create.constraints: Generate common order constraints

In CLME: Constrained Inference for Linear Mixed Effects Models

Description

Automatically generates the constraints in the format used by clme. Allowed orders are simple, simple tree, and umbrella orders.

Usage

create.constraints(P1, constraints)

Arguments

P1	the length of theta_1, the vector constrained coefficients.
constraints	List with the elements order, node, and decreasing. See Details for further information.

Details

The elements of constraints are:

• order: string. Currently “simple”, “simple.tree” and “umbrella” are supported.

• node: numeric, the node of the coefficients (unnecessary for simple orders).

• decreasing: logical. For simple orders, is the trend decreasing? For umbrella and simple tree, does the nodal parameter have the greatest value (e.g., the peak, instead of the valley)?

See clme for more information and a depiction of these three elements.

Value

The function returns a list containing the elements of input argument constraints as well as

• A matrix of dimension r x 2 containing the order constraints, where r is the number of linear constraints.

• B matrix containing the contrasts necessary for computation of the Williams' type test statistic (may be identical to A).

• Anull matrix similar to A which defines all possible constraints. Used to obtain parameter estimates under the null hypothesis.

• order the input argument for constraints\$order.

• node the input argument for constraints\$node.

• decreasing the input argument for constraints\$decreasing

See w.stat for more information on B

Note

The function clme also utilizes the argument constraints. For clme, this argument may either be identical to the argument of this function, or may be the output of create.constraints (that is, a list containing appropriate matrices A, Anull, and if necessary, B).

An example the the A matrix might be:

[1,]	[,1]	[,2]
[2,]	1	2
[3,]	2	3
[4,]	4	3
[5,]	5	4
[6,]	6	5

This matrix defines what CLME describes as a decreasing umbrella order. The first row defines the constraint that theta_1 <= theta_2, the second row defined the constraint theta_2 <= theta_3, the third row defines theta_4 <= theta_3, and so on. The values are indexes, and the left column is the index of the parameter constrained to be smaller.

See Also

clme, w.stat

Examples

## Not run: 
  # For simple order, the node does not matter
  create.constraints( P1 = 5, constraints = list( order='simple' , 
                                                  decreasing=FALSE ))
  
  # Compare constraints against decreasing=TRUE
  create.constraints( P1 = 5, constraints=list( order='simple' , 
                                                decreasing=TRUE ))
  
  # Umbrella order
  create.constraints( P1 = 5, constraints=list( order='umbrella' , node=3
                                                , decreasing=FALSE ))

## End(Not run)

CLME documentation built on July 8, 2020, 5:49 p.m.