Description Usage Arguments Details Value Note Author(s) References See Also Examples
iita
can be used to perform one of the three inductive item
tree analysis algorithms (original, corrected, and minimized
corrected) selectively.
1  iita(dataset, v)

dataset 
a required data frame or matrix consisting of binary, 1 or 0, numeric data. 
v 
a required numeric giving the inductive item tree analysis
algorithm to be performed; 
The three inductive item tree analysis algorithms are exploratory methods for extracting quasi orders (surmise relations) from data. In each algorithm, competing binary relations are generated (in the same way for all three versions), and a fit measure (differing from version to version) is computed for every relation of the selection set in order to find the quasi order that fits the data best. In all three algorithms, the idea is to estimate the numbers of counterexamples for each quasi order, and to find, over all competing quasi orders, the minimum value for the discrepancy between the observed and expected numbers of counterexamples. The three data analysis methods differ in their choices of estimates for the expected numbers of counterexamples. (For an item pair (i, j), the number of subjects solving item j but failing to solve item i, is the corresponding number of counterexamples. Their response patterns contradict the interpretation of (i, j) as 'mastering item j implies mastering item i.') The algorithms are described in the paper about the DAKS package by Uenlue and Sargin (2010), and in the paper by Sargin and Uenlue (2009).
iita
calls ind_gen
for constructing the set of
competing quasi orders according to the inductive generation
procedure. Subject to the selected version to be performed,
iita
computes the discrepancies between observed and expected
numbers of counterexamples under each relation, and finds a quasi
order with the minimum discrepancy (diff) value.
A set of implications, an object of the class
set
, consists of 2tuples (i, j) of
the class tuple
, where a 2tuple
(i, j) is interpreted as 'mastering item j implies
mastering item i.'
The data must contain only ones and zeros, which encode solving or failing to solve an item, respectively.
If the arguments dataset
and v
are of required types,
iita
returns a named list consisting of the following five
components:
diff 
a vector giving the diff values corresponding to the (inductively generated) competing quasi orders. 
implications 
an object of class 
error.rate 
a value giving the estimated error rate corresponding to the best fitting quasi order. 
selection.set.index 
a numeric giving the index of the solution quasi order in the selection set. 
v 
the version used; 
The function iita
can be used to perform one of the
three inductive item tree analysis procedures selectively. Whereas
for the functions orig_iita
, corr_iita
,
mini_iita
selection sets of competing quasi orders
have to be passed via an argument manually, iita
automatically generates a selection set from the data using the
inductive generation procedure implemented in ind_gen
.
The latter approach using iita
is common so far, in knowledge
space theory, where the inductive data analysis methods have been
utilized for exploratory derivations of surmise relations from data.
The functions orig_iita
, corr_iita
,
mini_iita
, on the other hand, can be used to select
among surmise relations for instance obtained from querying experts
or from competing psychological theories.
Anatol Sargin, Ali Uenlue
Sargin, A. and Uenlue, A. (2009) Inductive item tree analysis: Corrections, improvements, and comparisons. Mathematical Social Sciences, 58, 376–392.
Schrepp, M. (1999) On the empirical construction of implications between bivalued test items. Mathematical Social Sciences, 38, 361–375.
Schrepp, M. (2003) A method for the analysis of hierarchical dependencies between items of a questionnaire. Methods of Psychological Research, 19, 43–79.
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/.
orig_iita
for original inductive item tree analysis;
corr_iita
for corrected inductive item tree analysis;
mini_iita
for minimized corrected inductive item tree
analysis; ind_gen
for inductive generation procedure;
pop_variance
for population asymptotic variances of
diff coefficients; variance
for estimated
asymptotic variances of diff coefficients; z_test
for one and twosample Ztests;
pop_iita
for population inductive item tree analysis.
See also DAKSpackage
for general information about
this package.
1 2 
Loading required package: relations
Loading required package: sets
Inductive Item Tree Analysis
Algorithm: minimized corrected IITA
quasi order: {(1L, 2L), (1L, 3L), (1L, 4L), (1L, 5L), (2L, 3L), (2L, 4L), (2L, 5L),
(3L, 4L), (3L, 5L)}
Inductive Item Tree Analysis
Algorithm: original IITA
quasi order: {(1L, 4L), (1L, 5L), (2L, 4L), (2L, 5L)}
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