kequate(design, ...)EG design ‘x’ A vector of possible score values on the test X to be equated, ordered from the lowest to the highest score.
‘y’ A vector of possible score values on the test Y to be equated, ordered from the lowest to the highest score.
‘r’,‘s’ Numeric vectors containing the estimated or observed score probabilities for tests X and Y respectively. Alternatively objects of class ‘glm’.
‘DMP’, ‘DMQ’ The design matrices from the log-linear models for the estimated score probabilities for X and Y. Not needed if arguments r and s are of class ‘glm’.
‘N’, ‘M’ The sample sizes of the groups taking tests X and Y, respectively. Not needed if arguments r and s are of class ‘glm’.
‘hx’, ‘hy’ Optional arguments to specify the continuization parameters manually. (If linear=TRUE, then these arguments have no effect.)
‘hxlin’, ‘hylin’ Optional arguments to specify the continuization parameters manually in the linear case.
‘KPEN’ The constant used in deciding the optimal continuization parameter. Default is 0.
‘wpen’ An argument denoting at which point the derivatives in the second part of the penalty function should be evaluated. Default is 1/4.
‘linear’ Logical denoting if only a linear equating is to be performed. Default is FALSE.
‘irtx’, ‘irty’ Optional arguments to provide matrices of probabilities to answer correctly to the questions on the parallel tests X and Y, as estimated in an Item Response Theory (IRT) model.
‘smoothed’ A logical argument denoting if the data provided are pre-smoothed or not. Default is TRUE.
‘kernel’ A character vector indicating which kernel to use, either "gaussian", "logistic", "stdgaussian" or "uniform". Default is "gaussian".
‘slog’ The parameter used in defining the logistic kernel. Default is 1.
‘bunif’ The parameter used in defining the uniform kernel. Default is 0.5.
‘altopt’ Logical which sets the bandwidth parameter equal to a variant of Silverman's rule of thumb. Default is FALSE.
SG design ‘x’ A vector of possible score values on the test X to be equated, ordered from the lowest to the highest score.
‘y’ A vector of possible score values on the test Y to be equated, ordered from the lowest to the highest score.
‘P’ The estimated or observed probability matrix for scores on tests X and Y, where the columns denote scores on test Y and the rows denote scores on test X. Alternatively a vector of score probabilities or an object of class ‘glm’, where the entries are ordered first by the Y-scores and then by the X-scores.
‘DM’ The design matrix used in the log-linear model. Not needed if the argument P is of class ‘glm’.
‘N’ The sample size. Not needed if the argument P is of class ‘glm’.
‘hx’, ‘hy’ Optional arguments to specify the continuization parameter manually. (If linear=TRUE, then these arguments have no effect.)
‘hxlin’, ‘hylin’ Optional arguments to specify the continuization parameters manually in the linear case.
‘KPEN’ The constant used in deciding the optimal continuization parameter. Default is 0.
‘wpen’ An argument denoting at which point the derivatives in the second part of the penalty function should be evaluated. Default is 1/4.
‘linear’ Logical denoting if only a linear equating is to be performed. Default is FALSE.
‘irtx’, ‘irty’ Optional arguments to provide matrices of probabilities to answer correctly to the questions on the parallel tests X and Y, as estimated in an Item Response Theory (IRT) model.
‘smoothed’ A logical argument denoting if the data provided are pre-smoothed or not. Default is TRUE.
‘kernel’ A character vector indicating which kernel to use, either "gaussian", "logistic", "stdgaussian" or "uniform". Default is "gaussian".
‘slog’ The parameter used in defining the logistic kernel. Default is 1.
‘bunif’ The parameter used in defining the uniform kernel. Default is 0.5.
CB design ‘x’ A vector of possible score values on the test X to be equated, ordered from the lowest to the highest score.
‘y’ A vector of possible score values on the test Y to be equated, ordered from the lowest to the highest score.
‘P12’, ‘P21’ The estimated or observed probability matrices for scores on first taking test X and then taking test Y, and first taking test Y and then taking test X respectively, where the rows denote scores on tests X and the columns denote scores on test Y. Alternatively numeric vectors or objects of class ‘glm’, where the entries are ordered first by the Y-scores and then by the X-scores.
‘DM12’, ‘DM21’ The design matrices from the log-linear models for the estimated score probabilities for the two test groups. Not needed if arguments P12 and P21 are of class ‘glm’.
‘N’, ‘M’ The sample sizes for the tests X and A and the tests Y and A, respectively. Not needed if arguments P12 and P21 are of class ‘glm’.
‘hx’, ‘hy’ Optional arguments to specify the continuization parameters manually. (If linear=TRUE, then these arguments have no effect)
‘hxlin’, ‘hylin’ Optional arguments to specify the continuization parameters manually in the linear case. (Applies both when linear=FALSE and when linear=TRUE.)
‘wcb’ The weighting of the two groups. Default is 0.5.
‘KPEN’ Optional argument to specify the constant used in deciding the optimal continuization parameter. Default is 0.
‘wpen’ An argument denoting at which point the derivatives in the second part of the penalty function should be evaluated. Default is 1/4.
‘linear’ Optional logical argument denoting if only a linear equating is to be performed. Default is FALSE.
‘irtx’, ‘irty’ Optional arguments to provide matrices of probabilities to answer correctly to the questions on the parallel tests X and Y, as estimated in an Item Response Theory (IRT) model.
‘smoothed’ A logical argument denoting if the data provided are pre-smoothed or not. Default is TRUE.
‘kernel’ A character vector indicating which kernel to use, either "gaussian", "logistic", "stdgaussian" or "uniform". Default is "gaussian".
‘slog’ The parameter used in defining the logistic kernel. Default is 1.
‘bunif’ The parameter used in defining the uniform kernel. Default is 0.5.
‘altopt’ Logical which sets the bandwidth parameter equal to a variant of Silverman's rule of thumb. Default is FALSE.
NEAT PSE or NEC design ‘x’ A vector of possible score values on the test X to be equated, ordered from the lowest to the highest score.
‘y’ A vector of possible score values on the test Y to be equated, ordered from the lowest to the highest score.
‘P’, ‘Q’ The estimated or observed probability matrices for scores on tests X and A and tests Y and A respectively, where the rows denote scores on tests X or Y and the columns denote scores on test A. Alternatively numeric vectors or objects of class ‘glm’, where the entries are ordered first by the X-scores/Y-scores and then by the A-scores.
‘DMP’, ‘DMQ’ The design matrices from the log-linear models for the estimated score probabilities for X and A and Y and A. Not needed if arguments P and Q are of class ‘glm’.
‘N’, ‘M’ The sample sizes for the tests X and A and the tests Y and A, respectively. Not needed if arguments P and Q are of class ‘glm’.
‘w’ The weighting of the synthetic population. Default is 0.5.
‘hx’, ‘hy’ Optional arguments to specify the continuization parameters manually. (If linear=TRUE, then these arguments have no effect)
‘hxlin’, ‘hylin’ Optional arguments to specify the continuization parameters manually in the linear case. (Applies both when linear=FALSE and when linear=TRUE.)
‘KPEN’ Optional argument to specify the constant used in deciding the optimal continuization parameter. Default is 0.
‘wpen’ An argument denoting at which point the derivatives in the second part of the penalty function should be evaluated. Default is 1/4.
‘linear’ Optional logical argument denoting if only a linear equating is to be performed. Default is FALSE.
‘irtx’, ‘irty’ Optional arguments to provide matrices of probabilities to answer correctly to the questions on the parallel tests X and Y, as estimated in an Item Response Theory (IRT) model.
‘smoothed’ A logical argument denoting if the data provided are pre-smoothed or not. Default is TRUE.
‘kernel’ A character vector indicating which kernel to use, either "gaussian", "logistic", "stdgaussian" or "uniform". Default is "gaussian".
‘slog’ The parameter used in defining the logistic kernel. Default is 1.
‘bunif’ The parameter used in defining the uniform kernel. Default is 0.5.
‘altopt’ Logical which sets the bandwidth parameter equal to a variant of Silverman's rule of thumb. Default is FALSE.
NEAT CE design ‘x’ A vector of possible score values on the test X to be equated, ordered from the lowest to the highest score.
‘y’ A vector of possible score values on the test Y to be equated, ordered from the lowest to the highest score.
‘a’ A vector containing the possible score values on the anchor test, ordered from the lowest score to the highest.
‘P’, ‘Q’ The estimated or observed probability matrices for scores on tests X and A and tests Y and A respectively, where the rows denote scores on test X or Y and the columns denote scores on test A. Alternatively numeric vectors or objects of class ‘glm’, where the entries are ordered first by the X-scores/Y-scores and then by the A-scores.
‘DMP’, ‘DMQ’ The design matrices from the log-linear models for the estimated score probabilities for X and A and Y and A, respectively. Not needed if arguments P and Q are of class ‘glm’.
‘N’, ‘M’ The sample sizes for the tests X and A and the tests Y and A, respectively. Not needed if arguments P and Q are of class ‘glm’.
‘hxP’, ‘hyQ’, ‘haP’, ‘haQ’ Optional arguments to specify the continuization parameters manually. (If linear=TRUE, then these arguments have no effect.)
‘hxPlin’, ‘hyQlin’, ‘haPlin’, ‘haQlin’ Optional arguments to specify the continuization parameters manually in the linear case. (Applies both when linear=FALSE and when linear=TRUE.)
‘KPEN’ Optional argument to specify the constant used in deciding the optimal continuization parameter. Default is 0.
‘wpen’ An argument denoting at which point the derivatives in the second part of the penalty function should be evaluated. Default is 1/4.
‘linear’ Optional logical argument denoting if only a linear equating is to be performed. Default is FALSE.
‘irtx’, ‘irty’ Optional arguments to provide matrices of probabilities to answer correctly to the questions on the parallel tests X and Y, as estimated in an Item Response Theory (IRT) model.
‘smoothed’ A logical argument denoting if the data provided are pre-smoothed or not. Default is TRUE.
‘kernel’ A character vector indicating which kernel to use, either "gaussian", "logistic", "stdgaussian" or "uniform". Default is "gaussian".
‘slog’ The parameter used in defining the logistic kernel. Default is 1.
‘bunif’ The parameter used in defining the uniform kernel. Default is 0.5.
‘altopt’ Logical which sets the bandwidth parameter equal to a variant of Silverman's rule of thumb. Default is FALSE.
von Davier, A.A., Holland, P.W., Thayer, D.T. (2004). The Kernel Method of Test Equating. Springer-Verlag New York.
glm,kefreq
#EG toy example with different kernels
P<-c(5, 20, 35, 25, 15)
Q<-c(10, 30, 30, 20, 10)
x<-0:4
glmx<-glm(P~I(x)+I(x^2), family="poisson", x=TRUE)
glmy<-glm(Q~I(x)+I(x^2), family="poisson", x=TRUE)
keEG<-kequate("EG", 0:4, 0:4, glmx, glmy)
keEGlog<-kequate("EG", 0:4, 0:4, glmx, glmy, kernel="logistic", slog=sqrt(3)/pi)
keEGuni<-kequate("EG", 0:4, 0:4, glmx, glmy, kernel="uniform", bunif=sqrt(3))
plot(keEG)
#NEAT example using simulated data
data(simeq)
freq1 <- kefreq(simeq$bivar1$X, 0:20, simeq$bivar1$A, 0:10)
freq2 <- kefreq(simeq$bivar2$Y, 0:20, simeq$bivar2$A, 0:10)
glm1<-glm(frequency~I(X)+I(X^2)+I(X^3)+I(X^4)+I(X^5)+I(A)+I(A^2)+I(A^3)+I(A^4)+
I(A):I(X)+I(A):I(X^2)+I(A^2):I(X)+I(A^2):I(X^2), family="poisson", data=freq1, x=TRUE)
glm2<-glm(frequency~I(X)+I(X^2)+I(A)+I(A^2)+I(A^3)+I(A^4)+I(A):I(X)+I(A):I(X^2)+
I(A^2):I(X)+I(A^2):I(X^2), family="poisson", data=freq2, x=TRUE)
keNEATPSE <- kequate("NEAT_PSE", 0:20, 0:20, glm1, glm2)
keNEATCE <- kequate("NEAT_CE", 0:20, 0:20, 0:10, glm1, glm2)
summary(keNEATPSE)
summary(keNEATCE)
#IRT observed-score equating
keNEATCEirt <- kequate("NEAT_CE", 0:20, 0:20, 0:10, glm1, glm2, irtx=simeq$irtNEATx,
irty=simeq$irtNEATy)
getEquating(keNEATCEirt)
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