surp.fit: Objects resulting for assessing fit of surprisal matrix to...

In TestGardener: Information Analysis for Test and Rating Scale Data

Objects resulting for assessing fit of surprisal matrix to surprisal data

Description

This function is called by function smooth.surp() and computes the penalized verstion of the objective function value, its derivative vector and the second derivative matrix, as well as their unpenalized versions. Also returned are alternative fitting objects: the residual matrix, the root-mean-square of the matrix fit, and the entropy value.

Usage

surp.fit(Bvec, surpList)

Arguments

Bvec	The K by M-1 parameter matrix defining the fit to the data in row-wise column vector format for use with function lnsrch().
surpList	A list object containing objects M, binctr, Sbin, wtvec, Kmat, Zmat and Phimat.

Value

A named list of class surpFd with these members:

PENSSE	value of the penalized fitting criterion.
DPENSSE	gradient of the penalized fitting criterion.
D2PENSSE	hessian of the fitting criterion.
SSE	value of the error sum of squares.
DSSE	gradient of the error sum of squares.
D2SSE	hessian of the error sum of squares.
DvecSmatDvecB	cross derivative DvecSmatDvecX times DvecXmatDvecB of the surprisal curve and the basis coordinates.
Rmat	residual matrix for the fit to the surprisal matrix.
RMSE	root-mean-squared scalar fit value.
Entropy	entropy of the fit to the data.

Author(s)

Juan Li and James Ramsay

References

Ramsay, J. O., Li J. and Wiberg, M. (2020) Full information optimal scoring. Journal of Educational and Behavioral Statistics, 45, 297-315.

Ramsay, J. O., Li J. and Wiberg, M. (2020) Better rating scale scores with information-based psychometrics. Psych, 2, 347-360.

See Also

eval.surp, smooth.surp, Sbinsmth

Examples

# Assemble the objects in the list arguments Bmat and surpList
SfdList1 <- Quant_13B_problem_parmList$SfdList[[1]]
Bmat     <- SfdList1$Sfd$coef
binctr   <- Quant_13B_problem_parmList$binctr
M        <- SfdList1$M
Sbasis   <- SfdList1$Sfd$basis
Zmat     <- SfdList1$Zmat
Sbin     <- SfdList1$Sbin
Phimat   <- fda::eval.basis(binctr, Sbasis)
Snbasis  <- Sbasis$nbasis
Kmat     <- matrix(0,Snbasis,Snbasis)
wtvec    <- NULL
Bvec     <- matrix(Bmat, Snbasis*(M-1),1,byrow=TRUE)
#  display coefficient matrix
print(round(Bmat,2))
#  set up argument surpList
surpList <- list(binctr=binctr, Sbin=Sbin, wtvec=wtvec, 
                 Kmat=Kmat, Zmat=Zmat, Phimat=Phimat, M=M)
#  run surp.fit
result <- surp.fit(Bvec, surpList)
print(paste("Error sum of squares =",round(result$SSE,3)))
print(paste("Gradient norm =",round(norm(result$DSSE),5)))
print("Entropy of item = at bin centres")
print(round(result$Entropy,3))

TestGardener documentation built on Sept. 30, 2024, 9:35 a.m.