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.
a required numeric giving the number of items of the domain taken as basis for the simulation.
a required numeric giving the number of response patterns to be simulated (the sample size).
a required numeric giving the probability for a careless error.
a required numeric giving the probability for a lucky guess.
an optional object of class
a required (if
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
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
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
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.
If the arguments
delta are of required types,
returns a named list consisting of the following three components:
a matrix of binary, 1 or 0, numeric data.
an object of class
a matrix consisting of ones or zeros (the quasi
ordinal knowledge space), in which each row represents the
1/0-pattern of a knowledge state. This is the
knowledge structure corresponding to the set of implications
To pass a quasi order as the argument
may be more convenient to transform from knowledge states to
implications using the function
The probability specified in
delta does not necessarily
correspond to the ratio of implications in the randomly generated
quasi order, because the transitive closure is formed after having
added item pairs. In Sargin and Uenlue (2009) a normal
sampling scheme for drawing
delta values using
mean = 0.16 and sd = 0.06 for
nine items has been proposed. This sampling scheme provides far
better representative samples of quasi orders than sampling
delta values uniformly from the unit interval.
Anatol Sargin, Ali Uenlue
Doignon, J.-P. and Falmagne, J.-C. (1999) Knowledge Spaces. Berlin, Heidelberg, and New York: Springer-Verlag.
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
imp2state for transformation from
implications to knowledge states;
population inductive item tree analysis;
interface that provides the three (sample) inductive item tree
analysis methods under one umbrella. See also
DAKS-package for general information about this
simu(7, 20, 0.1, 0.1, delta = 0.15)
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