number of factors suggested by the different factor retention criteria ────── #> #> ◌ Comparison data: NA #> ◌ Empirical Kaiser criterion: 2 #> ◌ Hull method with CAF: 3 #> ◌ Hull method with CFI: 1 #> ◌ Hull method with RMSEA: 1 #> ◌ Kaiser-Guttman criterion with PCA: 3 #> ◌ Kaiser-Guttman criterion with SMC: 1 #> ◌ Kaiser-Guttman criterion with EFA: 1 #> ◌ Parallel analysis with PCA: 3 #> ◌ Parallel analysis with SMC: 3 #> ◌ Parallel analysis with EFA: 3 #> ◌ Sequential 𝜒² model tests: 3 #> ◌ Lower bound of RMSEA 90% confidence interval: 2 #> ◌ Akaike Information Criterion: 3

A type SPSS EFA to mimick the SPSS implementation with

promax rotation

EFA_SPSS <- EFA(test_models$baseline$cormat, n_factors = 3, type = "SPSS", rotation = "promax")

look at solution

EFA_SPSS #> #> EFA performed with type = 'SPSS', method = 'PAF', and rotation = 'promax'. #> #> ── Rotated Loadings ──────────────────────────────────────────────────────────── #> #> F1 F2 F3 h2 u2
#> V1 -.048 .035 .613 .367 .633 #> V2 -.001 .067 .482 .277 .723 #> V3 .060 .056 .453 .283 .717 #> V4 .101 -.009 .551 .378 .622 #> V5 .157 -.018 .438 .293 .707 #> V6 -.072 -.049 .704 .399 .601 #> V7 .001 .533 .093 .357 .643 #> V8 -.016 .581 .030 .349 .651 #> V9 .038 .550 -.001 .330 .670 #> V10 -.022 .674 -.071 .383 .617 #> V11 .015 .356 .232 .297 .703 #> V12 .020 .651 -.010 .432 .568 #> V13 .614 .086 -.067 .394 .606 #> V14 .548 -.068 .088 .322 .678 #> V15 .561 .128 -.070 .363 .637 #> V16 .555 -.050 .091 .344 .656 #> V17 .664 -.037 -.027 .390 .610 #> V18 .555 .004 .050 .350 .650 #> #> ── Factor Intercorrelations ──────────────────────────────────────────────────── #> #> F1 F2 F3
#> F1 1.000 0.617 0.648 #> F2 0.617 1.000 0.632 #> F3 0.648 0.632 1.000 #> #> ── Variances Accounted for ───────────────────────────────────────────────────── #> #> F1 F2 F3
#> SS loadings 2.198 2.074 2.034 #> Prop Tot Var 0.122 0.115 0.113 #> Cum Prop Tot Var 0.122 0.237 0.350 #> Prop Comm Var 0.349 0.329 0.323 #> Cum Prop Comm Var 0.349 0.677 1.000 #> #> ── Model Fit ─────────────────────────────────────────────────────────────────── #> #> CAF: .50 #> df: 102

A type psych EFA to mimick the psych::fa() implementation with

promax rotation

EFA_psych <- EFA(test_models$baseline$cormat, n_factors = 3, type = "psych", rotation = "promax")

compare the type psych and type SPSS implementations

COMPARE(EFA_SPSS$rot_loadings, EFA_psych$rot_loadings, x_labels = c("SPSS", "psych")) #> Mean [min, max] absolute difference: 0.0090 [ 0.0001, 0.0245] #> Median absolute difference: 0.0095 #> Max decimals where all numbers are equal: 0 #> Minimum number of decimals provided: 17 #> #> F1 F2 F3
#> V1 0.0150 0.0142 -0.0195 #> V2 0.0109 0.0109 -0.0138 #> V3 0.0095 0.0103 -0.0119 #> V4 0.0118 0.0131 -0.0154 #> V5 0.0084 0.0105 -0.0109 #> V6 0.0183 0.0169 -0.0245 #> V7 -0.0026 -0.0017 0.0076 #> V8 -0.0043 -0.0035 0.0102 #> V9 -0.0055 -0.0040 0.0117 #> V10 -0.0075 -0.0066 0.0151 #> V11 0.0021 0.0029 0.0001 #> V12 -0.0064 -0.0050 0.0136 #> V13 -0.0109 -0.0019 0.0163 #> V14 -0.0049 0.0028 0.0070 #> V15 -0.0107 -0.0023 0.0161 #> V16 -0.0051 0.0028 0.0074 #> V17 -0.0096 -0.0001 0.0136 #> V18 -0.0066 0.0014 0.0098

Average solution across many different EFAs with oblique rotations

EFA_AV <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500, method = c("PAF", "ML", "ULS"), rotation = "oblique", show_progress = FALSE)

look at solution

EFA_AV #> #> Averaging performed with averaging method mean (trim = 0) across 162 EFAs, varying the following settings: method, init_comm, criterion_type, start_method, rotation, k_promax, P_type, and varimax_type. #> #> The error rate is at 0%. Of the solutions that did not result in an error, 100% converged, 0% contained Heywood cases, and 100% were admissible. #> #> #> ══ Indicator-to-Factor Correspondences ═════════════════════════════════════════ #> #> For each cell, the proportion of solutions including the respective indicator-to-factor correspondence. A salience threshold of 0.3 was used to determine indicator-to-factor correspondences. #> #> F1 F2 F3 #> V1 .11 .00 1.00 #> V2 .11 .00 1.00 #> V3 .11 .00 .94 #> V4 .11 .00 1.00 #> V5 .11 .00 .94 #> V6 .11 .00 1.00 #> V7 .11 .94 .00 #> V8 .11 1.00 .00 #> V9 .11 .94 .00 #> V10 .11 1.00 .00 #> V11 .11 .89 .00 #> V12 .11 1.00 .00 #> V13 1.00 .00 .00 #> V14 1.00 .00 .00 #> V15 1.00 .00 .00 #> V16 1.00 .00 .00 #> V17 1.00 .00 .00 #> V18 1.00 .00 .00 #> #> #> ══ Loadings ════════════════════════════════════════════════════════════════════ #> #> ── Mean ──────────────────────────────────────────────────────────────────────── #> #> F1 F2 F3
#> V1 .025 .048 .576 #> V2 .060 .077 .451 #> V3 .115 .066 .425 #> V4 .157 .007 .518 #> V5 .198 -.002 .412 #> V6 .002 -.028 .658 #> V7 .074 .497 .102 #> V8 .056 .538 .046 #> V9 .100 .510 .018 #> V10 .048 .625 -.046 #> V11 .082 .336 .228 #> V12 .094 .606 .007 #> V13 .597 .083 -.047 #> V14 .531 -.056 .093 #> V15 .548 .122 -.049 #> V16 .540 -.041 .097 #> V17 .633 -.033 -.009 #> V18 .542 .009 .060 #> #> ── Range ─────────────────────────────────────────────────────────────────────── #> #> F1 F2 F3
#> V1 0.513 0.086 0.239 #> V2 0.431 0.093 0.186 #> V3 0.394 0.108 0.179 #> V4 0.415 0.110 0.214 #> V5 0.315 0.122 0.177 #> V6 0.514 0.104 0.267 #> V7 0.527 0.255 0.089 #> V8 0.520 0.275 0.078 #> V9 0.470 0.276 0.080 #> V10 0.533 0.313 0.097 #> V11 0.482 0.176 0.102 #> V12 0.548 0.324 0.103 #> V13 0.081 0.289 0.114 #> V14 0.063 0.220 0.117 #> V15 0.091 0.280 0.107 #> V16 0.072 0.230 0.122 #> V17 0.108 0.270 0.124 #> V18 0.081 0.246 0.118 #> #> #> ══ Factor Intercorrelations from Oblique Solutions ═════════════════════════════ #> #> ── Mean ──────────────────────────────────────────────────────────────────────── #> #> F1 F2 F3
#> F1 1.000 0.431 0.518 #> F2 0.431 1.000 0.454 #> F3 0.518 0.454 1.000 #> #> ── Range ─────────────────────────────────────────────────────────────────────── #> #> F1 F2 F3
#> F1 0.000 1.276 0.679 #> F2 1.276 0.000 1.316 #> F3 0.679 1.316 0.000 #> #> #> ══ Variances Accounted for ═════════════════════════════════════════════════════ #> #> ── Mean ──────────────────────────────────────────────────────────────────────── #> #> F1 F2 F3
#> SS loadings 2.443 1.929 1.904 #> Prop Tot Var 0.136 0.107 0.106 #> Prop Comm Var 0.389 0.307 0.303 #> #> ── Range ─────────────────────────────────────────────────────────────────────── #> #> F1 F2 F3
#> SS loadings 2.831 1.356 1.291 #> Prop Tot Var 0.157 0.075 0.072 #> Prop Comm Var 0.419 0.215 0.215 #> #> #> ══ Model Fit ═══════════════════════════════════════════════════════════════════ #> #> M (SD) [Min; Max] #> 𝜒²: 101.73 (34.62) [53.23; 125.98] #> df: 102 #> p: .369 (.450) [.054; 1.000] #> CFI: 1.00 (.00) [1.00; 1.00] #> RMSEA: .01 (.01) [.00; .02] #> AIC: -102.27 (34.62) [-150.77; -78.02] #> BIC: -532.16 (34.62) [-580.66; -507.91] #> CAF: .50 (.00) [.50; .50]

Perform a Schmid-Leiman transformation

SL <- SL(EFA_psych)

Based on a specific salience threshold for the loadings (here: .20):

factor_corres <- SL$sl[, c("F1", "F2", "F3")] >= .2

Compute omegas from the Schmid-Leiman solution

OMEGA(SL, factor_corres = factor_corres) #> Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors: #> #> tot hier sub H ECV PUC #> g 0.883 0.750 0.122 0.845 0.668 0.706 #> F1 0.769 0.498 0.272 0.465
#> F2 0.764 0.494 0.270 0.473
#> F3 0.745 0.543 0.202 0.380

Citation

If you use this package in your research, please acknowledge it by citing:

Steiner, M.D., & Grieder, S.G. (2020). EFAtools: An R package with fast and flexible implementations of exploratory factor analysis tools.Journal of Open Source Software, 5(53), 2521.https://doi.org/10.21105/joss.02521

Contribute or Report Bugs

If you want to contribute or report bugs, please open an issue on GitHub or email us at markus.d.steiner@gmail.com orsilvia.grieder@gmail.com.