MarginalMatrix {cmm}

MarginalMatrix

Description

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

Usage

MarginalMatrix(var, marg, dim, SubsetCoding = "Identity", vec = NULL)

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

vec

Vector containing the observed frequencies of all observed cells and possibly some cells with frequency equal to zero. The rownames of vec must equal the score patterns associated with the cells. vec is typically created using RecordsToFrequencies, and allows maximum empirical maximum likelihood estimation or empirical likelihood estimation of CMMs; two estimation methods that do no require the evaluation of all cells that are useful if the number of score patterns is large.

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

Value

matrix

Author(s)

W. P. Bergsma [e-mail]

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.

Van der Ark, L. A., Bergsma, W. P., & Koopman L. (2023) Maximum augmented empirical likelihood estimation of categorical marginal models for large sparse contingency tables. Paper submitted for publication.

See Also

ConstraintMatrix, DesignMatrix, DirectSum, RecordsToFrequencies, Margins

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 

# Example of maximum augmented empirical likelihood (MAEL) estimation 
data(acl)
dat <- acl[, 1:2] + 1                                 # select 2 items from ACL 
var <- 1 : ncol(dat)                                  # define the variables
marg <- Margins(var, c(0, 1))                         # margins are total (0) and 1st order 
dim <- rep(5, length(var))
n.obs <- RecordsToFrequencies(dat, var, dim, "obs")   # frequency vector with observed cells
t(n.obs)
n.1k  <- RecordsToFrequencies(dat, var, dim, "1k")    # frequency vector with observed and
                                                      # some unobserved cells
t(n.1k)
at.obs <- MarginalMatrix(var, marg, dim, vec = n.obs) # marginal matrix based on n.obs 
at.obs
at.1k  <- MarginalMatrix(var, marg, dim, vec = n.1k)  # marginal matrix based on n.1k
at.1k