# design.1locus: Setting-up design matrices for a polytomous model with a... In fat2Lpoly: Two-Locus Family-Based Association Test with Polytomous Outcome

## Description

This function sets up two identical lists of three design matrices, one for each linear predictor of the logit of the three outcome levels defined by the combination of two dichotomous traits against the reference level (0,0) under a model with the main effect of a single biallelic marker.

## Usage

 `1` ```design.1locus(x, par.constrained, constraints) ```

## Arguments

 `x` A numeric vector of values representing genotypes of a biallelic marker. The two homozygous genotypes must be coded 0 and 1, and the heterozygous genotype value depends on the genetic model: 0 (recessive), 1/2 (allelic) or 1 (dominant). `par.constrained` Optional matrix of dimensions (`n.levels`-1) x nc specifying the parameter (1, 2 or 3) in the linear predictor for each level involved in the nc constraints BETWEEN the logistic models for different levels of the response variable, one constraint per column. This functionality is not yet implemented. `constraints` Optional matrix of dimensions (`n.levels`-1) x nc specifying the nc linear constraints BETWEEN the logistic models for different levels of the response variable, involving the parameters specified in `par.constrained`, one constraint per column. A 0 means that the corresponding parameter is not involved in the constraint. This functionality is not yet implemented.

## Details

Let Y[1] and Y[2] be binary variables coding the presence (1) or absence (0) of the two traits (e.g. and endophenotype and a disease trait, respectively). The linear predictors (without intercept) of the logistic functions between outcome levels and the reference level Y[1] = 0 and Y[2] = 0 are as follows:

Y[1] = 1 , Y[2] = 0 : β[11] X

Y[1] = 0 , Y[2] = 1 : β[21] X

Y[1] = 1 , Y[2] = 1 : β[31] X

The vector X constitute the design matrix for each linear predictor of the above model.

## Value

 `x.e ` List of 3 design matrices containing the vector X `x.loc.e ` list of character strings containing the indices of the variables in `x` involved in each term of the model, i.e. "1" `x.l ` identical to `x.e` `x.loc.l ` identical to `x.l`

## Author(s)

Alexandre Bureau <alexandre.bureau@msp.ulaval.ca>

`fat2Lpoly, design.full, design.endo2disease`