Description
Principal component analysis (PCA) is a method to identify structures
in data. It is a well known method of data reduction which can also be
applied to any squared matrix. It is applied to the inter-construct
correlations in order to explore structures in the relations between
constructs in the case of grids. The default type of rotation used is
Varimax. Other methods can be chosen (see ?constructPca).
In comparison to the Root-mean-square statistic, a PCA accounts for the
sign of the correlation thus allowing the .
R-Code
The following codes calculates a PCA with three factors (default) and
varimax rotation (default).
constructPca(fbb2003)
#
# #################
# PCA of constructs
# #################
#
# Number of components extracted: 3
# Type of rotation: varimax
#
# Loadings:
# RC1 RC2 RC3
# clever - not bright 0.96 0.02 0.25
# disorganized - organized -0.82 -0.40 -0.17
# listens - doesn't hear 0.92 -0.26 0.12
# no clear view - clear view of life -0.45 -0.15 -0.76
# understands me - no understanding 0.87 -0.07 -0.08
# ambitious - no ambition 0.02 0.13 0.94
# respected - not respected 0.91 -0.01 0.22
# distant - warm -0.13 0.74 0.25
# rather aggressive - not aggressive 0.07 0.96 0.00
#
# RC1 RC2 RC3
# SS loadings 4.27 1.74 1.69
# Proportion Var 0.47 0.19 0.19
# Cumulative Var 0.47 0.67 0.86You can specify the number of components to extract. The following code yields the examples from Fransella et al. (2003, p.87). Two components are extracted using varimax rotation.
constructPca(fbb2003, nf=2)
#
# #################
# PCA of constructs
# #################
#
# Number of components extracted: 2
# Type of rotation: varimax
#
# Loadings:
# RC1 RC2
# clever - not bright 0.98 0.13
# disorganized - organized -0.79 -0.40
# listens - doesn't hear 0.95 -0.17
# no clear view - clear view of life -0.57 -0.54
# understands me - no understanding 0.84 -0.13
# ambitious - no ambition 0.20 0.64
# respected - not respected 0.93 0.09
# distant - warm -0.16 0.75
# rather aggressive - not aggressive -0.03 0.79
#
# RC1 RC2
# SS loadings 4.47 2.13
# Proportion Var 0.50 0.24
# Cumulative Var 0.50 0.73In case the results are needed for further processing you can save the ouput.
r <- constructPca(fbb2003, nf=2)To gain an easier overview of the data, a cutoff level can be set to surpress the printing of small loadings.
print(r, cut=.3)
#
# #################
# PCA of constructs
# #################
#
# Number of components extracted: 2
# Type of rotation: varimax
#
# Loadings:
# RC1 RC2
# clever - not bright 0.98
# disorganized - organized -0.79 -0.40
# listens - doesn't hear 0.95
# no clear view - clear view of life -0.57 -0.54
# understands me - no understanding 0.84
# ambitious - no ambition 0.64
# respected - not respected 0.93
# distant - warm 0.75
# rather aggressive - not aggressive 0.79
#
# RC1 RC2
# SS loadings 4.47 2.13
# Proportion Var 0.50 0.24
# Cumulative Var 0.50 0.73Different methods of rotation can be chosen: none,
varimax, promax, cluster.
constructPca(fbb2003, rotate="none")
constructPca(fbb2003, rotate="varimax")
constructPca(fbb2003, rotate="promax")
constructPca(fbb2003, rotate="cluster")As a default, the correlation matrix is calculated using
product-moment correlation. The methods that can be selected are
pearson, kendall, spearman.
constructPca(fbb2003, method="pearson") # default setting
constructPca(fbb2003, method="kendall")
constructPca(fbb2003, method="spearman")