mxPearsonSelCov
Perform Pearson Aitken selection
Description
![[Maturing]](../help/figures/lifecycle-maturing.svg)
These functions implement the Pearson Aitken selection formulae.
Usage
mxPearsonSelCov(origCov, newCov) mxPearsonSelMean(origCov, newCov, origMean)
Arguments
origCov |
covariance matrix. The covariance prior to selection. |
newCov |
covariance matrix. A subset of |
origMean |
column vector. A mean vector to adjust. |
Details
Which dimensions to condition on can be communicated in one
of two ways: (1) newCov is a submatrix of origCov.
The dimnames are matched to determine which
partition of origCov to replace with newCov.
Or (2) newCov is the same dimension as origCov.
The matrix entries are inspected to determine which entries have
changed. The changed entries determine which partition of
origCov to replace with newCov.
Let the n \times n covariance matrix R (origCov) be partitioned into non-empty,
disjoint sets p and q.
Let R_{ij} denote the covariance matrix between the p
and q variables where the subscripts denote the variable subsets (e.g. R_{pq}).
Let column vectors μ_p and μ_q contain the means of p and q
variables, respectively.
We wish to compute the conditional covariances of the variables in q
for a subset of the population where R_{pp} and μ_p are known (or partially known)—that is, we wish
to condition the covariances and means of q on those of p.
Let V_{pp} (newCov) be an arbitrary covariance matrix of the same
dimension as R_{pp}.
If we replace R_{pp} by V_{pp} then the mean
of q (origMean) is transformed as
See PDF version
and the covariance of p and q are transformed as
See PDF version
References
Aitken, A. (1935). Note on selection from a multivariate normal population. Proceedings of the Edinburgh Mathematical Society (Series 2), 4(2), 106-110. doi:10.1017/S0013091500008063
Examples
library(OpenMx)
m1 <- mxModel(
'selectionTest',
mxMatrix('Full', 10, 10, values=rWishart(1, 20, toeplitz((10:1)/10))[,,1],
dimnames=list(paste0('c',1:10),paste0('c',1:10)), name="m1"),
mxMatrix('Full', 2, 2, values=diag(2),
dimnames=list(paste0('c',1:2),paste0('c',1:2)), name="m2"),
mxMatrix('Full', 10, 1, values=runif(10),
dimnames=list(paste0('c',1:10),c('v')), name="u1"),
mxAlgebra(mxPearsonSelCov(m1, m2), name="c1"),
mxAlgebra(mxPearsonSelMean(m1, m2, u1), name="u2")
)
m1 <- mxRun(m1)