ConstraintMatrix {cmm} | R Documentation |
Returns hierarchical model constraint matrix, i.e., nullspace of design matrix
ConstraintMatrix(var, suffconfigs, dim, SubsetCoding = "Automatic")
var |
character or numeric vector containing variables |
suffconfigs |
subvector or list of subvectors of var indicating the sufficient configurations or highest order interactions in model |
dim |
numeric vector indicating the dimension of var (must be same length as var ) |
SubsetCoding |
allows a (character) type or a matrix to be assigned to variables for each element of suffconfigs |
, see examples
The model mu_ij = alpha + beta_i + gamma_j
has parametric form and can equivalently be described using constraints on the mu_ij,
by mu_ij - mu_il - mu_kj + mu_kl = 0.
Returns the transpose of the null space of DesignMatrix(var,marg,dim)
. Rows normally sum to zero.
See DesignMatrix
for more details.
matrix
W. P. Bergsma w.p.bergsma@lse.ac.uk
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.
ConstraintMatrix
, DesignMatrix
, DirectSum
, MarginalMatrix
# Constraint matrix for independence model var <- c("A","B") suffconfigs <- list(c("A"),c("B")) dim <- c(3, 3) ConstraintMatrix(var,suffconfigs,dim) # notation in one line ConstraintMatrix(c("A","B"),list(c("A"),c("B")),c(3,3)) # Constraint matrix for saturated model, two short specifications giving same result ConstraintMatrix(c("A","B"),c("A","B"),c(3,3)) ConstraintMatrix(c("A","B"),list(c("A","B")),c(3,3)) # Constraint matrix for univariate quadratic regression model var <- c("A") suffconfigs <- c("A") dim <- c(5) ConstraintMatrix(var,suffconfigs,dim,SubsetCoding=list(c("A"),"Quadratic")) # notation in one line ConstraintMatrix(c("A"),c("A"),c(5),SubsetCoding=list(c("A"),"Quadratic")) # Constraint matrix for linear by nominal model, various methods: # simplest method which assumes equidistant centered scores: ConstraintMatrix(c("A","B"),c("A","B"),c(3,3),SubsetCoding=list(c("A","B"),list("Linear","Nominal"))) # alternative specification with same result as above: ConstraintMatrix(c("A","B"),c("A","B"),c(3,3),SubsetCoding=list(c("A","B"),list(rbind(c(-1,0,1)),rbind(c(1,0,0),c(0,1,0))))) # specifying your own category scores scores=c(1,2,5); ConstraintMatrix(c("A","B"),c("A","B"),c(3,3),SubsetCoding=list(c("A","B"),list(rbind(scores),"Nominal"))) # Constraint matrix for nominal by nominal model, equating parameters of last two categories of second variable: ConstraintMatrix(c("A","B"),c("A","B"),c(3,3),SubsetCoding=list(c("A","B"),list("Nominal",rbind(c(1,0,0),c(0,1,1)))))