Format structural models from the psych or FactoMineR packages.

# S3 method for PCA
model_parameters(
model,
sort = FALSE,
threshold = NULL,
labels = NULL,
verbose = TRUE,
...
)

# S3 method for principal
model_parameters(
model,
sort = FALSE,
threshold = NULL,
labels = NULL,
verbose = TRUE,
...
)

# S3 method for omega
model_parameters(model, verbose = TRUE, ...)

## Arguments

model PCA or FA created by the psych or FactoMineR packages (e.g. through psych::principal, psych::fa or psych::omega). Sort the loadings. A value between 0 and 1 indicates which (absolute) values from the loadings should be removed. An integer higher than 1 indicates the n strongest loadings to retain. Can also be "max", in which case it will only display the maximum loading per variable (the most simple structure). A character vector containing labels to be added to the loadings data. Usually, the question related to the item. Toggle warnings and messages. Arguments passed to or from other methods.

## Details

For the structural models obtained with psych, the following indices are present:

• Complexity (Hoffman's, 1978; Pettersson and Turkheimer, 2010) represents the number of latent components needed to account for the observed variables. Whereas a perfect simple structure solution has a complexity of 1 in that each item would only load on one factor, a solution with evenly distributed items has a complexity greater than 1.

• Uniqueness represents the variance that is 'unique' to the variable and not shared with other variables. It is equal to 1 – communality (variance that is shared with other variables). A uniqueness of 0.20 suggests that 20% or that variable's variance is not shared with other variables in the overall factor model. The greater 'uniqueness' the lower the relevance of the variable in the factor model.

• MSA represents the Kaiser-Meyer-Olkin Measure of Sampling Adequacy (Kaiser and Rice, 1974) for each item. It indicates whether there is enough data for each factor give reliable results for the PCA. The value should be > 0.6, and desirable values are > 0.8 (Tabachnick and Fidell, 2013).

## References

• Kaiser, H.F. and Rice. J. (1974). Little jiffy, mark iv. Educational and Psychological Measurement, 34(1):111–117

• Pettersson, E., \& Turkheimer, E. (2010). Item selection, evaluation, and simple structure in personality data. Journal of research in personality, 44(4), 407-420.

• Revelle, W. (2016). How To: Use the psych package for Factor Analysis and data reduction.

• Tabachnick, B. G., and Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Boston: Pearson Education.

## Examples

# \donttest{
library(parameters)
if (require("psych", quietly = TRUE)) {
# Principal Component Analysis (PCA) ---------
pca <- psych::principal(attitude)
model_parameters(pca)

pca <- psych::principal(attitude, nfactors = 3, rotate = "none")
model_parameters(pca, sort = TRUE, threshold = 0.2)

principal_components(attitude, n = 3, sort = TRUE, threshold = 0.2)

# Exploratory Factor Analysis (EFA) ---------
efa <- psych::fa(attitude, nfactors = 3)
model_parameters(efa, threshold = "max", sort = TRUE, labels = as.character(1:ncol(attitude)))

# Omega ---------
omega <- psych::omega(mtcars, nfactors = 3)
params <- model_parameters(omega)
params
summary(params)
}

#> Composite | Total Variance (%) | Variance due to General Factor (%) | Variance due to Group Factor (%)
#> ------------------------------------------------------------------------------------------------------
#> g         |              97.28 |                              56.64 |                            26.42
#> F1*       |              90.12 |                              31.07 |                            59.05
#> F2*       |              91.37 |                              69.32 |                            22.04
#> F3*       |              87.36 |                              59.65 |                            27.71

# FactoMineR ---------
if (require("FactoMineR", quietly = TRUE)) {
model <- FactoMineR::PCA(iris[, 1:4], ncp = 2)
model_parameters(model)
attributes(model_parameters(model))\$scores

model <- FactoMineR::FAMD(iris, ncp = 2)
model_parameters(model)
}
#> Warning: ggrepel: 93 unlabeled data points (too many overlaps). Consider increasing max.overlaps
#> Warning: ggrepel: 93 unlabeled data points (too many overlaps). Consider increasing max.overlaps
#>
#> Variable     | Dim.1 |  Dim.2   | Complexity
#> --------------------------------------------
#> Sepal.Length | 0.75  |   0.07   |    1.02
#> Sepal.Width  | 0.23  |   0.51   |    1.41
#> Petal.Length | 0.98  | 1.32e-03 |    1.00
#> Petal.Width  | 0.94  |   0.01   |    1.00
#> Species      | 0.96  |   0.75   |    1.88
#>
#> The 2 latent factors accounted for 86.87% of the total variance of the original data (Dim.1 = 64.50%, Dim.2 = 22.37%).
#>
# }