PnodeQ: Accesses a state-wise Q-matrix associated with a Pnode

In ralmond/Peanut: Parameterized Bayesian Networks, Abstract Classes

Accesses a state-wise Q-matrix associated with a Pnode

Description

The function calcDPCTable has an argument Q, which allows the designer to specify that only certain parent variables are relevant for the state transition. The function PnodeQ accesses the local Q-matrix for the Pnode node.

Usage

PnodeQ(node)
PnodeQ(node) <- value

Arguments

node	A Pnode whose local Q-matrix is of interest
value	A logical matrix with number of rows equal to the number of outcome states of node minus one and number of columns equal to the number of parents of node. As a special case, if it has the value TRUE this is interpreted as a matrix of true values of the correct shape.

Details

Consider a partialCredit model, that is a Pnode for which the value of PnodeLink is "partialCredit". This model is represented as a series of transitions between the states s+1 and s (in calcDPCTable states are ordered from high to low). The log odds of this transition is expressed with a function Z_{s}(eTheta) where Z_{s}() is the value of PnodeRules(node) and eTheta is the result of the call PnodeParentTvals(node).

Let q_{sj} be true if the parent variable x_j is relevant for the transition between states s+1 and s. Thus the function which is evaluated to calculate the transition probabilities is Z_{s}(eTheta[,Q[s,]]); that is, the parent variables for which q_{sj} is false are filtered out. The default value of TRUE means that no values are filtered.

Note that this currently makes sense only for the partialCredit link function. The gradedResponse link function assumes that the curves are parallel and therefore all of the curves must have the same set of variables (and values for PnodeAlphas.

Value

A logical matrix with number of rows equal to the number of outcome states of node minus one and number of columns equal to the number of parents of node, or the logical scalar TRUE if all parent variables are used for all transitions.

Note

The functions PnodeQ and PnodeQ<- are abstract generic functions, and need specific implementations. See the PNetica-package for an example.

The values of PnodeLink, PnodeRules, PnodeQ, PnodeParentTvals, PnodeLnAlphas, and PnodeBetas all need to be consistent for this to work correctly, but no error checking is done on any of the setter methods.

Note that the setter form may destructively modify the Pnode object (this depends on the implementation).

Author(s)

Russell Almond

References

Almond, R. G. (2013) Discretized Partial Credit Models for Bayesian Network Conditional Probability Tables. Draft manuscript available from author.

Almond, R. G. (2015) An IRT-based Parameterization for Conditional Probability Tables. Paper presented at the 2015 Bayesian Application Workshop at the Uncertainty in Artificial Intelligence Conference.

See Also

Pnode, PnodeRules, PnodeLink, PnodeLnAlphas, PnodeAlphas, BuildTable, PnodeParentTvals, maxCPTParam calcDPCTable, mapDPC

Examples

## Not run: 
library(PNetica) ## Requires implementation
sess <- NeticaSession()
startSession(sess)

tNet <- CreateNetwork("TestNet",session=sess)


theta1 <- NewDiscreteNode(tNet,"theta1",
                         c("VH","High","Mid","Low","VL"))
PnodeStateValues(theta1) <- effectiveThetas(PnodeNumStates(theta1))
PnodeProbs(theta1) <- rep(1/PnodeNumStates(theta1),PnodeNumStates(theta1))
theta2 <- NewDiscreteNode(tNet,"theta2",
                         c("VH","High","Mid","Low","VL"))
PnodeStateValues(theta2) <- effectiveThetas(PnodeNumStates(theta2))
PnodeProbs(theta2) <- rep(1/PnodeNumStates(theta2),PnodeNumStates(theta2))

partial3 <- NewDiscreteNode(tNet,"partial3",
                            c("FullCredit","PartialCredit","NoCredit"))
PnodeParents(partial3) <- list(theta1,theta2)

partial3 <- Pnode(partial3,Q=TRUE, link="partialCredit")
PnodePriorWeight(partial3) <- 10
BuildTable(partial3)

## Default is all nodes relevant for all transitions   
stopifnot(
   length(PnodeQ(partial3)) == 1,
   PnodeQ(partial3) == TRUE
)

## Set up so that first skill only needed for first transition, second
## skill for second transition; adjust alphas to match
PnodeQ(partial3) <- matrix(c(TRUE,TRUE,
                             TRUE,FALSE), 2,2, byrow=TRUE)
PnodeLnAlphas(partial3) <- list(FullCredit=c(-.25,.25),
                                PartialCredit=0)
BuildTable(partial3)


partial4 <- NewDiscreteNode(tNet,"partial4",
                            c("Score4","Score3","Score2","Score1"))
PnodeParents(partial4) <- list(theta1,theta2)
partial4 <- Pnode(partial4, link="partialCredit")
PnodePriorWeight(partial4) <- 10

## Skill 1 used for first transition, Skill 2 used for second
## transition, both skills used for the 3rd.

PnodeQ(partial4) <- matrix(c(TRUE,TRUE,
                             FALSE,TRUE,
                             TRUE,FALSE), 3,2, byrow=TRUE)
PnodeLnAlphas(partial4) <- list(Score4=c(.25,.25),
                                Score3=0,
                                Score2=-.25)
BuildTable(partial4)

DeleteNetwork(tNet)
stopSession(sess)

## End(Not run)

ralmond/Peanut documentation built on Sept. 19, 2023, 8:27 a.m.