Principal Component Analysis (PCA)
This function performs a principal component analysis (PCA) and returns the loadings as a data frame.
principal_components( x, n = "auto", rotation = "none", sort = FALSE, threshold = NULL, standardize = TRUE, ... ) closest_component(x) rotated_data(x) ## S3 method for class 'parameters_efa' predict(object, newdata = NULL, names = NULL, keep_na = TRUE, ...)
x |
A data frame or a statistical model. |
n |
Number of components to extract. If |
rotation |
If not |
sort |
Sort the loadings. |
threshold |
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 |
standardize |
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). |
... |
Arguments passed to or from other methods. |
object |
An object of class |
newdata |
An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used. |
names |
Optional character vector to name columns of the returned data frame. |
keep_na |
Logical, if |
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.
A data frame of loadings.
There is a summary()-method that prints the Eigenvalues and
(explained) variance for each extracted component.
closest_component() will return a numeric vector with the assigned
component index for each column from the original data frame.
rotated_data() will return the rotated data, including missing
values, so it matches the original data frame. There is also a
plot()-method
implemented in the
see-package.
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, 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, doi: 10.1016/j.jrp.2010.03.002
Tabachnick, B. G., and Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Boston: Pearson Education.
check_itemscale to compute various
measures of internal consistencies applied to the (sub)scales (i.e.
components) extracted from the PCA. Use get_scores to compute
scores for each subscale.
library(parameters)
if (require("psych")) {
principal_components(mtcars[, 1:7], n = "all", threshold = 0.2)
principal_components(mtcars[, 1:7],
n = 2, rotation = "oblimin",
threshold = "max", sort = TRUE
)
principal_components(mtcars[, 1:7], n = 2, threshold = 2, sort = TRUE)
pca <- principal_components(mtcars[, 1:5], n = 2, rotation = "varimax")
pca # Print loadings
summary(pca) # Print information about the factors
predict(pca, names = c("Component1", "Component2")) # Back-predict scores
# which variables from the original data belong to which extracted component?
closest_component(pca)
}
# Automated number of components
principal_components(mtcars[, 1:4], n = "auto")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.