cmm (version 0.12)

MarginalMatrix: MarginalMatrix

Description

Returns marginal matrix; i.e., matrix required to obtained marginal frequencies

Usage

MarginalMatrix(var, marg, dim, SubsetCoding="Identity",SelectCells="All")

Value

matrix

Arguments

var

character or numeric vector containing variables

marg

list of character or numeric indicating marginals

dim

numeric vector indicating the dimension of var

SubsetCoding

allows a (character) type or a matrix to be assigned to variables for each element of suffconfigs, see examples and DesignMatrix

SelectCells

Useful option for empirical likelihood. Default "All" includes all columns, if a list of cells in the table is given only the corresponding columns of MarginalMatrix are included.

Author

W. P. Bergsma

Details

Gives the matrix which, multiplied by a probability vector, gives the marginal probabilities. The probability vector is assumed to be a vectorized form of the probabilities in a table, such that the last variable changes value fastest, then the before last variable, etc. For example, the cells of a \(2 \times 3\) table are arranged in vector form as (11,12,13,21,22,23). To achieve this, the appropriate way to vectorize a data frame dat is using c(t(ftable(dat))).

Special case of transposed DesignMatrix:

 MarginalMatrix <- function(var,marg,dim,SubsetCoding="Identity")
 t(DesignMatrix(var,marg,dim,SubsetCoding=SubsetCoding,MakeSubsets=FALSE))

Allows weighted sums of probabilities using SubsetCoding

References

Bergsma, W. P. (1997). Marginal models for categorical data. Tilburg, The Netherlands: Tilburg University Press. http://stats.lse.ac.uk/bergsma/pdf/bergsma_phdthesis.pdf

Bergsma, W. P., Croon, M. A., & Hagenaars, J. A. P. (2009). Marginal models for dependent, clustered, and longitudunal categorical data. Berlin: Springer.

See Also

ConstraintMatrix, DesignMatrix, DirectSum

Examples

# Computing marginal frequencies
n <- c(1:6)  #example list of frequencies
var <- c("A","B")
marg <- list(c("A"),c("B"))
dim <- c(2,3)
at <- MarginalMatrix(var,marg,dim)
# list of marginal frequencies:
at 

# identitymatrix: several ways of specifying:
marg <- c("A","B")
MarginalMatrix(var, marg,dim)
MarginalMatrix(var, marg, dim,
 SubsetCoding = list(c("A", "B"), list("Identity", "Identity")))
MarginalMatrix(var, marg, dim,
 SubsetCoding = list(c("A","B"), list(rbind(c(1,0),c(0,1)), rbind(c(1,0,0),c(0,1,0),c(0,0,1)))))

# omit second category of first variable
at <- MarginalMatrix(var, marg, dim,
 SubsetCoding = list(c("A","B"), list(rbind(c(1,0)),"Identity")))
at 

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