simu can be used to simulate binary, of type $1$/$0$,
data using a basic local independence model. The number of
items, the sample size, and two parameters for the careless error
and lucky guess probabilities can be set explicitly. The underlying
combinatorial structure used for simulating the data can either be
specified manually or is generated randomly.
simu(items, size, ce, lg, imp = NULL, delta)imp = NULL) numeric giving the
probability for adding an item pair to the randomly generated
quasi order (reflexive pairs are always included a priori).items, size, ce, lg,
imp, and delta are of required types, simu
returns a named list consisting of the following three components:set
representing the underlying set of implications (assumed to be a
quasi order) used for simulating the data. If imp = NULL,
this is the quasi order that was randomly generated; otherwise
identical to the set of implications specified in the argument
imp.implications.simu simulates data using a special case of the
basic local independence model, which is a fundamental restricted
latent class model in knowledge space theory
(Doignon and Falmagne, 1999). The single careless error
ce and lucky guess lg probabilities are assumed to be
constant over all items. The most general case that can be
specified thus includes two error probabilities at each item, the
same two rates for all items. The general form of the basic local
independence model allows for varying careless error and lucky guess
rates from item to item (not identifiable in general, however). If a quasi order is specified in imp explicitly, Birkhoff's
theorem is used to derive its corresponding quasi ordinal knowledge
space, which is equipped with the error probabilities ce and
lg to give the basic local independence model used for
simulating the data. If imp = NULL, the underlying quasi
order is generated randomly as follows. All reflexive pairs are
added to the relation. The constant specified in delta is
utilized as the probability for adding each of the remaining
non-reflexive item pairs to the relation. The transitive closure of
this relation is computed, and the resulting quasi order is then the
relation underlying the simulation.
A set of implications, an object of the class
set, consists of $2$-tuples $(i, j)$ of
the class tuple, where a $2$-tuple
$(i, j)$ is interpreted as `mastering item $j$ implies
mastering item $i$.'
The simulated dataset contains only ones and zeros, which encode solving or failing to solve an item, respectively.
Sargin, A. and Uenlue, A. (2009) Inductive item tree analysis: Corrections, improvements, and comparisons. Mathematical Social Sciences, 58, 376--392.
Uenlue, A. and Sargin, A. (2010) DAKS: An R package for data analysis methods in knowledge space theory. Journal of Statistical Software, 37(2), 1--31. URL http://www.jstatsoft.org/v37/i02/.
state2imp for transformation from knowledge states to
implications; imp2state for transformation from
implications to knowledge states; pop_iita for
population inductive item tree analysis; iita, the
interface that provides the three (sample) inductive item tree
analysis methods under one umbrella. See also
DAKS-package for general information about this
package.
simu(7, 20, 0.1, 0.1, delta = 0.15)
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