discrete.smooth {SNSequate}

Pre-smoothing using discrete kernels.

Description

This function fits discrete kernels to score data and provides estimates of the (vector of) score probabilities.

Usage

discrete.smooth(scores,kert,h,x)

Arguments

scores

Data.

kert

kernel type.

h

bandwidth.

x

The points of the grid at which the density is to be estimated.

Details

This function fits discrete kernels as described in XXXX, and XXXXX.

Particular cases of this general equation for each of the equating designs can be found in Von Davier et al (2004) (e.g., Equations (7.1) and (7.2) for the "EG" design, Equation (8.1) for the "SG" design, Equations (9,1) and (9.2) for the "CB" design).

Value

prob.est

The estimated score probabilities

Author(s)

Jorge Gonzalez [e-mail]

References

Gonzalez, J. (2014). SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating. Journal of Statistical Software, 59(7), 1-30.

Holland, P. and Thayer, D. (1987). Notes on the use of loglinear models for fitting discrete probability distributions. Research Report 87-31, Princeton NJ: Educational Testing Service.

Von Davier, A., Holland, P., and Thayer, D. (2004). The Kernel Method of Test Equating. New York, NY: Springer-Verlag.

[1] Moses, T. "Paper SA06_05 Using PROC GENMOD for Loglinear Smoothing Tim Moses and Alina A. von Davier, Educational Testing Service, Princeton, NJ".

See Also

glm, ker.eq

Examples

  data("SEPA", package = "SNSequate")
  
  # create score frequency distributions using freqtab from package equate
  library(equate)
  
  SEPAx<-freqtab(x=SEPA$xscores,scales=0:50)
  SEPAy<-freqtab(x=SEPA$yscores,scales=0:50)
  
  psxB<-discrete.smooth(scores=rep(0:50,SEPAx),kert="bino",h=0.25,x=0:50)
  psxT<-discrete.smooth(scores=rep(0:50,SEPAx),kert="triang",h=0.25,x=0:50)
  psxD<-discrete.smooth(scores=rep(0:50,SEPAx),kert="dirDU",h=0.0,x=0:50)

  plot(0:50,as.matrix(SEPAx)/sum(as.matrix(SEPAx)),lwd=2.0,xlab="Scores", 
  ylab="Relative    Frequency",type="h")
  points(0:50,psxB$prob.est,type="b",pch=0)
  points(0:50,psxT$prob.est,type="b",pch=1)