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TAM (version 0.04-43)

tam.jml: Joint Maximum Likelihood Estimation

Description

This function estimate unidimensional item response models with joint maximum likelihood (JML, see e.g. Linacre, 1994).

Usage

tam.jml(resp, group = NULL, disattenuate = FALSE, bias = TRUE, 
    xsi.fixed = NULL, xsi.inits = NULL, A = NULL, B = NULL, Q = NULL, 
    R = NULL, ndim = 1, pweights = NULL, control = list())

tam.jml2(resp, group = NULL, disattenuate = FALSE, bias = TRUE, 
    xsi.fixed = NULL, xsi.inits = NULL, A = NULL, B = NULL, Q = NULL, 
    R = NULL, ndim = 1, pweights = NULL, control = list())

Arguments

resp
A matrix of item responses. Missing responses must be declared as NA.
group
An optional vector of group identifier
disattenuate
Should the person parameters disattenuated due to unreliability? The disattenuation is conducted by applying the Kelley formula.
bias
A logical which indicates if JML bias shold be reduced by multiplying item parameters by the adjustment factor of $(I-1)/I$
xsi.fixed
An optional matrix with two columns for fixing some of the basis parameters $\xi$ of item intercepts. 1st column: Index of $\xi$ parameter, 2nd column: Fixed value of $\xi$ parameter
xsi.inits
An optional vector of initial $\xi$ parameters
A
A design array $A$ for item category intercepts. For item $i$ and category $k$, the threshold is specified is $\sum _j a_{ikj} \xi_j$.
B
A design array for scoring item category responses. Entries in $B$ represent item loadings on abilities $\theta$.
Q
A $Q$ matrix which defines loadings of items on dimensions.
R
This argument is not yet used.
ndim
Number of dimensions in the model. The default is 1.
pweights
An optional vector of person weights.
control
A list of control arguments. See tam for more details.

Value

  • A list with following entries
  • xsiVector of item parameters $\xi$
  • errorPStandard error of item parameters $\xi$
  • thetaWLE in final step
  • errorWLEStandard error of WLE
  • WLEWLE in last iteration
  • WLEreliabilityWLE reliability
  • PersonScoresScores for each person (sufficient statistic)
  • ItemScoreSufficient statistic for each item parameter
  • PersonMaxMaximum person score
  • ItemMaxMaximum item score
  • outfitPersonPerson outfit statistic
  • outfitItemItem outfit statistic
  • infitPersonPerson infit statistic
  • infitItemItem infit statistic
  • outfitPerson_tThe $t$ value of person outfit
  • outfitItem_tThe $t$ value of item outfit
  • infitPerson_tThe $t$ value of person infit
  • infitItem_tThe $t$ value of item infit
  • devianceDeviance
  • deviance.historyDeviance history in iterations
  • respOriginal data frame
  • resp.indResponse indicator matrix
  • groupVector of group identifiers (if provided as an argument)
  • pweightsVector of person weights
  • ADesign matrix $A$ of item intercepts
  • BLoading (or scoring) matrix $B$
  • nitemsNumber of items
  • maxKMaximum number of categories
  • nstudNumber of persons in resp
  • resp.ind.listLike resp.ind, only in the format of a list
  • xsi.fixedFixed $\xi$ item parameters
  • controlControl list
  • ...

Details

The function tam.jml2 is just a faster implementation of tam.jml. It is in general recommended to use tam.jml2.

References

Linacre, J. M. (1994). Many-Facet Rasch Measurement. Chicago: MESA Press.

See Also

For estimating the same class of models with marginal maximum likelihood estimation see tam.

Examples

Run this code
data(sim.rasch)
# estimate the Rasch model with JML
mod <- tam.jml2(resp=sim.rasch)

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