compef {lazy.sasef} R Documentation

## Comparison of Two Different Parametrization of a Linear Model

### Description

Comparison of Two Different Parametrization of a Linear Model

### Usage

```compef(obj1 = NULL, obj2 = NULL, print = 0)
```

### Arguments

 `obj1` A design object for model1 `obj2` A design object for model2 `print` = 1 to print the result

### Details

This program compares the following two equivalent linear models:
model1: yhat = X beta and model2: yhat = Z alpha
where Z is a design matrix of full column rank.

Note that the estimable function of model1 is:
Q = L matSwp(t(X)%*%X)%*%t(X)%*%X
and that Z can be expressed as
Z = X%*%matSwp(t(X)%*%X)%*%t(X)%*%Z .
By multiplying L matSwp(t(X)%*%X)%*%t(X) to the both sides of
X beta = Z alpha
we have,
L matSwp(t(X)%*%X)%*%t(X) %*% X beta = L matSwp(t(X)%*%X)%*%t(X) %*% Z alpha
Q beta = L matSwp(t(X)%*%X)%*%t(X)%*% X%*%matSwp(t(X)%*%X)%*%t(X)%*%Z alpha
Q beta = L matSwp(t(X)%*%X)%*%t(X)%*%X %*%matSwp(t(X)%*%X)%*%t(X)%*%Z alpha
Q beta = Q matSwp(t(X)%*%X)%*%t(X)%*%Z alpha

The correspondence from alpha to beta is obtained by
beta = R %*% alpha
where
R = Q matSwp(t(X)%*%X)%*%t(X)%*%Z

A design object is a list of the design matrix (X), infomation list (info) and parameter list (param) where

X is the design matrix
and
info is a list whose length is the number of effects.

info[[i]] contains the following:
ename name of effect[i]
order order of effect[i]: 0, 1, ..., maxorder
elevels # of levels of effect[i]
df degrees of freedom of effect[i]
erange range of effect[i] in the (full rank) estimable functions
range=cbind(from,to) where
from is the starting independent colmn of effect[i] in X
to is the ending independent column of effect[i] in X
rangef=cbind(from,to) where
from is the starting colmn of effect[i] in X
to is the ending column of effect[i] in X
menum vector of main effect number involved in effect[i] contained vector of effect numbers which contains effect[i]
where effect number is defined according to the order of column of X.
contains vector of effects which effect[i] contais.
param is a list consisting of

type, drop, maxorder, sort, pattern

ef Information of estimable function..

### Value

List of Q, R, Rf, Rc
where Q is the numeric form of estimable functions
R = Q matSwp(t(X)%*%X)%*%t(X)%*%Z
Rf Fractional expression of R
Rc Character version of R

### Examples

```# SAS type III EF in terms of the Cell Means
data <- du23[,1:2]
res1 <- design_mat( data,  type=-1, pattern="a", sort=0 )
ef1 <- sasef_III( res1, print=1 )
res2 <- design_mat( data,  type=-2 )
temp=compef( ef1, res2, print=3 )

# Cell Means in terms of SAS type III EF
data <- du23[,1:2]
res2 <- design_mat( data,  type=-1, pattern="a", sort=0 )
res1 <- design_mat( data,  type=-2 )
ef1 <- res1
temp=compef( ef1, res2, print=3 )

# Zero-Sum  in terms of the Cell Means
data <- du23[,1:2]
res1 <- design_mat( data,  type=0, pattern="a", sort=0 )
ef1 <- sasef_III( res1, print=1 )
res2 <- design_mat( data,  type=-2 )
temp=compef( ef1, res2, print=3 )

# Cell Means in terms of Zero-Sum
data <- du23[,1:2]
res2 <- design_mat( data,  type=0, pattern="a", sort=0 )
res1 <- design_mat( data,  type=-2 )
ef1 <- res1
temp=compef( ef1, res2, print=3 )

# type III in terms of zero-sum
data=du23[,1:2]
res1=design_mat( data,  type=-1, pattern="a", sort=0 )
ef1=sasef_III( res1, print=2 )
res2=design_mat( data,  type=0 )
temp=compef( ef1, res2, print=3 )

# zero-sum in terms of sas non-full-rank X:
# This should gives us the type III ef.
data=du23[,1:2]
res2=design_mat( data,  type=-1, pattern="a", sort=0 )
res1=design_mat( data,  type=0 )
ef1=res1
temp=compef( ef1, res2, print=3 )
```

[Package lazy.sasef version 0.1.2 Index]