elizabeth silver’s scientific contributions

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Publications (1)

Figure 3: Structural Models to test independence relations In Figure 3 (a), β = 0 if and only if L 1 _||_ L 3 | L 2. 3 In Figure 3 (b), β = 0 if and only if L 2 _||_ L 4 | L 1 , L 3. If we attach measurement models to these structural models, and estimate the resulting full structural equation models, then the Fisher Information matrix of the coefficient estimates provides asymptotically correct standard errors (Bollen, 89). We can thus use an asymptotically correct statistical inference on β as a surrogate for an asymptotically correct test of L 1 _||_ L 3 | L 2 in Figure 3 (a), and as an asymptotically correct test of L 2 _||_ L 4 | L 1 , L 3. in Figure 3 (b), with no sample size correction needed.
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Figure 7: True positive adjacency rates (i.e. # correct adjacencies in output / # adjacencies in true graph), ± two standard errors. Grouped by the three structural models (see Figure 5), sample size of 150 vs. 1000, pure vs. impure measurement models, and continuous v. binary data. 
Figure 8: False positive adjacency rates (i.e. # incorrect adjacencies in output / # gaps in true graph), ± two standard errors. Grouped by the three structural models (see Figure 5), sample size of 150 vs. 1000, pure vs. impure measurement models, and continuous v. binary data. 
Figure 12: True discovery orientation rate or precision (i.e. # correctly oriented edges in output / # oriented edges in output). Model 1 is omitted because there are no orientable edges in the equivalence class, so an oriented edge in the output is guaranteed to be incorrect, making the false positive rate a better measure of performance. 

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Discovering Prerequisite Relationships among Knowledge Components
  • Conference Paper
  • Full-text available

January 2014

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606 Reads

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36 Citations

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richard scheines

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elizabeth silver

Knowing the prerequisite structure among the knowledge components in a domain is crucial for designing instruction and for assessing mastery. Treating KCs as latent variables, we investigate how data on the items that test these skills can be used to discover the prerequisite structure among such skills. Our method assumes that we know or have discovered the Q-matrix (the measurement model) that connects latents representing the skill to items measuring the skills. By modeling the pre-requisite relations as a causal graph, we can then search for the causal structure among the latents via an extension of an algorithm introduced by Spirtes, Glymour, and Scheines in 2000. We validate the algorithm using simulated data, and discuss a potential application to a High School geometry assessment dataset.

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Citations (1)

... Hence, S 1 can be respected as one of the causes of S 2 . Regardless of the interpretation, prerequisite and causal relationships share similar conditional independence in the data (Scheines, Silver, and Goldin 2014). Therefore, we can adapt techniques used for causal structure learning to discover prerequisite relationships Unfortunately, toward this goal, there are still some challenges. ...

Reference:

Causal-Driven Skill Prerequisite Structure Discovery
Discovering Prerequisite Relationships among Knowledge Components

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richard scheines

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elizabeth silver