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longitudinalData (version 2.1.2)

imputation: ~ Function: imputation ~

Description

imputation is a function that offer different methods to impute missing value of a LongData (or a matrix).

Usage

imputation(traj,method="copyMean",lowerBound="min",upperBound="max")

Arguments

traj
[LongData] or [matrix] : trajectories to impute.
method
[character]: Name of the imputation method (see detail)
lowerBound
[character] or [numeric]: fixes the smallest value that an imputed value can take. If a single value is given, it is duplicate for all the column. The special value 'min' means that the lower bound wil
upperBound
[character] or [numeric]: fixes the biggest value that an imputed value can take. If a single value is given, it is duplicate for all the column. The special value 'max' means that the upper bound will

Value

  • A LongData or a matrix with no missing values.

item

  • 'linearInterpol.global' (linear interpolation, global slope)
  • Monotone:
  • 'linearInterpol.local' (linear interpolation, global slope)
  • Monotone at start:
  • Monotone at end:
  • 'linearInterpol.bisector' (linear interpolation, bisector)
  • Monotone:
  • 'copyMean.locf' (copy mean, locf)
  • 'copyMean.global' (copy mean, global slope)
  • 'copyMean.local' (copy mean, local slope)
  • 'copyMean.bisector' (copy mean, bisector)
  • locf (Last Occurence Carried Forward)
  • Monotone at start:
  • nocb (Next Occurence Carried Backward)
  • Monotone at end:
  • trajMean
  • trajMedian
  • trajHotDeck
  • crossMean
  • crossMedian
  • crossHotDeck

itemize

  • Intermitant and monotone at start:

Author

Christophe Genolini 1. UMR U1027, INSERM, Universit� Paul Sabatier / Toulouse III / France 2. CeRSME, EA 2931, UFR STAPS, Universit� de Paris Ouest-Nanterre-La D�fense / Nanterre / France

Details

imputation is a function that impute missing value of a LongData or a matrix. Several imputation methods are available. A brief description follows. For a fully detailled description, see [gen12] (submitted). Illustrating examples showing strenghs and weakness of methods are presented section "examples". For each method, the imputation has to deal with monotone missing value (at start and at end of the trajectories) and intermitant (in the middle). Here is a brief description of each methods.
  • 'linearInterpol.locf' (linear interpolation, locf)
{
  • Intermitant:
{ values imediatly surounding the missing are join by a line.} Monotone:{ imputed by 'locf' or 'nocb'.} }

References

[1] C. Genolini and B. Falissard "KmL: k-means for longitudinal data" Computational Statistics, vol 25(2), pp 317-328, 2010 [2] C. Genolini and B. Falissard "KmL: A package to cluster longitudinal data" Computer Methods and Programs in Biomedicine, 104, pp e112-121, 2011

See Also

LongData, Partition, qualityCriterion

Examples

Run this code
##################
### Preparation of the data
par(ask=TRUE)
timeV <- 1:14

matMissing <- matrix(
    c(NA  ,NA  ,NA  ,18  ,22  ,NA  ,NA  ,NA  ,NA  , 24  , 22  , NA  , NA  , NA,
      24  ,21  ,24  ,26  ,27  ,32  ,30  ,22  ,26  , 26  , 28  , 24  , 23  , 21,
      14  ,13  , 10 , 8  , 7  ,18  ,16  , 8  ,12  ,  6  ,  10 ,  10 ,  9  ,  7,
       3  ,1   , 1  , 1  ,  3,9   , 7  , -1 , 3   ,  2   ,  4 ,  1  ,  0  , -2
   ),4,byrow=TRUE
)


matplot(t(matMissing),col=c(2,1,1,1),lty=1,type="l",lwd=c(3,1,1,1),pch=16,
   xlab="Black=trajectories; Green=mean trajectory
Red=trajectory to impute",
   ylab="",main="Four trajectories")
moy <- apply(matMissing,2,mean,na.rm=TRUE)
lines(moy,col=3,lwd=3)

 # # # # # # # # # # # # # # # # # # # # # # # # # #
#   Illustration of the different imputing method   #
 #           The best are at end  !!!              #
  # # # # # # # # # # # # # # # # # # # # # # # # #



##################
### Methods using cross sectionnal information (cross-methods)

par(mfrow=c(1,3))
mat2 <- matrix(c(
  NA, 9, 8, 8, 7, 6,NA,
   7, 6,NA,NA,NA, 4,5,
   3, 4, 3,NA,NA, 2,3,
  NA,NA, 1,NA,NA, 1,1),4,7,byrow=TRUE)

### crossMean
matplot(t(imputation(mat2,"crossMean")),type="l",ylim=c(0,10),lty=1,col=1,main="crossMean")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### crossMedian
matplot(t(imputation(mat2,"crossMedian")),type="l",ylim=c(0,10),lty=1,col=1,main="crossMedian")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### crossHotDeck
matplot(t(imputation(mat2,"crossHotDeck")),type="l",ylim=c(0,10),lty=1,col=1,main="crossHotDeck")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)



##################
### Methods using trajectory information (traj-methods)

par(mfrow=c(2,3))
mat1 <- matrix(c(NA,NA,3,8,NA,NA,2,2,1,NA,NA),1,11)

### locf
matplot(t(imputation(mat1,"locf")),type="l",ylim=c(0,10),main="locf
 DO NOT USE, BAD METHOD !!!")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### nocb
matplot(t(imputation(mat1,"nocb")),type="l",ylim=c(0,10),main="nocb
 DO NOT USE, BAD METHOD !!!")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### trajMean
matplot(t(imputation(mat1,"trajMean")),type="l",ylim=c(0,10),main="trajMean")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### trajMedian
matplot(t(imputation(mat1,"trajMedian")),type="l",ylim=c(0,10),main="trajMedian")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### trajHotDeck
matplot(t(imputation(mat1,"trajHotDeck")),type="l",ylim=c(0,10),main="trajHotDeck 1")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### spline
matplot(t(imputation(mat1,"spline",lowerBound=NA,upperBound=NA)),type="l",ylim=c(-10,10),main="spline")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)





##################
### Different linear interpolation

par(mfrow=c(2,2))

### linearInterpol.locf
matplot(t(imputation(mat1,"linearInterpol.locf",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="linearInterpol.locf")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)

### linearInterpol.global
matplot(t(imputation(mat1,"linearInterpol.global",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="linearInterpol.global")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)

### linearInterpol.local
matplot(t(imputation(mat1,"linearInterpol.local",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="linearInterpol.local")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)

### linearInterpol.bisector
matplot(t(imputation(mat1,"linearInterpol.bisector",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="linearInterpol.bisector")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)



##################
### Copy mean

mat3 <- matrix(c(
  NA, 9, 8, 8, 7, 6,NA,
   7, 6,NA,NA,NA, 4,5,
   3, 4, 3,NA,NA, 2,3,
  NA,NA, 1,NA,NA, 1,1),4,7,byrow=TRUE)


par(mfrow=c(2,2))

### copyMean.locf
matplot(t(imputation(mat2,"copyMean.locf",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="copyMean.locf")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### copyMean.global
matplot(t(imputation(mat2,"copyMean.global",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="copyMean.global")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### copyMean.local
matplot(t(imputation(mat2,"copyMean.local",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="copyMean.local")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### copyMean.bisector
matplot(t(imputation(mat2,"copyMean.bisector",NA,NA)),type="l",ylim=c(-5,10),lty=1,col=1,main="copyMean.bisector")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)




### crossMean
matImp <- imputation(matMissing,method="crossMean")
matplot(t(matImp),col=c(2,1,1,1),lty=c(2,1,1,1),type="l",lwd=c(2,1,1,1),pch=16, xlab="Dotted red=imputed trajectory
Full red=trajectory to impute",ylab="",main="Method 'crossMean'")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)


### crossMedian
matImp <- imputation(matMissing,method="crossMedian")
matplot(t(matImp),col=c(2,1,1,1),lty=c(2,1,1,1),type="l",lwd=c(2,1,1,1),pch=16, xlab="Dotted red=imputed trajectory
Full red=trajectory to impute",ylab="",main="Method 'crossMedian'")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### crossHotDeck
matImp <- imputation(matMissing,method="crossHotDeck")
matplot(t(matImp),col=c(2,1,1,1),lty=c(2,1,1,1),type="l",lwd=c(2,1,1,1),pch=16, xlab="Dotted red=imputed trajectory
Full red=trajectory to impute",ylab="",main="Method 'crossHotDeck'")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)


##################
### Method using trajectory

par(mfrow=c(2,3))
### trajMean
matImp <- imputation(matMissing,method="trajMean")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### trajMedian
matImp <- imputation(matMissing,method="trajMedian")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### trajHotDeck
matImp <- imputation(matMissing,method="trajHotDeck")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### locf
matImp <- imputation(matMissing,method="locf")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="locf")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### nocb
matImp <- imputation(matMissing,method="nocb")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

par(mfrow=c(2,2))

### linearInterpol.locf
matImp <- imputation(matMissing,method="linearInterpol.locf")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### linearInterpol.local
matImp <- imputation(matMissing,method="linearInterpol.local")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### linearInterpol.global
matImp <- imputation(matMissing,method="linearInterpol.global")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### linearInterpol.bisector
matImp <- imputation(matMissing,method="linearInterpol.bisector")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)


par(mfrow=c(2,2))

### copyMean.locf
matImp <- imputation(matMissing,method="copyMean.locf")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

### copyMean.local
matImp <- imputation(matMissing,method="copyMean.local")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

### copyMean.global
matImp <- imputation(matMissing,method="copyMean.global")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

### copyMean.bisector
matImp <- imputation(matMissing,method="copyMean.bisector")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

par(ask=FALSE)

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