downward.connect {LCAextend}

performs a downward step for a connector

Description

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

Usage

downward.connect(connect, parent1, parent2, bro.connect, status, 
                 probs, fyc, p.ybarF.c, res.upward)

Arguments

connect

a connector in the pedigree (individual with parents and children in the pedigree),

parent1

one of the connector parent who is also a connector,

parent2

the other parent of the connector (not a connector),

bro.connect

siblings of the connector,

status

a vector of symptom status,

probs

a list of all probability parameters of the model,

fyc

a matrix of n times K+1 given the density of observations of each individual if allocated to class k, where n is the number of individuals and K is the total number of latent classes in the model. the K+1 corresponds to the unaffected class,

p.ybarF.c

a array of dimension n times 2 times K+1 giving the probability of observations above the individual, depending on his status and his class and conditionally to his class,

res.upward

the result of the upward step of the peeling algorithm, see upward.

Details

If Y_above(i) is the measurements above connector i and S_i and C_i are his status and his class respectively, the function computes P(Y_above(i),S_i,C_i) by computing a downward step for the parent of connector i who is also a connector.

Value

The function returns p.ybarF.c updated for connector i.

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 downward

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)
#the 2nd connector
generat <- peel$generation-1
connect <- peel$peel.connect[generat,]
connect <- connect[connect>0][1]
parent1.connect <- intersect(peel$peel.connect[generat+1,],c(dad[id==connect],
                                                             mom[id==connect]))
parent2.connect <- setdiff(c(dad[id==connect],mom[id==connect]),parent1.connect)
bro.connect <- union(id[dad==parent1.connect],id[mom==parent1.connect])
bro.connect <- setdiff(bro.connect,connect)
#probs and param
data(probs)
data(param.cont)
#densities of the observations
fyc <- matrix(1,nrow=length(id),ncol=length(probs$p)+1)
fyc[status==2,1:length(probs$p)] <- t(apply(y[status==2,],1,dens.norm,param.cont,NULL))
#probability of the observations below
p.ybarF.c <- array(1,dim=c(length(id),2,length(probs$p)+1))
#the upward step
res.upward <- upward(id,dad,mom,status,probs,fyc,peel)
#the function
downward.connect(connect,parent1.connect,parent2.connect,bro.connect,status,
                 probs,fyc,p.ybarF.c,res.upward)