deducorrect (version 1.3.7)

solSpace: Solution space for missing values under equality constraints

Description

Solution space for missing values under equality constraints

solSpace method for editmatrix

This function finds the space of solutions for a numerical record $x$ with missing values under linear constraints $Ax=b$. Write $x=(x_{obs},x_{miss})$. Then the solution space for $x_{miss}$ is given by $x_0 + Cz$, where $x_0$ is a constant vector, $C$ a constant matrix and $z$ is any real vector of dimension ncol(C). This function computes $x_0$ and $C$.

Usage

solSpace(E, x, ...)
"solSpace"(E, x, adapt = logical(length(x)), checkFeasibility = TRUE, ...)
"solSpace"(E, x, b, adapt = logical(length(x)), tol = sqrt(.Machine$double.eps), ...)

Arguments

E

and editmatrix or equality constraint matrix

x

a named numeric vector.

...

Extra parameters to pass to solSpace.matrix

adapt

A named logical vector with variables in the same order as in x

checkFeasibility

Check if the observed values can lead to a consistent record

b

Equality constraint constant vector

tol

tolerance used to determine 0-singular values when determining generalized inverse and to round coefficients of C to zero. See MASS::ginv.

Value

A list with elements $x0$ and $C$ or NULL if the solution space is empty

Details

The user can specify extra fields to include in $x_{miss}$ by specifying adapt. Also note that the method rests on the assumtion that all nonmissng values of $x$ are correct.

The most timeconsuming step involves computing the generalized inverse of $A_{miss}$ using MASS::ginv (code copied from MASS to avoid dependency). See the package vignette and De Waal et al. (2011) for more details.

References

T. De Waal, J. Pannekoek and S. Scholtus (2011) Handbook of statistical data editing Chpt 9.2.1

Venables, W. N. & Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer, New York. ISBN 0-387-95457-0

See Also

deduImpute, deductiveZeros

Examples

# This example is taken from De Waal et al (2011) (Examples 9.1-9.2)
E <- editmatrix(c(
    "x1 + x2      == x3",
    "x2           == x4",
    "x5 + x6 + x7 == x8",
    "x3 + x8      == x9",
    "x9 - x10     == x11",
    "x6 >= 0",
    "x7 >= 0"
))


dat <- data.frame(
    x1=c(145,145),
    x2=c(NA,NA),
    x3=c(155,155),
    x4=c(NA,NA),
    x5=c(NA, 86),
    x6=c(NA,NA),
    x7=c(NA,NA),
    x8=c(86,86),
    x9=c(NA,NA),
    x10=c(217,217),
    x11=c(NA,NA)
)

# example with solSpace method for editmatrix
# example 9.1 of De Waal et al (2011).
x <-t(dat)[,1]
s <- solSpace(E,x)
s

# some values are uniquely determined and may be imputed directly:
imputess(x,s$x0,s$C)


# To impute everything, we choose z=1 (arbitrary)
z <- rep(1,sum(is.na(x)))
(y <- imputess(x,s$x0,s$C,z))

# did it work? (use a tolerance in checking to account for machine rounding)
# (FALSE means an edit is not violated)
any(violatedEdits(E,y,tol=1e-8))


# here's an example showing that solSpace only looks at missing values unless
# told otherwise.
Ey <- editmatrix(c(
    "yt == y1 + y2 + y3",
    "y4 == 0"))
y <- c(yt=10, y1=NA, y2=3, y3=7,y4=12)
# since solSpace by default checks the feasibility, we get no solution (since
# y4 violates the second edit)"
solSpace(Ey,y)


# If we ask solSpace not to check for feasibility, y4 is left alone (although
# the imputed answer is clearly wrong).
(s <- solSpace(Ey,y,checkFeasibility=FALSE))
imputess(y, s$x0, s$C)

# by setting 'adapt' we can include y4 in the imputation Since we know that
# with this adapt vector, imputation can be done consistently, we save some
# time by switching the feasibility check off.
(s <- solSpace(Ey,y,adapt=c(FALSE,FALSE,FALSE,FALSE,TRUE), 
  checkFeasibility=FALSE))
imputess(y,s$x0,s$C)