The functions principal_components() and factor_analysis() can
be used to perform a principal component analysis (PCA) or a factor analysis
(FA). They return the loadings as a data frame, and various methods and
functions are available to access / display other information (see the
Details section).
factor_analysis(
x,
n = "auto",
rotation = "none",
sort = FALSE,
threshold = NULL,
standardize = TRUE,
cor = NULL,
...
)principal_components(
x,
n = "auto",
rotation = "none",
sparse = FALSE,
sort = FALSE,
threshold = NULL,
standardize = TRUE,
...
)
rotated_data(pca_results, verbose = TRUE)
# S3 method for parameters_efa
predict(
object,
newdata = NULL,
names = NULL,
keep_na = TRUE,
verbose = TRUE,
...
)
# S3 method for parameters_efa
print(x, digits = 2, sort = FALSE, threshold = NULL, labels = NULL, ...)
# S3 method for parameters_efa
sort(x, ...)
closest_component(pca_results)
A data frame of loadings.
A data frame or a statistical model.
Number of components to extract. If n="all", then n is set as
the number of variables minus 1 (ncol(x)-1). If n="auto" (default) or
n=NULL, the number of components is selected through n_factors() resp.
n_components(). Else, if n is a number, n components are extracted.
If n exceeds number of variables in the data, it is automatically set to
the maximum number (i.e. ncol(x)). In reduce_parameters(), can also
be "max", in which case it will select all the components that are
maximally pseudo-loaded (i.e., correlated) by at least one variable.
If not "none", the PCA / FA will be computed using the
psych package. Possible options include "varimax",
"quartimax", "promax", "oblimin", "simplimax",
or "cluster" (and more). See psych::fa() for details.
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 logical value indicating whether the variables should be standardized (centered and scaled) to have unit variance before the analysis (in general, such scaling is advisable).
An optional correlation matrix that can be used (note that the
data must still be passed as the first argument). If NULL, will
compute it by running cor() on the passed data.
Arguments passed to or from other methods.
Whether to compute sparse PCA (SPCA, using sparsepca::spca()).
SPCA attempts to find sparse loadings (with few nonzero values), which improves
interpretability and avoids overfitting. Can be TRUE or "robust" (see
sparsepca::robspca()).
The output of the principal_components() function.
Toggle warnings.
An object of class parameters_pca or parameters_efa
An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
Optional character vector to name columns of the returned data frame.
Logical, if TRUE, predictions also return observations
with missing values from the original data, hence the number of rows of
predicted data and original data is equal.
Argument for print(), indicates the number of digits
(rounding) to be used.
Argument for print(), character vector of same length as
columns in x. If provided, adds an additional column with the labels.
n_components() and n_factors() automatically estimates the optimal
number of dimensions to retain.
performance::check_factorstructure() checks the suitability of the
data for factor analysis using the sphericity (see
performance::check_sphericity_bartlett()) and the KMO (see
performance::check_kmo()) measure.
performance::check_itemscale() computes various measures of internal
consistencies applied to the (sub)scales (i.e., components) extracted from
the PCA.
Running summary() returns information related to each component/factor,
such as the explained variance and the Eivenvalues.
Running get_scores() computes scores for each subscale.
Running closest_component() will return a numeric vector with the
assigned component index for each column from the original data frame.
Running rotated_data() will return the rotated data, including missing
values, so it matches the original data frame.
Running
plot()
visually displays the loadings (that requires the
see-package to work).
Complexity 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 (Hofman, 1978; Pettersson and Turkheimer, 2010).
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).
There is a simplified rule of thumb that may help do decide whether to run a factor analysis or a principal component analysis:
Run factor analysis if you assume or wish to test a theoretical model of latent factors causing observed variables.
Run principal component analysis If you want to simply reduce your correlated observed variables to a smaller set of important independent composite variables.
(Source: CrossValidated)
Use get_scores() to compute scores for the "subscales" represented by the
extracted principal components. get_scores() takes the results from
principal_components() and extracts the variables for each component found
by the PCA. Then, for each of these "subscales", raw means are calculated
(which equals adding up the single items and dividing by the number of items).
This results in a sum score for each component from the PCA, which is on the
same scale as the original, single items that were used to compute the PCA.
One can also use predict() to back-predict scores for each component,
to which one can provide newdata or a vector of names for the components.
Use summary() to get the Eigenvalues and the explained variance for each
extracted component. The eigenvectors and eigenvalues represent the "core"
of a PCA: The eigenvectors (the principal components) determine the
directions of the new feature space, and the eigenvalues determine their
magnitude. In other words, the eigenvalues explain the variance of the
data along the new feature axes.
Kaiser, H.F. and Rice. J. (1974). Little jiffy, mark iv. Educational and Psychological Measurement, 34(1):111–117
Hofmann, R. (1978). Complexity and simplicity as objective indices descriptive of factor solutions. Multivariate Behavioral Research, 13:2, 247-250, tools:::Rd_expr_doi("10.1207/s15327906mbr1302_9")
Pettersson, E., & Turkheimer, E. (2010). Item selection, evaluation, and simple structure in personality data. Journal of research in personality, 44(4), 407-420, tools:::Rd_expr_doi("10.1016/j.jrp.2010.03.002")
Tabachnick, B. G., and Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Boston: Pearson Education.