# estble-subspace: Find an estimable subspace In rvlenth/estimability: Tools for Assessing Estimability of Linear Predictions

## Description

Determine a transformation `B` of the rows of a matrix `L` such that `B %*% L` is estimable. A practical example is in jointly testing a set of contrasts `L` in a linear model, and we need to restrict to the subspace spanned by the rows of `L` that are estimable.

## Usage

 `1` ```estble.subspace (L, nbasis, tol = 1e-8) ```

## Arguments

 `L` A matrix of dimensions k by p `nbasis` A k by b matrix whose columns form a basis for non-estimable linear functions – such as is returned by `nonest.basis` `tol` Numeric tolerance for assessing nonestimability. See `is.estble`.

## Details

We require `B` such that all the rows of `M = B %*% L` are estimable, i.e. orthogonal to the columns of `nbasis`. Thus, we need `B %*% L %*% nbasis` to be zero, or equivalently, `t(B)` must be in the null space of `t(L %*% nbasis)`. This can be found using `nonest.basis`.

## Value

An r by p matrix `M = B %*% L` whose rows are all orthogonal to the columns of `nbasis`. The matrix `B` is attached as `attr(M, "B")`. Note that if any rows of `L` were non-estimable, then r will be less than k. In fact, if there are no estimable functions in the row space of `L`, then r = 0.

## Author(s)

Russell V. Lenth <[email protected]>

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```### Find a set of estimable interaction contrasts for a 3 x 4 design ### with two empty cells. des <- expand.grid(A = factor(1:3), B = factor(1:4)) des <- des[-c(5, 12), ] # cells (2,2) and (3,4) are empty X <- model.matrix(~ A * B, data = des) N <- nonest.basis(X) L <- cbind(matrix(0, nrow = 6, ncol = 6), diag(6)) # i.e., give nonzero weight only to interaction effects estble.subspace(L, N) # Tougher demo: create a variation where all rows of L are non-estimable LL <- matrix(rnorm(36), ncol = 6) %*% L estble.subspace(LL, N) ```

rvlenth/estimability documentation built on Feb. 15, 2018, 10:12 p.m.