# downward {LCAextend}

### Description

computes the probability of measurements above connectors and their classes given the model parameters, and returns the unnormalized triplet and individual weights. This is an internal function not meant to be called by the user.

### Usage

downward(id, dad, mom, status, probs, fyc, peel, res.upward)

### Arguments

- id
- individual ID of the pedigree,
- dad
- dad ID,
- mom
- mom ID,
- status
- symptom status: (2: symptomatic, 1: without symptoms, 0: missing),
- probs
- a list of 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, - peel
- a list of pedigree peeling containing connectors by peeling order and couples of parents,
- res.upward
- result of the upward step of the peeling algorithm, see
`upward`

.

### Details

This function computes the probability of observations above connectors and their classes using the function `downward.connect`

, for each connector, if `Y_above(i)`

is the observations above connector `i`

and `S_i`

and `C_i`

are his status and his class respectively, the functions 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. These quantities are used by the function `weight.nuc`

to compute the unnormalized triplet weights `ww`

and the unnormalized individual weights `w`

.

### Values

The function returns a list of 2 elements:

- ww
- unnormalized triplet weights, an array of
`n`

times 2 times`K+1`

times`K+1`

times`K+1`

, where`n`

is the number of individulas and`K`

is the total number of latent classes in the model, see`e.step`

for more details, - w
- unnormalized individual weights, an array of
`n`

times 2 times`K+1`

, see`e.step`

.

### 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.connect`

.

### 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) #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)) #the upward step res.upward <- upward(id,dad,mom,status,probs,fyc,peel) #the function downward(id,dad,mom,status,probs,fyc,peel,res.upward)

Documentation reproduced from package LCAextend, version 1.2. License: GPL