View source: R/supplementaryObservations4PLSCA.R
supplementaryObservations4PLSCA | R Documentation |
tepPLSCA
.supplementaryObservations4PLSCA
:
computes the latent variables for
supplementary observations for a PLSCA model
computed with tepPLSCA
.
supplementaryObservations4PLSCA(
resPLSCA,
Xsup = NULL,
Ysup = NULL,
dimNames = "Dimension "
)
resPLSCA |
the results of a |
Xsup |
an |
Ysup |
an |
dimNames |
Names for the
dimensions (i.e., factors) for the
supplementary loadings (Default: |
The original analysis is performed with
tepPLSCA
on the original data matrices
X (N
by I
) and Y (N
by J
).
The supplementary data matrices should have I
columns for Xsup and J
columns for Ysup. Note that PLSCA
is used
with qualitative variables (i.e., factors) recoded
as 0/1 variables with disjunctive coding
(i.e., with makeNominalData
),
the supplementary
variables need to be recoded in the same way.
For PLSCA
the observations need to be pre-processed in
the same way as the original observations. Often, in PLSCA
,
the observations are described by qualitative variables
(in general coded as factors) which are then recoded
(e.g., with the function
makeNominalData
from ExPosition
) as a set of 0/1 vectors prior to
ruccing PLSCA
.
So
When this , the supplementary observations should becoded
as factors too with the same levels (aka modalities) as
the active observations
(see also makeNominalData
).
The projections of supplementary observations in PLSC
is obtained using the standard transition formulas
from correspondence analysis (with an additional scaling factor
to get the covariance of the latent variables equal to their
singular values).
The latent variables
can be obtained from
the loadings of their set. For example:
if we denote Delta the diagonal matrix of
the singular values,
F (resp. G) the singular value normalized
loadings (denoted fi
, resp. fj
,
in PLSCA
),
and Lx (resp. Ly) the row (resp. column)
latent variables (called lx
and ly
in
tepLSCA
),
the latent variables of one set are derived from the set loadings:
Lx = sqrt(N
) XF inv(Delta) and
Ly = sqrt(N
) YG inv(Delta). Eq.1
with: inv(Delta) being the inverse of Delta, N
being the number of rows (i.e., observations) of X and Y,
and X and Y are row profile versions of the original
data sets.
Supplementary observations latent variable values
are obtained by using the transition formulas from
correspondence analysis (see Eq.1, Section above).
So, the values for the latent variable
for the supplementary observations
from the Xset
and the Yset
can be obtained from their row profiles
(denoted Xsup and Ysup)
by replacing in Eq.1
X by Xsup and Y by Ysup:
Lxsup = sqrt(N
) Xsup F inv(Delta) and
Lysup = sqrt(N
) Ysup G inv(Delta). Eq.2
A list with lx.sup
and ly.sup
giving the latent variables values
of the supplementary observations
for (respectively) X
and Y
.
Hervé Abdi
See:
Beaton, D., Dunlop, J., ADNI, & Abdi, H. (2016). Partial Least Squares-Correspondence Analysis (PLSCA): A framework to simultaneously analyze behavioral and genetic data. Psychological Methods, 21, 621-651.
Abdi H. & Béra, M. (2018). Correspondence analysis. In R. Alhajj and J. Rokne (Eds.), Encyclopedia of Social Networks and Mining (2nd Edition). New York: Springer Verlag.
Abdi, H. (2007). Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp. 907-912.
tepPLSCA
makeRowProfiles
supplementaryVariables4PLSCA
supplementaryObservations4PLSC
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