upward.connect {LCAextend}

performs the upward step for a connector

Description

computes the probability of the measurements below a connector conditionally to the connector latent class given the model parameters. This is an internal function not meant to be called by the user.

Usage

upward.connect(connect, spouse.connect, children.connect, status,
probs, p.yF.c, fyc, sum.child)

Arguments

connect

a connector in the pedigree,

spouse.connect

spouse of the connector,

children.connect

children of the connector,

status

a vector of symptom status of the whole pedigree,

probs

a list of probability parameters of the model,

p.yF.c

an array of dimension n times 2 times K+1 giving the probability of measurements below the individual, depending on his status and his class, where n is the number of individuals and K is the total number of latent classes in the model,

fyc

a matrix of n times K+1 given the density of measurements of each individual if allocated to class k,

sum.child

an array of dimension nber.indiv times K+1 times K+1 such that sum.child[i,c_1,c_2] is the probability of individual i measurements when his parent are assigned to classes c_1 and c_1.

Details

If Y_above(i) is the observations below connector i and C_i is his class, the functions computes P(Y_below(i)|C_i).

Value

The function returns a list of 2 elements:

sum.child

an array of dimension n times K+1 times K+1 such that sum.child[i,c_1,c_2] is the probability of individual i observations when his parent are assigned to classes c_1 and c_2,

p.yF.c

a array of dimension n times 2 times K+1 giving the probability of measurements below the individual, depending on his status and his class, updated for the current connector.

References

TAYEB et al.: Solving Genetic Heterogeneity in Extended Families by Identifying Sub-types of Complex Diseases. Computational Statistics, 2011, DOI: 10.1007/s00180-010-0224-2.

See Also

See also upward

Examples

#data
data(ped.cont)
data(peel)
fam <- ped.cont[,1]
id <- ped.cont[fam==1,2]
dad <- ped.cont[fam==1,3]
mom <- ped.cont[fam==1,4]
status <- ped.cont[fam==1,6]
y <- ped.cont[fam==1,7:ncol(ped.cont)]
peel <- peel[[1]]
#standardize id to be 1, 2, 3, ...
id.origin <- id
standard <- function(vec) ifelse(vec%in%id.origin,which(id.origin==vec),0)
id <- apply(t(id),2,standard)
dad <- apply(t(dad),2,standard)
mom <- apply(t(mom),2,standard)
peel$couple <- cbind(apply(t(peel$couple[,1]),2,standard),
                     apply(t(peel$couple[,2]),2,standard))
for(generat in 1:peel$generation) 
peel$peel.connect[generat,] <- apply(t(peel$peel.connect[generat,]),2,standard)
#a nuclear family
#connector in the pedigree 1
connect <- peel$peel.connect[1,1]
#soupse of connector connect
spouse.connect <- peel$couple[peel$couple[,1]==connect,2]
#children of connector connect
children.connect <- union(id[dad==connect],id[mom==connect])
#probs and param
data(probs)
data(param.cont)
#probabilitiy of observations above
p.yF.c <- matrix(1,nrow=length(id),ncol=length(probs$p)+1)
#densities of the observations
fyc <- matrix(1,nrow=length(id),ncol=length(probs$p)+1)
fyc[status==2,1:length(probs$p)] <- t(apply(y[status==2,],1,dens.norm,
                                      param.cont,NULL))
#sums over childs
sum.child <- array(0,c(length(id),length(probs$p)+1,length(probs$p)+1))
#the function
upward.connect(connect,spouse.connect,children.connect,status,probs,
               p.yF.c,fyc,sum.child)