kequate (version 1.5.0)

cdist: Conditional Mean, Variance, Skewness and Kurtosis

Description

Calculates conditional means, variances, skewnesses and kurtoses for observed and estimated bivariate probability distributions of test scores.

Usage

cdist(est, obs, xscores, ascores)

Arguments

est

Matrix of estimated bivariate score probabilities.

obs

Matrix of observed bivariate score probabilities.

xscores

Optional argument to specify the score vector for test X.

ascores

Optional argument to specify the score vector for test A.

Value

An object of class 'cdist' containing the following slots

est1

Matrix of conditional means, variances, skewnesses and kurtoses of X given A for the estimated score distribution.

est2

Matrix of conditional means, variances, skewnesses and kurtoses of A given X for the estimated score distribution.

obs1

Matrix of conditional means, variances, skewnesses and kurtoses of X given A for the observed score distribution.

obs2

Matrix of conditional means, variances, skewnesses and kurtoses of A given X for the observed score distribution.

References

von Davier, A.A., Holland, P.W., Thayer, D.T. (2004). The Kernel Method of Test Equating. Springer-Verlag New York.

Holland, P.W., Thayer, D. (1998). Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions ETS Technical Report No 98-1.

See Also

kequate PREp

Examples

freqdata<-data.frame(X=c(1,2,2,1,2,2,2,2,3,1,2,1,4,2,1,1,3,3,3,3), 
A=(c(0,2,1,1,0,3,1,2,2,0,2,0,3,1,1,2,2,2,1,2)))
Pdata<-kefreq(freqdata$X, 0:5, freqdata$A, 0:3)
Pglm<-glm(frequency~X+I(X^2)+A+I(A^2)+X:A, data=Pdata, family="poisson", x=TRUE)
Pobs<-matrix(Pdata$freq, nrow=6)/sum(Pglm$y)
Pest<-matrix(Pglm$fitted.values, nrow=6)/sum(Pglm$y)
cdP<-cdist(Pest, Pobs, 0:5, 0:3)
plot(cdP)