OCP: Observable Characteristic Plot

In ralmond/CPTtools: Tools for Creating Conditional Probability Tables

Observable Characteristic Plot

Description

The observable characteristic plot is an analogue of the item characteristic curve for latent class models. Estimates of the class success probability for each latent is plotted. Reference lines are added for various groups which are expected to have roughly the same probability of success.

Usage

OCP(x, n, lclabs, pi, pilab = names(pi), lcnames = names(x),
    a = 0.5, b = 0.5, reflty = 1, ..., newplot = TRUE,
    main = NULL, sub = NULL, xlab = "Latent Classes", ylab = "Probability",
    cex = par("cex"), xlim = NULL, ylim = NULL, cex.axis = par("cex.axis"))
OCP2(x, n, lclabs, pi, pilab = names(pi), lcnames = names(x),
     set1 = seq(1, length(x)-1, 2), setlabs = c("Set1", "Set2"),
     setat = -1, a = 0.5, b = 0.5, reflty = 1, ..., newplot = TRUE,
     main = NULL, sub = NULL, xlab = "Latent Classes", ylab = "Probability",
     cex = par("cex"), xlim = NULL, ylim = NULL, cex.axis = par("cex.axis")) 

Arguments

x	Vector of success counts for each latent class.
n	Vector of of the same size as x of latent class sizes.
lclabs	Character vector of plotting symbols for each latent class
pi	Vector of probability estimates for various levels.
pilab	Character vector of names for each level.
lcnames	Character vector of names for each latent class for axis.
set1	For OCP2, a vector of indexes of the elements of x that form the first set.
setlabs	Character vectors of set labels for OCP2.
setat	Numeric scalar giving the x-coordinate for set labels.
a	The first parameter for beta pseudo-prior, passed to betaci. This should either be a scalar or the same length as x.
b	The second parameter for beta pseudo-prior, passed to betaci. This should either be a scalar or the same length as n.
reflty	Provides the line type (see par(lty)) for reference lines. Should be scalar or same length as pi.
...	Additional graphics parameters passed to plot.window and title.
newplot	Logical. If true, a new plotting window is created. Otherwise, information is added to existing plotting window.
main	Character scalar giving main title (see title).
sub	Character scalar giving sub title (see title).
xlab	Character scalar giving x-axis label (see title).
ylab	Character scalar giving x-axis label (see title).
cex	Scalar giving character expansion for plotting symbols (see par(cex)).
xlim	Plotting limits for x-axis (see plot.window).
ylim	Plotting limits for y-axis (see plot.window).
cex.axis	Scalar giving character expansion for latent class names (axis tick labels; cex values passed to par(axis)).

Details

Most cognitively diagnostic models for assessments assume that students with different patterns of skills will have different patterns of success and failures. The goal of this plot type is to empirically check to see if the various groups conform to their expected probability.

The assumption is that the population is divided into a number of latent classes (or groups of latent classes) and that the class label for each member of the class is known. The latent classes are partitioned into levels, where each level is assumed to have roughly the same proportion of success. (This is often c("-","+") for negative and positive skill patterns, but there could be multiple levels.)

The key idea of the observable characteristic plot is to compare a credibility interval for the success probability in each latent class, to the modelled success probability given by its level. A beta credibility interval is computed for each latent class using betaci(x,n,a,b), with the expected value set at (x+a)/(n+a+b). The plotting symbols given in lclabs are plotted at the mean (usually, these correspond to the latent class is in), with vertical error bars determined by betaci. Horizontal reference lines are added at the values given by pi. The idea is that if the error bars cross the reference line for the appropriate level, then the latent class fits the model, if not it does not.

The variant OCP2 is the same except that the latent classes are further partitioned into two sets, and the labels for the latent classes for different sets are plotted on different lines. This is particularly useful for testing whether attributes which are not thought to be relevant to a given problem are actually irrelevant.

Value

The output of betaci is returned invisibly.

Author(s)

Russell Almond

References

Almond, R.G., Mislevy, R.J., Steinberg, L.S., Williamson, D.M. and Yan, D. (2015) Bayesian Networks in Educational Assessment. Springer. Chapter 10.

Sinharay, S. and Almond, R.G. (2006). Assessing Fit of Cognitively Diagnostic Models: A case study. Educational and Psychological Measurement. 67(2), 239–257.

Sinharay, S., Almond, R. G. and Yan, D. (2004). Assessing fit of models with discrete proficiency variables in educational assessment. ETS Research Report. http://www.ets.org/research/researcher/RR-04-07.html

See Also

betaci

Examples

nn <- c(30,15,20,35)
pi <- c("+"=.15,"-"=.85)
grouplabs <- c(rep("-",3),"+")
x <- c("(0,0)"=7,"(0,1)"=4,"(1,0)"=2,"(1,1)"=31)
OCP (x,nn,grouplabs,pi,c("-","+"),ylim=c(0,1), reflty=c(2,4),
     main="Data that fit the model")

x1 <- c("(0,0)"=7,"(0,1)"=4,"(1,0)"=11,"(1,1)"=31)
OCP (x1,nn,grouplabs,pi,c("-","+"),ylim=c(0,1), reflty=c(2,4),
     main="Data that don't fit the model")

nnn <- c("(0,0,0)"=20,"(0,0,1)"=10,
         "(0,1,0)"=10,"(0,1,0)"=5,
         "(1,0,0)"=10,"(1,0,1)"=10,
         "(1,1,1)"=10,"(1,1,1)"=25)
xx <- c("(0,0,0)"=5,"(0,0,1)"=2,
       "(0,1,0)"=2,"(0,1,1)"=2,
       "(1,0,0)"=2,"(1,0,1)"=0,
       "(1,1,0)"=9,"(1,1,1)"=21)
grouplabs1 <- rep(grouplabs,each=2)

OCP2 (xx,nnn,grouplabs1,pi,c("-","+"),ylim=c(0,1), reflty=c(2,4),
     setlabs=c("Low Skill3","High Skill3"),setat=-.8,
     main="Data for which Skill 3 is irrelevant")

xx1 <- c("(0,0,0)"=2,"(0,0,1)"=5,
       "(0,1,0)"=1,"(0,1,1)"=3,
       "(1,0,0)"=0,"(1,0,1)"=2,
       "(1,1,0)"=5,"(1,1,1)"=24)
OCP2 (xx1,nnn,grouplabs1,pi,c("-","+"),ylim=c(0,1), reflty=c(2,4),
      setlabs=c("Low Skill3","High Skill3"),setat=-.8,
      main="Data for which Skill 3 is relevant")

ralmond/CPTtools documentation built on Dec. 27, 2024, 7:15 a.m.