buildmodel {SparseMSE}

Build model for multiple systems estimation

Description

For multiple systems estimation model corresponding to a specified set of two-list effects, set up the GLM model formula and data matrix.

Usage

buildmodel(zdat, mX)

Arguments

zdat

Data matrix with t+1 columns. The first t columns, each corresponding to a particular list, are 0s and 1s defining the capture histories observed. The last column is the count of cases with that particular capture history. List names A, B, ... are constructed if not supplied. Where a capture history is not explicitly listed, it is assumed that it has zero counts.

mX

A 2 \times k matrix giving the k two-list effects to be included in the model. Each column of mX contains the numbers of the corresponding pair of lists. If mX = 0, then all two-list effects are included. If mX = NULL, no such effects are included and the main effects model is fitted.

Value

A list with components as below.

datamatrix A matrix with all possible capture histories, other than those equal to or containing non-overlapping pairs indexed by parameters that are within the model specified by mX. A non-overlapping pair is a pair of lists (i,j) such that no case is observed in both lists, regardless of whether it is present on any other lists. If (i,j) is within the model specified by mX, all capture histories containing both i and j are then excluded.

modelform The model formula suitable to be called by the Generalized Linear Model function glm. Model terms corresponding to non-overlapping pairs are not included, because they are handled by removing appropriate rows from the data matrix supplied to glm. The list of non-overlapping pairs are provided in emptyoverlaps. See Chan, Silverman and Vincent (2019) for details.

emptyoverlaps A matrix with two rows, whose columns give the indices of non-overlapping pairs of lists where the parameter indexed by the pair is within the specified model. The column names give the names of the lists corresponding to each pair.

References

Chan, L., Silverman, B. W., and Vincent, K. (2019). Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges when there are Non-Overlapping Lists. Available from https://arxiv.org/abs/1902.05156.

Examples

data(NewOrl)
buildmodel(NewOrl, mX=NULL)
#Build a matrix that contains all two-list effects
m=dim(Artificial_3)[2]-1
mX = t(expand.grid(1:m, 1:m)); mX = mX[ , mX[1,]<mX[2,]]
# With one two-list effect
buildmodel(NewOrl, mX=mX[,1])
#With three two-list effects
buildmodel(NewOrl, mX=mX[,1:3])