Deduce imputation values for categorical data. By substituting all known values and interatively eliminating the unknowns from the set of edits, unique imputation values are derived where possible.

1 2 | ```
deductiveLevels(E, x, adapt = rep(FALSE, length(x)),
checkFeasibility = TRUE)
``` |

`E` |
editarray |

`x` |
a named |

`adapt` |
boolean vector indicating which variables may be adapted. |

`checkFeasibility` |
Test wether the assumed-correct values (observed and not designated by adapt) can lead to a consistent record. |

Imputation values are derived for missing variables (NA) and for variables indicated by 'adapt'.

A named vector with imputation values for `x`

T. De Waal, J. Pannekoek and S. Scholtus (2011) Handbook of statistical data editing Chpt 9.2.1 - 9.2.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | ```
# a simple example. We know the subject is pregnant. What is the gender?
E <- editarray(c(
"gender \%in\% c('male','female')",
"pregnant \%in\% c(TRUE,FALSE)",
"if ( gender=='male') !pregnant"))
# a record with unknown gender
x <- c(gender=NA,pregnant=TRUE)
# find imputations
(s <- deductiveLevels(E,x))
# imputation can be done as follows:
x[names(s)] <- s
# Here's an example from De Waal et al (2011) (ex. 9.3)
E <- editarray(c(
"x1 \%in\% letters[1:4]",
"x2 \%in\% letters[1:3]",
"x3 \%in\% letters[1:3]",
"x4 \%in\% letters[1:2]",
"if (x2 == 'c' & x3 != 'c' & x4 == 'a' ) FALSE",
"if (x2 != 'a' & x4 == 'b') FALSE",
"if (x1 != 'c' & x2 != 'b' & x3 != 'a') FALSE",
"if (x1 == 'c' & x3 != 'a' & x4 == 'a' ) FALSE"
))
x <- c(x1='c',x2='b',x3=NA,x4=NA)
(s <- deductiveLevels(E,x))
x[names(s)] <- s
# another example, partial imputation
y <- c(x1=NA,x2=NA,x3=NA,x4='b')
(s <- deductiveLevels(E,y))
y[names(s)] <- s
``` |

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