# constancy: Constancy Spaces for Aster Models In aster2: Aster Models

## Description

Produce basis for constancy space of an aster model. Test whether the difference of two canonical parameter vectors is in the constancy space (so the two parameter vectors correspond to the same probability model).

## Usage

 ```1 2 3``` ```constancy(data, parm.type = c("theta", "phi")) is.same(parm1, parm2, data, parm.type = c("theta", "phi"), tolerance = sqrt(.Machine\$double.eps)) ```

## Arguments

 `data` an object of class `"asterdata"` produced by `asterdata` or “by hand” such that `is.validasterdata(data)` returns `TRUE`. The specification of the aster model. `parm.type` the parametrization for which the constancy space is wanted. `parm1` a parameter vector of the type specified by `parm.type` for the saturated aster model specified by `data`. `parm2` another parameter vector of the type specified by `parm.type` for the saturated aster model specified by `data`. `tolerance` numeric >= 0. Relative errors smaller than `tolerance` are not considered in the comparison.

## Details

There is no need for functions to test whether different mean value parameters (xi or mu) correspond to the same probability distribution because these parametrizations are identifiable (different valid parameter vectors correspond to different probability distributions).

## Value

for `is.same` a logical value; for `constancy` a matrix whose rows constitute a basis for the constancy space. This means that if delta is a linear combination of rows of this matrix then for all real s the distributions having parameter vectors psi and psi + s * delta are the same, where psi = theta or psi = phi depending on whether `parm.type = "theta"` or `parm.type = "phi"`. Conversely, if psi1 and psi2 are valid parameter vectors of the same type, then they correspond to the same probability distribution only if psi1 - psi2 is a linear combination of rows of this matrix.

## See Also

`asterdata`

## Examples

 ```1 2 3 4 5 6 7 8``` ```data(test1) fred <- asterdata(test1, vars = c("m1", "m2", "m3", "n1", "n2", "b1", "p1", "z1"), pred = c(0, 0, 0, 1, 1, 2, 3, 6), group = c(0, 1, 2, 0, 4, 0, 0, 0), code = c(1, 1, 1, 2, 2, 3, 4, 5), families = list(fam.multinomial(3), "normal.location.scale", "bernoulli", "poisson", "zero.truncated.poisson")) cmat <- constancy(fred, parm.type = "phi") ```

aster2 documentation built on May 2, 2019, 11:02 a.m.