density_plot {TestGardener}

Plot the probability density function for a set of test scores

Description

Plots the probability density function of a set of score values that are not at the score boundaries as a smooth curve, and also plots the proportions of score values at both boundaries as points. The score values are typically either the values of the score index values index or the infoSurp or information score values.

Usage

density_plot(scrvec, scrrng, Qvec, xlabstr=NULL, titlestr=NULL, 
                         scrnbasis=15, nfine=101)

Arguments

scrvec

A vector of N score values

scrrng

A vector of length 2 containing boundary values

Qvec

A vector of length 5 containing the score values corresponding to the marker percentages 5, 25, 50, 75 and 95.

xlabstr

Label for abscissa

titlestr

Label for plot

scrnbasis

The number of spline basis functions used for representing the smooth density function

nfine

Number of plotting points

Value

A plot of the density function and a list vector densfine containing:

densfine:

Density values over a mesh of equally-spaced values of length 101.

N_min:

The number of examinees estimated to have zero information.

N_max:

The number of examinees estimated to have full information.

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

scoreDensity

Examples

#  Example 1.  Display probability density curve for the 
#  score index values for the short SweSAT multiple choice test with 
#  24 items and 1000 examinees
index <- Quant_13B_problem_parmList$index
Qvec  <- Quant_13B_problem_parmList$Qvec
#  plot the density for the score indices within interval c(0,100)
oldpar <- par(no.readonly=TRUE)
on.exit(oldpar)
par(mfrow=c(2,1))
density_plot(index, c(0,100), Qvec, xlabstr="Score index", 
             titlestr="SweSAT 13B Theta Density",  
             scrnbasis=11, nfine=101)
#  arc length or information values
scopevec <- Quant_13B_problem_infoList$scopevec
Qinfovec <- Quant_13B_problem_infoList$Qinfovec
infoSurp <- Quant_13B_problem_infoList$infoSurp
#  plot the density for the score indices within interval c(0,infoSurp)
density_plot(scopevec, c(0,infoSurp), Qinfovec, xlabstr="Score index", 
             titlestr="SweSAT 13B Theta Density",  
             scrnbasis=11, nfine=101)