Root Mean Square Deviation (RMSD) Item Fit Statistic
Computed the item fit statistics root mean square deviation (RMSD), mean absolute deviation (MAD) and mean deviation (MD). See Oliveri and von Davier (2011) for details.
The RMSD statistics was denoted as the RMSEA statistic in older
publications, see itemfit.rmsea.
If multiple groups are defined in the model object, a weighted item fit statistic (WRMSD; Yamamoto, Khorramdel, & von Davier, 2013; von Davier, Weeks, Chen, Allen & van der Velden, 2013) is additionally computed.
IRT.RMSD(object) ## S3 method for class 'IRT.RMSD' summary(object, file=NULL, digits=3, ...) ## core computation function IRT_RMSD_calc_rmsd( n.ik, pi.k, probs, eps=1E-30 )
object |
Object for which the methods |
n.ik |
Expected counts |
pi.k |
Probabilities trait distribution |
probs |
Item response probabilities |
eps |
Numerical constant avoiding division by zero |
digits |
Number of digits used for rounding |
file |
Optional file name for a file in which |
... |
Optional parameters to be passed. |
The RMSD and MD statistics are in operational use in PISA studies since PISA 2015. These fit statistics can also be used for investigating uniform and nonuniform differential item functioning.
List with entries
RMSD |
Item-wise and group-wise RMSD statistic |
RMSD_bc |
Item-wise and group-wise RMSD statistic with analytical bias correction |
MAD |
Item-wise and group-wise MAD statistic |
MD |
Item-wise and group-wise MD statistic |
chisquare_stat |
Item-wise and group-wise χ^2 statistic |
... |
Further values |
Oliveri, M. E., & von Davier, M. (2011). Investigation of model fit and score scale comparability in international assessments. Psychological Test and Assessment Modeling, 53, 315-333.
von Davier, M., Weeks, J., Chen, H., Allen, J., & van der Velden, R. (2013). Creating simple and complex derived variables and validation of background questionnaire data. In OECD (Eds.). Technical Report of the Survey of Adults Skills (PIAAC) (Ch. 20). Paris: OECD.
Yamamoto, K., Khorramdel, L., & von Davier, M. (2013). Scaling PIAAC cognitive data. In OECD (Eds.). Technical Report of the Survey of Adults Skills (PIAAC) (Ch. 17). Paris: OECD.
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# EXAMPLE 1: data.read | 1PL model in TAM
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data(data.read, package="sirt")
dat <- data.read
#*** Model 1: 1PL model
mod1 <- TAM::tam.mml( resp=dat )
summary(mod1)
# item fit statistics
imod1 <- CDM::IRT.RMSD(mod1)
summary(imod1)
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# EXAMPLE 2: data.math| RMSD and MD statistic for assessing DIF
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data(data.math, package="sirt")
dat <- data.math$data
items <- grep("M[A-Z]", colnames(dat), value=TRUE )
#-- fit multiple group Rasch model
mod <- TAM::tam.mml( dat[,items], group=dat$female )
summary(mod)
#-- fit statistics
rmod <- CDM::IRT.RMSD(mod)
summary(rmod)
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# EXAMPLE 3: RMSD statistic DINA model
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data(sim.dina)
data(sim.qmatrix)
dat <- sim.dina
Q <- sim.qmatrix
#-- fit DINA model
mod1 <- CDM::gdina( dat, q.matrix=Q, rule="DINA" )
summary(mod1)
#-- compute RMSD fit statistic
rmod1 <- CDM::IRT.RMSD(mod1)
summary(rmod1)
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