Scott -
A Bayes network (BN) typically has unobserved state nodes (eg the
classification
variable(s) - I don't think you mentioned it specifically) and question nodes
corresponding to the items that will be set by the survey-taker. The
basic concept is conditional independence, which means that given the
state of the classification node, (ie, "holding it constant") the question
nodes are probabilistically independent. This is a property, for example,
of Naive Bayes models.
If you have reason to believe that quetion nodes are NOT conditionally
independent given the classification, then the BN can express their
dependence by arcs among question nodes. In fact to be
consistent in that case the BN should have these arcs. But note that question
variables are already dependent in the unconditional sense (marginally
dependent)
by virtue of their dependency via the classification nodes.
Its not clear to me how you would define local independence in such a BN.
- -john mark
>Hello!
>
>Please excuse the setup before the question (which is at the bottom for
>those in a hurry).
>
>I am a graduate student interested in creating an adaptive version of a job
>analysis survey. Briefly, a job analysis survey is a 300+ item
>multidimensional questionnaire given a wide range of workers to determine
>the knowledge, skills and behaviors needed to perform their job. They have
>underlying dimensions (via factor analysis) such as leadership, written/oral
>communication, supervising others, etc. Since the surveys are so long and
>time consuming, they are expensive to administer and disliked by workers. In
>addition, many of the questions are either slightly redundant or not
>applicable to certain jobs.
>
>What I plan to do use existing data from the paper-and-pencil version to
>create a Bayesian network for an adaptive version which will administer only
>relevant items based on prior information about how other workers in similar
>jobs responded.
>
>My question centers around local independence, which is one assumption of
>Item Response Theory. Local independence states that the responses to items
>within the survey are statistically independent when holding constant the
>underlying dimension. Specifically, I was wondering if the network nodes
>created for one of the dimensions of a multidimensional survey could be
>related to other nodes in other dimensions. Therefore, responses to items
>about written/oral communication could be related to items about leadership,
>etc.
>
>
>
>Question 1: If one was to create a network of a multidimensional survey, do
>the network nodes (and particular survey items associated with the nodes)
>need to be locally independent (i.e., need to be unrelated to nodes and
>items of other dimensions)?
>
>Question 2: Would anyone know of quality sources which may help someone
>create adaptive multidimensional surveys using Bayesian networks?
>
>Thanks!
>
>Scott T. Bublitz
>NC State University
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