tam.wle.RdCompute the weighted likelihood estimator (Warm, 1989)
for objects of classes tam, tam.mml and tam.jml,
respectively.
tam.wle(tamobj, ...) tam.mml.wle( tamobj, score.resp=NULL, WLE=TRUE, adj=.3, Msteps=20, convM=.0001, progress=TRUE, output.prob=FALSE ) tam.mml.wle2(tamobj, score.resp=NULL, WLE=TRUE, adj=0.3, Msteps=20, convM=1e-04, progress=TRUE, output.prob=FALSE, pid=NULL ) tam_jml_wle(tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM, PersonScores, theta, xsi, Msteps, WLE=FALSE, theta.fixed=NULL, progress=FALSE, output.prob=TRUE, damp=0, version=2) # S3 method for tam.wle summary(object, file=NULL, digits=3, ...) # S3 method for tam.wle print(x, digits=3, ...)
| tamobj | An object generated by |
|---|---|
| score.resp | An optional data frame for which WLEs or MLEs
should be calculated. In case of the default |
| WLE | A logical indicating whether the weighted likelihood estimate
(WLE, |
| adj | Adjustment in MLE estimation for extreme scores (i.e. all or none
items were correctly solved). This argument is not used if
|
| Msteps | Maximum number of iterations |
| convM | Convergence criterion |
| progress | Logical indicating whether progress should be displayed. |
| output.prob | Logical indicating whether evaluated probabilities should be included in the list of outputs. |
| pid | Optional vector of person identifiers |
| resp | Data frame with item responses (only for |
| resp.ind | Data frame with response indicators (only for |
| A | Design matrix \(A\) (applies only to |
| B | Design matrix \(B\) (applies only to |
| nstud | Number of persons (applies only to |
| nitems | Number of items (applies only to |
| maxK | Maximum item score (applies only to |
| PersonScores | A vector containing the sufficient statistics for the
person parameters (applies only to |
| theta | Initial \(\theta\) estimate (applies only to |
| xsi | Parameter vector \(\xi\) (applies only to |
| theta.fixed | Matrix for fixed person parameters \(\theta\). The first column includes the index whereas the second column includes the fixed value. |
| damp | Numeric value between 0 and 1 indicating amount of dampening increments in \(\theta\) estimates during iterations |
| version | Integer with possible values 2 or 3. In case of missing item responses,
|
| ... | Further arguments to be passed |
| object | Object of class |
| x | Object of class |
| file | Optional file name in which the object summary should be written. |
| digits | Number of digits for rounding |
For tam.wle.mml and tam.wle.mml2, it is a data frame with following
columns:
Person identifier
Score of each person
Maximum score of each person
Weighted likelihood estimate (WLE) or MLE
Standard error of the WLE or MLE
WLE reliability (same value for all persons)
Weighted likelihood estimate (WLE) or MLE
Standard error of the WLE or MLE
Mean change between updated and previous ability estimates from last iteration
Penfield, R. D., & Bergeron, J. M. (2005). Applying a weighted maximum likelihood latent trait estimator to the generalized partial credit model. Applied Psychological Measurement, 29, 218-233.
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450. doi: 10.1007/BF02294627
See the PP::PP_gpcm function
in the PP package for more person
parameter estimators for the partial credit model (Penfield & Bergeron, 2005).
See the S3 method IRT.factor.scores.tam.
############################################################################# # EXAMPLE 1: 1PL model, data.sim.rasch ############################################################################# data(data.sim.rasch) # estimate Rasch model mod1 <- TAM::tam.mml(resp=data.sim.rasch) # WLE estimation wle1 <- TAM::tam.wle( mod1 ) ## WLE Reliability=0.894 print(wle1) summary(wle1) # scoring for a different dataset containing same items (first 10 persons in sim.rasch) wle2 <- TAM::tam.wle( mod1, score.resp=data.sim.rasch[1:10,]) #--- WLE estimation without using a TAM object #* create an input list input <- list( resp=data.sim.rasch, AXsi=mod1$AXsi, B=mod1$B ) #* estimation wle2b <- TAM::tam.mml.wle2( input ) if (FALSE) { ############################################################################# # EXAMPLE 2: 3-dimensional Rasch model | data.read from sirt package ############################################################################# data(data.read, package="sirt") # define Q-matrix Q <- matrix(0,12,3) Q[ cbind( 1:12, rep(1:3,each=4) ) ] <- 1 # redefine data: create some missings for first three cases resp <- data.read resp[1:2, 5:12] <- NA resp[3,1:4] <- NA ## > head(resp) ## A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 ## 2 1 1 1 1 NA NA NA NA NA NA NA NA ## 22 1 1 0 0 NA NA NA NA NA NA NA NA ## 23 NA NA NA NA 1 0 1 1 1 1 1 1 ## 41 1 1 1 1 1 1 1 1 1 1 1 1 ## 43 1 0 0 1 0 0 1 1 1 0 1 0 ## 63 1 1 0 0 1 0 1 1 1 1 1 1 # estimate 3-dimensional Rasch model mod <- TAM::tam.mml( resp=resp, Q=Q, control=list(snodes=1000,maxiter=50) ) summary(mod) # WLE estimates wmod <- TAM::tam.wle(mod, Msteps=3) summary(wmod) ## head(round(wmod,2)) ## pid N.items PersonScores.Dim01 PersonScores.Dim02 PersonScores.Dim03 ## 2 1 4 3.7 0.3 0.3 ## 22 2 4 2.0 0.3 0.3 ## 23 3 8 0.3 3.0 3.7 ## 41 4 12 3.7 3.7 3.7 ## 43 5 12 2.0 2.0 2.0 ## 63 6 12 2.0 3.0 3.7 ## PersonMax.Dim01 PersonMax.Dim02 PersonMax.Dim03 theta.Dim01 theta.Dim02 ## 2 4.0 0.6 0.6 1.06 NA ## 22 4.0 0.6 0.6 -0.96 NA ## 23 0.6 4.0 4.0 NA -0.07 ## 41 4.0 4.0 4.0 1.06 0.82 ## 43 4.0 4.0 4.0 -0.96 -1.11 ## 63 4.0 4.0 4.0 -0.96 -0.07 ## theta.Dim03 error.Dim01 error.Dim02 error.Dim03 WLE.rel.Dim01 ## 2 NA 1.50 NA NA -0.1 ## 22 NA 1.11 NA NA -0.1 ## 23 0.25 NA 1.17 1.92 -0.1 ## 41 0.25 1.50 1.48 1.92 -0.1 ## 43 -1.93 1.11 1.10 1.14 -0.1 # (1) Note that estimated WLE reliabilities are not trustworthy in this example. # (2) If cases do not possess any observations on dimensions, then WLEs # and their corresponding standard errors are set to NA. ############################################################################# # EXAMPLE 3: Partial credit model | Comparison WLEs with PP package ############################################################################# library(PP) data(data.gpcm) dat <- data.gpcm I <- ncol(dat) #**************************************** #*** Model 1: Partial Credit Model # estimation in TAM mod1 <- TAM::tam.mml( dat ) summary(mod1) #-- WLE estimation in TAM tamw1 <- TAM::tam.wle( mod1 ) #-- WLE estimation with PP package # convert AXsi parameters into thres parameters for PP AXsi0 <- - mod1$AXsi[,-1] b <- AXsi0 K <- ncol(AXsi0) for (cc in 2:K){ b[,cc] <- AXsi0[,cc] - AXsi0[,cc-1] } # WLE estimation in PP ppw1 <- PP::PP_gpcm( respm=as.matrix(dat), thres=t(b), slopes=rep(1,I) ) #-- compare results dfr <- cbind( tamw1[, c("theta","error") ], ppw1$resPP) head( round(dfr,3)) ## theta error resPP.estimate resPP.SE nsteps ## 1 -1.006 0.973 -1.006 0.973 8 ## 2 -0.122 0.904 -0.122 0.904 8 ## 3 0.640 0.836 0.640 0.836 8 ## 4 0.640 0.836 0.640 0.836 8 ## 5 0.640 0.836 0.640 0.836 8 ## 6 -1.941 1.106 -1.941 1.106 8 plot( dfr$resPP.estimate, dfr$theta, pch=16, xlab="PP", ylab="TAM") lines( c(-10,10), c(-10,10) ) #**************************************** #*** Model 2: Generalized partial Credit Model # estimation in TAM mod2 <- TAM::tam.mml.2pl( dat, irtmodel="GPCM" ) summary(mod2) #-- WLE estimation in TAM tamw2 <- TAM::tam.wle( mod2 ) #-- WLE estimation in PP # convert AXsi parameters into thres and slopes parameters for PP AXsi0 <- - mod2$AXsi[,-1] slopes <- mod2$B[,2,1] K <- ncol(AXsi0) slopesM <- matrix( slopes, I, ncol=K ) AXsi0 <- AXsi0 / slopesM b <- AXsi0 for (cc in 2:K){ b[,cc] <- AXsi0[,cc] - AXsi0[,cc-1] } # estimation in PP ppw2 <- PP::PP_gpcm( respm=as.matrix(dat), thres=t(b), slopes=slopes ) #-- compare results dfr <- cbind( tamw2[, c("theta","error") ], ppw2$resPP) head( round(dfr,3)) ## theta error resPP.estimate resPP.SE nsteps ## 1 -0.476 0.971 -0.476 0.971 13 ## 2 -0.090 0.973 -0.090 0.973 13 ## 3 0.311 0.960 0.311 0.960 13 ## 4 0.311 0.960 0.311 0.960 13 ## 5 1.749 0.813 1.749 0.813 13 ## 6 -1.513 1.032 -1.513 1.032 13 }