samonevalIM {samon}

Evaluates the loss function at a range of smoothing parameters

Description

Computes the loss function for a range of smoothing parameters

Usage

samonevalIM( mat, Npart = 10, sigmaList = c(1), inmodel =
inmodel, seed = 1, type="both")

Arguments

mat

matrix with (i,j) entry representing value for subject i at time-point j.

Npart

number of parts to partition the data when evaluating the loss functions lossH and lossF.

sigmaList

vector of sigmas at which to evaluate the loss function.

inmodel

NT by 6 matrix indicating which variables to include in logistic model.

seed

seed to use when imputing intermittent data.

type

one of "H", "F" or "both" to evaluate lossH, lossF or both for sigmaH or sigmaF in indicated range.

Details

Stepping through the values in sigmaList this functions computes the values of a loss function. If type is set to "H" or "h" then the loss function associated with dropout is computed. If type is set to "F" or "f" then the loss function associated with outcome is computed. If type is set any other value then both types of loss function are evaluated.

Since the input matrix, mat, can possess intermittent missing data, samonevalIM imputes these values using a logistic model. This is the model specified by inmodel.

inmodel is an NT by 6 matrix and contains a row for each time-point represented in the mat matrix. Since there are no intermittent missing data at time 1 and at time NT these rows should be set to zero.

A separate logistic model is fit for each timepoint t0, with t0 ranging from 2 to NT-1. The dependent variable in these models is an indicator indicating that an individual provided data at time t0. Only individuals who are on study at time t0+1 are considered in these models. Setting the ith column in inmodel to 1 indicates that the following terms should be included in the model:

1

the intercept.

2

the previous value of Y, that is the value of Y at t0-1.

3

the next available value of Y after time t0.

4

if the next available value of Y is at time t1, then this is (t1 - t0 - 1).

5

an interaction between the variable in column 3 and column 4.

6

0 if an individual is last observed at time NT, 1 if they are last observed at time NT - 1, 2 if they are last observed at time NT - 2, etc.

For the model that runs at the penultimate time, NT-1, including all six terms in the model will lead to over specification.

To include as many terms as possible in each model set inmodel to be

0	0	0	0	0	0
1	1	1	1	1	1
1	1	1	1	1	1
.	.	.
.	.	.
1	1	1	1	1	1
1	1	1	0	0	0
0	0	0	0	0	0

At a given timepoint t0, there may not be enough intermittent missing data to support all six terms. In such cases variables are removed from the model until the regression converges. If less than 4 observations have intermittent missing data at a given timepoint a model fitting the mean is used.

samonevalIM sequentially imputes intermittent missing data using these models. Once the intermittent data is imputed a loss function is evaluated on the data.

Value

Returns an N by 2 matrix of results if type is "H" or "F" or an N by 4 matrix if type is "both". There is one row for each value of sigma. If type is "P" then the columns are sigmaH and lossH, if type is "F" then the columns are sigmaF and lossF, and, if type = "both" then the columns are sigmaH, lossH, sigmaF, and lossF.

Examples

  data("VAS1")

  ## inputation moddel.
  NT                <- ncol(VAS1)
  inmodel           <- matrix(1,NT,6)
  inmodel[1,]       <- 0
  inmodel[NT,]      <- 0
  inmodel[NT-1,4:6] <- 0

  ## outcome loss function
  F1 <- samonevalIM( mat = VAS1, Npart = 10,
           sigmaList = seq(1,10,by=1),
           inmodel = inmodel,
           seed = 26,
           type = "F" )