Description Usage Arguments Details Value Author(s) References See Also Examples
This function computes the parameter estimates of a rating scale model for polytomous item responses by using CML estimation.
1 |
X |
Input data matrix or data frame with item responses (starting from 0); rows represent individuals, columns represent items. Missing values are inserted as |
W |
Design matrix for the RSM. If omitted, the function will compute W automatically. |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
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
.
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 |
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 |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
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.
1 2 3 4 5 | ##RSM with 10 subjects, 3 items
res <- RSM(rsmdat)
res
summary(res) #eta and beta parameters with CI
thresholds(res) #threshold parameters
|
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
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.