RSM: Estimation of rating scale models

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

This function computes the parameter estimates of a rating scale model for polytomous item responses by using CML estimation.

Usage

1
RSM(X, W, se = TRUE, sum0 = TRUE, etaStart)

Arguments

X

Input data matrix or data frame with item responses (starting from 0); rows represent individuals, columns represent items. Missing values are inserted as NA.

W

Design matrix for the RSM. If omitted, the function will compute W automatically.

se

If TRUE, the standard errors are computed.

sum0

If TRUE, the parameters are normed to sum-0 by specifying an appropriate W. If FALSE, the first parameter is restricted to 0.

etaStart

A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used.

Details

The design matrix approach transforms the RSM into a partial credit model and estimates the corresponding basic parameters by using CML. Available methods for RSM-objects are print, coef, model.matrix, vcov, summary, logLik, person.parameters, plotICC, LRtest.

Value

Returns an object of class 'Rm', 'eRm' and contains the log-likelihood value, the parameter estimates and their standard errors.

loglik

Conditional log-likelihood.

iter

Number of iterations.

npar

Number of parameters.

convergence

See code output in nlm.

etapar

Estimated basic item difficulty parameters (item and category parameters).

se.eta

Standard errors of the estimated basic item parameters.

betapar

Estimated item-category (easiness) parameters.

se.beta

Standard errors of item parameters.

hessian

Hessian matrix if se = TRUE.

W

Design matrix.

X

Data matrix.

X01

Dichotomized data matrix.

call

The matched call.

Author(s)

Patrick Mair, Reinhold Hatzinger

References

Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.

Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.

Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.

See Also

RM,PCM,LRtest

Examples

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##RSM with 10 subjects, 3 items
res <- RSM(rsmdat)
res
summary(res)                            #eta and beta parameters with CI
thresholds(res)                         #threshold parameters

Example output

Results of RSM estimation: 

Call:  RSM(X = rsmdat) 

Conditional log-likelihood: -107.5618 
Number of iterations: 11 
Number of parameters: 7 

Item (Category) Difficulty Parameters (eta):
                I2        I3         I4         I5         I6      Cat 2
Estimate 0.3051523 0.2558638 0.06730786 -0.1601342 -0.4442440 -0.1673936
Std.Err  0.2053696 0.2028161 0.19650733  0.1965178  0.2084872  0.4596567
             Cat 3
Estimate 0.1379066
Std.Err  0.7324949



Results of RSM estimation: 

Call:  RSM(X = rsmdat) 

Conditional log-likelihood: -107.5618 
Number of iterations: 11 
Number of parameters: 7 

Item (Category) Difficulty Parameters (eta): with 0.95 CI:
      Estimate Std. Error lower CI upper CI
I2       0.305      0.205   -0.097    0.708
I3       0.256      0.203   -0.142    0.653
I4       0.067      0.197   -0.318    0.452
I5      -0.160      0.197   -0.545    0.225
I6      -0.444      0.208   -0.853   -0.036
Cat 2   -0.167      0.460   -1.068    0.734
Cat 3    0.138      0.732   -1.298    1.574

Item Easiness Parameters (beta) with 0.95 CI:
           Estimate Std. Error lower CI upper CI
beta I1.c1    0.024      0.195   -0.359    0.407
beta I1.c2    0.215      0.600   -0.961    1.391
beta I1.c3   -0.066      0.932   -1.894    1.762
beta I2.c1   -0.305      0.205   -0.708    0.097
beta I2.c2   -0.443      0.636   -1.689    0.803
beta I2.c3   -1.053      1.011   -3.035    0.928
beta I3.c1   -0.256      0.203   -0.653    0.142
beta I3.c2   -0.344      0.629   -1.577    0.888
beta I3.c3   -0.905      0.997   -2.860    1.049
beta I4.c1   -0.067      0.197   -0.452    0.318
beta I4.c2    0.033      0.607   -1.157    1.223
beta I4.c3   -0.340      0.951   -2.204    1.524
beta I5.c1    0.160      0.197   -0.225    0.545
beta I5.c2    0.488      0.593   -0.675    1.651
beta I5.c3    0.342      0.910   -1.440    2.125
beta I6.c1    0.444      0.208    0.036    0.853
beta I6.c2    1.056      0.597   -0.114    2.226
beta I6.c3    1.195      0.884   -0.537    2.927


Design Matrix Block 1:
   Location Threshold 1 Threshold 2 Threshold 3
I1  0.02202    -0.02395    -0.19134     0.28135
I2  0.35112     0.30515     0.13776     0.61045
I3  0.30183     0.25586     0.08847     0.56116
I4  0.11328     0.06731    -0.10009     0.37261
I5 -0.11417    -0.16013    -0.32753     0.14517
I6 -0.39828    -0.44424    -0.61164    -0.13894

eRm documentation built on Oct. 3, 2018, 9:04 a.m.