rasch {ltm} | R Documentation |
Fit the Rasch model under the Item Response Theory approach.
rasch(dat, start.val, na.action = NULL, control = list())
dat |
a data.frame (that will be converted to a numeric matrix using
data.matrix() ) or a numeric matrix of manifest variables. The binary responses
must be in 0/1 format. |
start.val |
a numeric vector of p+1 starting values for the algorithm. The first p
values correspond to the difficulty parameters while the last value corresponds to the discrimination
parameter. If it is not supplied randomly chosen starting values are used instead. |
na.action |
the na.action to be used on dat . In case of missing data, if
na.action=NULL the model uses the available cases, i.e., it takes into account the observed
part of sample units with missing values (valid under MAR mechanisms if the model is correctly specified).
If you want to apply a complete case analysis then use na.action=na.exclude . |
control |
a list of control values,
|
The Rasch model is special case of the unidimensional latent trait model when all the discrimination parameters are equal. This model was first discussed by Rasch (1960) and it is used mainly in educational testing where the aim is to study the abilities of a particular set of individuals.
The model is defined as follows
logit (π_i) = beta_{i0} + beta z,
where π_i denotes the probability of responding correctly to the ith item, beta_{i0} denotes the difficulty parameter for the ith item, β is the discrimination parameter (the same for all the items) and z denotes the latent ability.
The optimization algorithm works under the constraint that the discrimination parameter is always positive.
An object of class rasch
with components,
coefficients |
the loadings' values at convergence. |
log.Lik |
the log-likelihood value at convergence. |
convergence |
the convergence identifier returned by optim . |
hessian |
the Hessian matrix at convergence returned by optim . |
patterns |
a list with two components: (i) mat a numeric matrix
that contains the observed response patterns. (ii) dat a data.frame that contains the observed and expected
frequencies for each observed response pattern. |
GH |
a list with two components used in the Gauss-Hermite rule: (i) Z a numeric matrix that contains
the quadrature points. (ii) GHw a numeric vector that contains the corresponding weights. |
max.sc |
the maximum absolute value of the score vector at convergence. |
X |
the responses data matrix. |
control |
the values used in the control argument. |
call |
the matched call. |
In case the Hessian matrix at convergence is not positive definite, try
to re-fit the model. rasch
will use new random starting values.
Baker, F. and Kim, S-H. (2004) Item Response Theory, 2nd ed. New York: Marcel Dekker.
Rasch, G. (1960) Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen: Paedagogiske Institute.
coef.rasch
,
summary.rasch
,
anova.rasch
,
plot.rasch
,
margins
,
factor.scores
## The Rasch model for the Wirs data: rasch(Wirs) ## The Rasch model for the Lsat data: rasch(Lsat) ## The Rasch model for the Abortion data: rasch(Abortion)