# alpha.compute: computes cumulative logistic coefficients using probabilities In LCAextend: Latent Class Analysis (LCA) with familial dependence in extended pedigrees

## Description

computes cumulative logistic coefficients using probabilities.

## Usage

 `1` ```alpha.compute(p) ```

## Arguments

 `p` a vector of probabilities (positive entries summing to 1).

## Details

If `p` has one value (equal to 1) `alpha.compute` returns `NA`, if it has `S (S>=2)` values, `alpha.compute` returns `S-1` coefficients `alpha` such that if `Y` is a random variable taking values in `{1,...,S}` with probabilities `p`, coefficients `alpha[i]` are given by:

\code{p[1]+...+p[i]=P(Y<=i)=exp(alpha[1]+...+alpha[i])/(1+exp(alpha[1]+...+alpha[i]))},

for all `i<=S-1`.

## Value

The function returns `alpha`: a vector of `S-1` cumulative logistic coefficients.

`alpha.compute` is the inverse function of `p.compute`
 ```1 2 3 4 5``` ```# a vector of probability p <- c(0,0.2,0,0,0.3,0.4,0.1,0,0) alpha.compute(p) #gives -Inf -1.38 0 0 1.38 0 2.19 Inf Inf p.compute(alpha.compute(rep(1/5,5))) ```