Description Usage Arguments Details Value References Examples
Estimate random intercept latent regression models for binary and ordinal item response data considering partially missing covariate data.
1 2 |
Y |
data frame containing item responses. They can be binary or ordinal items. The
responses must be coded starting at |
Ymis |
character string how to treat |
X |
data frame containing person-level covariates. They can be numeric or factor
variables and contain missing values coded as |
S |
integer vector of individual cluster membership. A random intercept model with
|
itermcmc |
number of MCMC iterations. |
burnin |
number of burnin iterations. |
thin |
thinning interval, i.e., retain only every |
tdf |
degrees of freedom of multivariate-t proposal distribution for category cutoff parameters for ordinal items. |
cartctrl1 |
minimum number of observations in any terminal CART node during covariates imputation cycles. |
cartctrl2 |
complexity parameter. Any CART split that does not decrease the overall
lack of fit by a factor of |
rilrm
uses a fully Bayesian estimation approach. Independent conjugate prior
distributions are chosen to develop a Metropolis-within-Gibbs sampling algorithm based on
the device of data augmentation (Tanner & Wong, 1987). The function generates a sample from
the posterior distribution of a one dimensional two-parameter normal ogive IRT model
(Albert, 1992)
y_{cij}^*=α_j θ_{ci} - β_j + \varepsilon_{cij}
including a (multivariate) regression equation of a cluster level random intercept and person level predictors on the mean vector of latent abilities
θ_{ci}=ω_c + x_{ci}γ + e_{ci}.
This corresponds to the most basic
multilevel specification (Fox & Glas, 2001). Partially observed person-level covariates are
imputed in each sampling iteration. Sequential CART (Burgette & Reiter, 2010) are utilized
as approximations to the full conditional distributions of missing values in X
.
list with elements MCMCdraws
and M-Hacc
containing a list of posterior
samples matrices (rows correspond to iterations and columns to parameters) and, if
estimated, a vector of Metropolis-Hastings acceptance rates of category cutoff parameters
for ordinal items.
Albert, J. H. (1992). Bayesian estimation of normal ogive item response curves using gibbs sampling. Journal of Educational Statistics, 17(3), 251-269.
Burgette, L. F., & Reiter, J. P. (2010). Multiple imputation for missing data via sequential regression trees. American Journal of Epidemiology, 172(9), 1070-1076.
Fox, J.-P., & Glas, C. A. W. (2001). Bayesian estimation of a multilevel irt model using Gibbs sampling. Psychometrika, 66(2), 271-288.
Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528-549.
1 2 3 4 5 6 7 8 9 | ## prepare data input
data(simdata_40rilrm)
Y <- simdata_40rilrm[, grep("Y", names(simdata_40rilrm), value = TRUE)]
X <- simdata_40rilrm[, grep("X", names(simdata_40rilrm), value = TRUE)]
## estimation setup: MCMC chains of length 20 with 4 initial burn-in samples
## for testing purposes (for your applications itermcmc > 10000 needed)
##
results <- rilrm(Y = Y, X = X, S = simdata_40rilrm$S, itermcmc = 10, burnin = 2, thin = 2)
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