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Bayesian Networks in Educational Assessment

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Activity Selection Process?
The Activity Selection Process is the part of the Assessment Cycle that selects a task or other activity for presentation to an examinee.
Acyclic directed graph
A directed graph that has no directed cycles. Note that if the directions of the arrows are dropped there may be cycles.
The Administrator is the person responsible for setting up and maintaining the assessment. The Administrator is responsible for starting the process and configuring various choices; for example, whether or not item level feedback will be displayed during the assessment.
Assembly Model?
The Assembly Model, one of a collection of six different types of models that comprise the Conceptual Assessment Framework? (CAF?), provides the information required to control the selection of tasks for the creation of an assessment.
An Assessment is a system (computer, manual, or some combination of the these) that presents examinees, or participants, with work and evaluates the results. This includes high stakes examinations, diagnostic tests, and coached-practice systems, which include embedded assessment.
Assessment Cycle
The Assessment Cycle is comprised of four basic processes: Activity Selection, Presentation, Response Processing, and Summary Scoring. The Activity Selection Process selects a task or other activity for presentation to an examinee. The Presentation Process displays the task to the examinee and captures the results (or Work Products) when the examinee performs the task. Response Processing identifies the essential features of the response and records these as a series of Observations. The Summary Scoring Process updates the scoring based on the input it receives from Response Processing. This four-process architecture can work in either synchronous or asynchronous mode.
Assessment Designer
A person who is responsible for the building and/or maintaining the Conceptual Assessment Framework for an assessment.


Bayesian network?
A Bayesian network (or Bayes net) is a method of representing a probability distribution with an acyclic directed graph. The nodes of the graph represent variables in the problem and the pattern of edges represent conditional independence relationships (see d-separation). The variables in a Bayesian network are generally required to be discrete. Bayesian networks are a special case of graphical models.
Beta distribution
The beta distribution is a continuous probability distribution with the following probability density function: f(\theta|a,b) = \left[{1\over B(a,b)} \right] \theta^{a-1}(1-\theta)^{b-1}, where B(a,b) is the "beta function", B(a,b) = \int_0^1 t^{a-1}(1-t)^{b-1}\,dt = {\Gamma(a)\Gamma(b)\over \Gamma(a+b)} . The beta distribution is interesting because it is a natural conjugate of the binomial distribution. In particular, if \theta is interpreted as the probability of 'success', then the parameter a corresponds to the number of observed successes and the parameter b corresponds to the number of observed failures. The Dirichlet distribution is a generalization of the beta distribution. B(1,1) is the uniform distribution.
Binomial (Bernoulli) distribution
A single event or trial which can 'succeed' with a probability \theta is said to follow a Bernoulli distribution. If the experiment is repeated for $n$ independent trials, then the count of the number of 'successes' is said to follow a binomial distribution. The probability mass function is: p(Y=y|\theta,n) = {n\choose y}\theta^y(1-\theta)^{n-y} for y=0,\ldots,n. The multinomial distribution is a generalization of the binomial where each trial has more than two possible outcomes.


Choosing a set of parameters for a measurement model? based on data collected from that model. In Bayesian terms this means calculating a posterior law for parameters based on the prior law and the collected data.
In a Graph?, the child is the node that is the second position in the edge, that is, that the arrow points from the parent node to the child node. In a Bayes net, a child node has a conditional probability distribution that depends on one or more other nodes, which are its parents. The descendents of a node A is any node that is a child, a child of a child, a child of a child of a child, or so forth.
A claim is a proposition, educationally relevant and stated in natural language, about the kinds of things a student might know or be able to do, in what kinds of circumstances. Claims are what users of assessments want to be able to say about examinees, and are the basis of Score Reports. A Reporting Rule maps information from probability distributions over Student Model Variables to summary statements about the amount and direction of evidence to support a claim.
A maximally connected set of nodes in a graph. This means that all nodes in the clique are neighbors and there is no other node in the graph which is a neighbor of all of the nodes in the clique. The cliques of a graphical model are important because they define the spaces over which the computations take place. The cliques of the graph are often arranged into a tree of cliques or junction tree. The treewidth of a graph is the size of its largest clique and generally the dominant term in the cost of probability calculations within that graph.
Compensatory Distribution
A design pattern for a conditional probability table with multiple parents (usually representing proficiencies) where more of one skill can compensate for less of another. For example, when driving a car, planning ahead can compensate for reaction time.
Competency Model
An alternative term used for proficiency model because the term "proficiency" has taken on a special meaning under the No Child Left Behind Act.
Computer Adaptive Testing (CAT)
An assessment in which the form of the assessment, that is, the sequence of tasks seen by the examinee, is dynamically created by a computer at the time of the assessment, usually each task is based on observed outcomes from previous tasks. This is often contrasted with a linear test, in which each form \

has a fixed sequence of tasks. See Invalid BibTex Entry!

Conditional Independence
Two events A and B are conditionally independent given a third event X if when the state of X is known, knowledge of A provides no information about B. This can be stated in terms of probabilities as \Pr(A|X,B) = \Pr(A|X,\neg B) = \Pr(A|X). When two events are conditionally independent their joint conditional probabilities can be calculated by the product of the conditional probabilities: \Pr(A,B|X) = \Pr (A|X) \Pr(B|X).
Conditional Multinomial Distribution
This is the natural distribution for a conditional probability table in a Bayesian network where every row of the conditional probability table, corresponding to a configuration of the parent variables, is an independent multinomial distribution. The natural conjugate distribution for the parameters of this distribution is the hyper-Dirichlet law.
Conceptual Assessment Framework (CAF)
The Conceptual Assessment Framework builds specific models for use in a particular assessment product (taking into account the specific purposes and requirements of that product). The conceptual assessment framework consists of a collection of six different types of models that define what objects are needed and how an assessment will function for a particular purpose. The models of the CAF are as follows: the Student Model, the Task Model, the Evidence Model, the Assembly Model, the Presentation Model, and the Delivery Model. Delivery Model. The Delivery Model, one of a collection of six different types of models that comprise the Conceptual Assessment Framework (CAF), describes which other models will be used, as well as other properties of the assessment that span all four processes, such as platform and security requirements.
Conjunctive Distribution
A design pattern for a conditional probability table with multiple parents (usually representing proficiencies) where all skills are necessary in order to solve the problem. For example, both reading and writing skills are necessary for a book report task. This is sometimes called a noisy-and distribution.


A set of rules for when a observing a set of variables S makes two other variables (or sets of variables) A and B independent Invalid BibTex Entry!. This provides the rules for reading conditional independence relationships from a directed graph. For A and B to be independent, there must be at least one variable in S along every path from A to B or B to A, as well as at least one variable of S along the path from any common ancestor to A and B. Additionally, no common descendant of A and B may appear in S.
An abbreviation for Directed Acyclic Graph, a term often used in place of acyclic directed graph. Technically incorrect (a directed acyclic graph would be a tree which is directed), but has a better abbreviation.
Demographic Variable
A variable, often appearing in a proficiency model, that is known and provides background information about an examinee. Examples include Race, Gender, Number of previous Algebra courses taken, Prefers large print test forms.
DiBello--Samejima Distribution
A conditional probability table in a Bayesian network that is constructed using a procedure first described by Lou DiBello that employs Samejima's graded response model to generate the conditional probabilities. Under this procedure, first each state of each parent variable is assigned a real number value called its effective theta. These are combined using a structure function that reflects the domain experts view of how the skills interact in a particular task (popular choices are conjunctive, disjunctive, compensatory, and inhibitor), to produce an effective theta value for each parent combination. The resulting value is used as the ability parameter in Samejima's graded response model to produce the conditional probability distribution for that row. Invalid BibTex Entry!Invalid BibTex Entry!
Differential Item (Task) Functioning (DIF)
One way in which an assessment needs to be fair, is that it should have the same measurement properties for different subgroups (often defined by demographic variables). In the language of Bayes nets, the outcome variables from any task should be conditionally independent from group membership given the proficiency variables. Any task in which the observables are not conditionally independent from group membership is said to exhibit DIF for that group. Traditionally, testing for DIF has been very important when the group membership variable indicates race or gender, however, DIF based on language group is also well studied, especially in the context of multilingual tests.
A parameter for a conditional probability distribution that controls what level of skill is necessary to achieve a high probability of getting an observed outcome in a higher state. In item response theory (IRT) models, the difficulty parameter is often subtracted from the proficiency variable and expressed on the same scale as the proficiency variables. In conditional probability distributions, the difficulty is often expressed as an intercept parameter with a negative sign. In general higher difficulty, means that fewer members of the population will get the item right.
Direct Evidence
If a proficiency variable is a parent of an observed outcome variable, then that variable provides "direct evidence" for the proficiency. If the proficiency variable is connected, but not a parent, then the observed outcome may still provide indirect evidence for the proficiency.
Directed Graph (Digraph)
A Graph? whose edges are considered to be ordered; therefore, in a directed graph (A,B) and (B,A) are considered to be distinct edges, where in an undirected or simple graph they would be considered the same. The edges of a directed graph are often depicted with an arrow going from the parent node to the child node. The terms parent and child can be extended using the obvious analogy: an node A is an ancestor of B if there is a directed path from A to B and B is then a descendent of A. Directed graphs are important in the construction of Bayesian networks as the variables of the model are represented by nodes in the graph and the probability distribution for any variable is given conditional on its parent in the graph.
Directed Hypergraph
A Graph? that instead of having edges consisting of pairs of nodes, has directed hyperedges that consist of a partitioned set of nodes, divided into parents and children. Directed hypergraphs are often drawn with nodes as circles and hyperedges as squares, with tentacles connecting the nodes and the hyperedges (drawn as an arrow two the hyperedge if the node is in the parent partition, and as a arrow towards the node if the node is in the child partition).

Directed hypergraphs are useful representing Bayesian networks when emphasizing the factorization structure, as the hyperedges correspond to the component factors of the joint probability distribution (each one represents a conditional probability distribution from its parents to its children). In this representation, the glyph used to indicate the hyperedge can be annotated with the type of distribution (e.g., conjunctive, compensatory).

Dirichlet Law
A generalization of the beta distribution that is the natural conjugate law for the parameter of a categorical or multinomial distribution. The random vector consists of K values between zero and one, \{\theta_1,\ldots,\theta_K\}, with the restriction that \sum_{k=1}^K \theta_k =1. The Dirichlet distribution then has the following density function:

f(\theta_1,\ldots,\theta_K | \alpha_1,\ldots,\alpha_K)  = C \prod_{k=1}^K \theta_k^{\alpha_k-1}, where C = \Gamma(\sum_{k=1}^K \alpha_k) / \prod_{k=1}^K \Gamma(\alpha_k), is a normalizing constant. The parameter \alpha_1,\ldots,\alpha_K is a collection of positive numbers which can be interpreted as a series of pseudo counts of observed cases.

A parameter which determines the difference in

probability for an observable for people for which a claim holds those for which the claim does not hold. In IRT models (and pseudo-IRT models like the DiBello--Samejima models) the discrimination parameter is a slope; i.e., in {$P(X) = \textrm{logit}^{-1} \left ( a(\theta-b) \right)$}, the parameter $a$ is the discrimination parameter.

Disjunctive Distribution
A design pattern for a conditional probability table with multiple parents (usually representing proficiencies) where any one of the skills are necessary in order to solve the problem. For example, a mathematics problem with two different solution strategies would be modeled with a disjunctive distribution. This is sometimes called a noisy-or distribution.


A pair of nodes in a Graph? that are considered to be joined in some way. Note that in a directed graph the edge is ordered so that (A,B) and (B,A) are distinct edges, but in an undirected or simple graph they are considered to be the same. In a hypergraph, hyperedges are generalized edges that may contain more one, two, or more nodes.
The process of asking questions (usually of an expert) to obtain the parameters or hyperparameters of a model. In constructing a Bayesian network, the elicitation usually takes place in several steps. First the analysts elicit the graphical structure of the model. Next, they elicit a design pattern or distribution type for each conditional probability table and prior laws for the parameters of those distributions. Finally, the experts must specify hyperparameters for all of the prior laws.
Equating in the process of creating a function that maps a pattern of observed outcomes to a score such that the score obtained from two different forms of an assessment are equivalent. The idea, coming from the world of high-stakes testing, is that there should be no inherent advantage in receiving Form A or Form B. For equating to be meaningful, it must be reasonable that the two forms are equivalent, i.e., they are built to the same specifications. When comparable scores are needed from non-equivalent forms, then the weaker term, linking is used instead.
Expected A Posteriori (EAP) Score
A score that is obtained by taking the expected value (mean) of the posterior distribution over score profiles. Consider a function h({\bf s} that maps a proficiency profile {\bf s} to a numeric value. For example, it might map to the integers 0, 1 or 2 based on whether or not a given proficiency variable is low, medium, or high. The EAP score is the expected value of h({\bf s}) with respect to the posterior distribution (after observing evidence).
Evaluation Rules
Evaluation Rules are a type of Evidence Rules that set the values of Observable Variables.
In educational assessment, Evidence is information or observations that allow inferences to be made about aspects of an examinee's proficiency (which are unobservable) from evaluations of observable behaviors in given performance situations.
Evidence Accumulation Process
In the Four-Process Architecture this is the process that is responsible for compiling evidence across multiple tasks to draw inferences about student proficiency. Usually, the evidence accumulation process maintains some kind of scoring record which records the current best information about the student proficiency. The evidence accumulation process performs two critical roles: (1) it accepts the observable outcomes from the Evidence Identification Process and uses them to update the scoring record, and (2) it calculates information about how much evidence any potential task might yield for the Activity Selection Process (if the assessment is adaptive).
Evidence-Centered Assessment Design (ECD)
Evidence-Centered Assessment Design (ECD) is a methodology for designing assessments that underscores the central role of evidentiary reasoning in assessment design. ECD is based on three premises: (1) An assessment must build around the important knowledge in the domain of interest, and an understanding of how that knowledge is acquired and put to use; (2) the chain of reasoning from what participants say and do in assessments to inferences about what they know, can do, or should do next, must be based on the principles of evidentiary reasoning; (3) Purpose must be the driving force behind design decisions, which reflect constraints, resources, and conditions of use.
Evidence Identification Process
This is the part of the Four-Process Architecture that is responsible for processing the raw work product from a task and setting the values of the observable outcome variables. This could be as simple as matching the observed response to the key in a multiple-choice item or as complex as identifying key features in the output from a simulator. It could also be a human process, such as a rater assigning a holistic or trait scores to an essay.
Evidence Model
The Evidence Model is a set of instructions for interpreting the output of a specific task. It is the bridge between the Task Model, which describes the task, and the Student Model, which describes the framework for expressing what is known about the examinee's state of knowledge. The Evidence Model generally has two parts: (1) A series of Evidence Rules which describe how to identify and characterize essential features of the Work Product; (2) A Statistical Model that tells how the scoring should be updated given the observed features of the response.
Evidence Rules
Evidence Rules are the rubrics, algorithms, assignment functions, or other methods for evaluating the response (Work Product). They specify how values are assigned to Observable Variables, and thereby identify those pieces of evidence that can be gleaned from a given response (Work Product).
Evidence Rule Data
Evidence Rule Data is data found within the Response Processing. It often takes the form of logical rules.
Examinee. See Participant
Examinee Record
The Examinee Record is a record of tasks to which the participant is exposed, as well as the participant's Work Products, Observables, and Scoring Record.
Expected Weight of Evidence
This is a measure of how much information a task provides for a particular hypothesis or claim. Consider, a hypothesis H which is any true of false claim about a student. Let \{e_{j},j=1,...,n\} be the possible observed outcomes from a task E and let W(H:e_{j}) be the weight of evidence e_{j} would provide for H. Then the expected weight of evidence that E would provide for H is EW(H:E) = \sum_{j=1}^{n} W(H:e_{j})\Pr(e_{j} \mid H). Invalid BibTex Entry!


Four Processes
Any assessment must have four different logical processes. The four processes that comprise the Assessment Cycle include the following: (1) The Activity Selection Process: the system responsible for selecting a task from the task library; (2) The Presentation Process: the process responsible for presenting the task to the examinee; (3) Response Processing: the first step in the scoring process, which identifies the essential features of the response that provide evidence about the examinee's current knowledge, skills, and abilities; (4) The Summary Score Process: the second stage in the scoring process, which updates beliefs about the examinee's knowledge, skills, and abilities based on the evidence provided by the preceding process. Instructions. Instructions are commands sent by the Activity Selection Process to the Presentation Process.


A mathematical graph (or network) is two coordinated sets <V,E>, where V is a set of vertices or nodes and E is a set of edges which consists of pairs of nodes. In a simple graph, the edges are considered unordered, and in a directed graph the edges are ordered pairs. In a hypergraph, the notion of edge is extended to allow any positive number of nodes. In a graphical model or a Bayesian network, the nodes in the graph correspond to variables in the problem space and the edges describe the factorization structure and conditional independence properties in the joint probability distribution.
Graphical Model
A representation of the joint probability distribution using a graph where (1) the variables in the model are represented by nodes in the graph, and (2) separation in the graph (d-separation if the graph is directed), implies that the variables are conditionally independent. The term is sometimes used generically to refer to both representations using both undirected and directed (i.e., Bayesian networks) graphs, and sometime specifically to refer only to representations on undirected graphs. In that case, the joint probability distribution can be represented as the product of a collection of potentials over the cliques of the graph.


Hyper-Dirichlet Law
This is the natural conjugate distribution for the parameters of a conditional multinomial distribution. It is essentially an independent Dirichlet distribution for each row of the conditional probability table. The usage in this book is slightly different from the definition in Spiegelhalter and Lauritzen (1990)Invalid BibTex Entry! where it refers to a Bayesian network with hyper-Dirichlet distributions for every conditional probability table.
A generalized edge used in a hypergraph. Unlike ordinary Graphs?, where an edge must have exactly two nodes, a hyperedge can contain one, two, or more nodes. Undirected hyperedges are often drawn as a closed curve containing all of the nodes. In a directed hyperedge, the nodes in the edge are partitioned into a set of parents and children. Directed hyperedges are often drawn as a symbol with tentacles (arrows) connecting the symbol to the nodes (the direction of the arrow indicates whether the node is a parent or a child. When a hypergraph is used to represent the factorization structure of a joint probability distribution, the hyperedge is represents one factor. The symbol used to represent a directed hyperedge can be based on way the corresponding conditional probability distribution is parameterized.
A generalization of a Graph? in which the notion of edge is extended to allow one, two, or more nodes. The resulting edges are called hyperedges. Like ordinary graphs, hypergraphs come in directed and undirected versions. Both are useful for representing the factorization structure of a joint probability distribution over many variables. In the hypergraph the edges of the graph correspond to the factors in the model.
The parameters of a law providing the distribution for other parameters. In Bayesian inference, the parameters of interest are assigned a prior law, and the hyperparameters of that law must be elicited from an expert. If the hyperparameters are themselves assigned a prior law, the parameters of that distribution are also called hyperparameters (an so forth up the hierarchy).


Item Response Theory (IRT)
Two events are said to be independent if knowledge about Event A provides no information about Event B. In terms of probability, this implies: \Pr(A|B) =\Pr(A|\neg B) = \Pr(A). In this situation, the joint probability of Event A and Event B is the product of the individual probabilities: \Pr(A,B) = \Pr(A)\Pr(B).
Indirect Evidence
Evidence that is not about a targeted proficiency variable, but rather evidence about a proficiency variable that is highly correlated with the targeted proficiency in the target population. For example, the ability to produce written text fluently is highly correlated with critical thinking skills in writing. Therefore, text length in a timed essay provides indirect evidence about critical thinking skills.
Influence Diagram
An extension of a Bayesian network that allows the following additional features: (a) decision variables whose values can be set by the decision maker and (b) utilities which provide the values of potential outcomes and the costs of potential decisions. The solution to an influence diagram is a decision rule or policy for setting the decision variables (given the observed values of other variables which are available at the time of the decision) to maximize expected utility. Invalid BibTex Entry!,

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Inhibitor Distribution
A design pattern for conditional probability tables with two parent variables in which one parent is thought of as a valve or gate keeper for the others. Unless the value of the inhibiting value has reached a certain level, then conditional probability tables are the same as if the participant was at the lowest level of the other skill. After reaching the threshold value, more of the inhibiting skill does not contributed to the outcome. For example, when solving mathematical word problems, proficiency in the language of the assessment is an inhibitor skill: a certain minimal level is necessary to understand the problem, but beyond that more does not help.


Junction Tree
A re-expression of a Bayesian network into a tree shape such that each node in the tree represents a group of variables

that either form a clique in the original network (possible after additional edges have been filled-in to make the graph triangulated) or an intersection of one or more cliques. The junction tree is a Markov Tree and many probability calculations in a Bayesian network can be expressed as message passing algorithms in a junction tree. The computational complexity of those calculations is usually driven by the size of the largest node in the junction tree which is known as its treewidth. The process of building a junction tree from a Bayesian network is often called compiling the network.



Another word for distribution. Stephan Lauritzen suggests that do avoid ambiguity when describing Bayesian networks that the term distribution be used for the conditional probability tables in the network, and the term law be used for the prior/posterior distributions for the parameters of those distributions, as well as for any higher-level distribution for the hyperparameters.
This word can be used in two different ways. Student learning refers to how the knowledge, skills and abilities of an individual change over time, in particular in response to instruction. Parameter learning refers to the act of Bayesian inference, that is using data about a system to replace prior laws for model parameters with posterior laws.
The conditional probability of observable evidence given a hypothesized state and set of parameters. This is often written \Pr(X|\theta) where X represents the observable evidence, and \theta is a parameter or unknown variable. A popular alternative to Bayesian inference involve choosing a parameter value to maximize the likelihood function, however, this involves the implicit assumption that all parameter values are equally likely a priori.
Link (Model)
A task-specific version of an evidence model. Consider a collection of tasks all made from the same task model, and an evidence model that is used to evaluate evidence from work products from this task model. The individual tasks may vary slightly in their difficulty or other properties. The links are task-specific version of the evidence model that share the same graphical structure and distribution families, but differ in the parameter values.
Local Independence
This is a desirable property of educational assessments that observable variables from distinct tasks should be conditionally independent given the proficiency variables. Note that the Bayesian network formulation uses a more relaxed version of this assumption than other measurement model frameworks, as activities that produce observables that locally dependent observables can be placed within the same task and hence, the dependence among the observables can be modeled within the evidence model. Invalid BibTex Entry!.


Maximum A Posterior (MAP) Score
Maximum Likelihood
Marginal Distribution
Markov Chain Monte Carlo (MCMC)
Markov Tree
A transformed version of a Bayesian network that has nodes corresponding to sets of variables in the original model, and whose nodes are connected to have the running intersection property: the set of nodes containing any given variable forms a connected subtree. Many probability calculations within the Bayesian network can be expressed as passing messages in this tree. The two most common examples of a Markov tree are the junction tree and the tree of cliques.
Measurement Model
The Measurement Model is that part of the Evidence Model that explains how the scoring should be updated given the observed features of the response. Model. A Model is a design object in the CAF that provides requirements for one or more of the Four Processes, particularly for the data structures used by those processes (e.g., Tasks and Scoring Records). A Model describes variables, which appear in data structures used by the Four Processes, whose values are set in the course of authoring the tasks or running the assessment.
Multinomial Distribution


Another name for a Graph?.
Normalization Constant


Observables/Observable Outcome Variables
Observables are variables that are produced through the application of Evidence Rules to the task Work Product. Observables describe characteristics to be evaluated in the Work Product and/or may represent aggregations of other observables.
An Observation is a specific value for an observable variable for a particular participant.
Outcome Pattern/Vector
Outcome Space


A Participant is the person whose skills are being assessed. A Participant directly engages with the assessment for any of a variety of purposes (e.g., certification, tutoring, selection, drill and practice, etc.).
Platform refers to method that will be used to deliver the presentation materials to the examinees. Platform is defined broadly to include human, computer, paper and pencil, etc.
Posterior Distribution
Posterior Predictive Distribution
Presentation Material
Presentation Material is material that is presented to a participant as part of a task (including stimulus, rubric, prompt, possible options for multiple choice).
Presentation Process
The Presentation Process is the part of the Assessment Cycle that displays the task to the examinee and captures the results (or Work Products) when the examinee performs the task.
Pretest Data
Prior Distribution
Proficiency (Variable)
Proficiency Model
Profile Score




Rasch Model
Reporting Rule
Reporting Rules describe how Student Model Variables should be combined or sampled to produce scores, and how those scores should be interpreted.
Response. See Work Product
Response Processing
Response Processing is the part of the Assessment Cycle that identifies the essential features of the examinee's response and records these as a series of Observations. At one time referred to as the "Evidence Identification Process," it emphasizes the key observations in the Work Product that provide evidence.
Response Processing Data
See Evidence Rule Data.


Scoring Model
Sensitivity Analysis
Simple Graph
Strategy refers to the overall method that will be used to select tasks in the Assembly Model.
Student Model
The Student Model is a collection of variables representing knowledge, skills, and abilities of an examinee about which inferences will be made. A Student Model is comprised of the following types of information: (1) Student Model Variables that correspond to aspects of proficiency the assessment is meant to measure; (2) Model Type that describes the mathematical form of the Student Model (e.g., univariate IRT, multivariate IRT, or discrete Bayesian Network); (3) Reporting Rules that explain how the Student Model Variables should be combined or sampled to produce scores.
Summary Scoring Process
The Summary Scoring Process is the part of the Assessment Cycle that updates the scoring based on the input it receives from Response Processing. At one time referred to as the "Evidence Accumulation Process," the Summary Scoring Process plays an important role in accumulating evidence.


A Task is a unit of work requested from an examinee during the course of an assessment. In ECD, a task is a specific instance of a Task Model.
Task/Evidence Composite Library
The Task/Evidence Composite Library is a database of task objects along with all the information necessary to select and score them. For each such Task/Evidence Composite, the library stores (1) descriptive properties that are used to ensure content coverage and prevent overlap among tasks; (2) specific values of, or references to, Presentation Material and other environmental parameters that are used for delivering the task; (3) specific data that are used to extract the salient characteristics of Work Products; and (4) Weights of Evidence that are used to update the scoring from performances on this task, specifically, scoring weights, conditional probabilities, or parameters in a psychometric model.
Task Model
A Task Model is a generic description of a family of tasks that contains (1) a list of variables that are used to describe key features of the tasks, (2) a collection of Presentation Material Specifications that describe material that will be presented to the examinee as part of a stimulus, prompt, or instructional program, and (3) a collection of Work Product Specifications that describe the material that the task will be return to the scoring process.
Task Model Variables
Task Model Variables describe features of the task that are important for designing, calibrating, selecting, executing, and scoring it. These variables describe features of the task that are important descriptors of the task itself, such as substance, interactivity, size, and complexity, or are descriptors of the task performance environment, such as tools, help, and scaffolding.




Value of Information


Weak prior
Weight of Evidence
Work Product
A Work Product is the Examinee's response a task from a given task model. This could be expressed as a transcript of examinee actions, an artifact created by the examinee and/or other appropriate information. The Work Product provides an important bridge between the Task Model and the Evidence Model. In particular, work products are the input to the Evidence Rules.





  • You can create a Wiki page for any term in this list by wrapping its name in [[ ]] . End lines with \ to get the line wrapping to look right.
  • The hidden agenda of this page is to solicit help in writing the glossary for our book Bayesian Networks in Educational Assessment, but it makes a great starting point for the ECD Wiki.


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Page last modified on April 01, 2009, at 03:25 PM