## Investigating Generative Factors of Score Matrices

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### BibTeX

@MISC{A_investigatinggenerative,

author = {Titus Winters A and Christian R. Shelton A and Tom Payne A},

title = {Investigating Generative Factors of Score Matrices},

year = {}

}

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### Abstract

Abstract. An implicit assumption in psychometrics and educational statistics is that the generative model for student scores on test questions is governed by the

### Citations

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Citation Context ...gorithms, how they are used to produce the certainty groups underlying the precision-recall curves, and describe those that readers may be unfamiliar with. 4.2.1. Clustering We are evaluating k-means =-=[7]-=-, spectral clustering [8] single-linkage [9], completelinkage [10], and average-linkage [11] algorithms. All of these can give an ordering on which questions are most certainly grouped by sorting the ... |

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Citation Context ...tion algorithms can also be used to find the underlying structure of the data. For dimensionality reduction, we evaluated Singular Value Decomposition (SVD) [12], Independent Component Analysis (ICA) =-=[13]-=-, and a non-negative matrix factorization (NNMF) [14]. We also evaluate slight alterations of SVD and ICA. In the base versions of these algorithms group membership is determined by the maximum absolu... |

801 | Algorithms for non-negative matrix factorization
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Citation Context ...ng structure of the data. For dimensionality reduction, we evaluated Singular Value Decomposition (SVD) [12], Independent Component Analysis (ICA) [13], and a non-negative matrix factorization (NNMF) =-=[14]-=-. We also evaluate slight alterations of SVD and ICA. In the base versions of these algorithms group membership is determined by the maximum absolute value in the output vector corresponding to each q... |

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Citation Context ... curves, and describe those that readers may be unfamiliar with. 4.2.1. Clustering We are evaluating k-means [7], spectral clustering [8] single-linkage [9], completelinkage [10], and average-linkage =-=[11]-=- algorithms. All of these can give an ordering on which questions are most certainly grouped by sorting the questions by the distance to their cluster center. Another set of algorithms that we are inv... |

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Citation Context ...measurement. One of the most important developments in psychometrics was the development of common factor analysis (CFA), which became the primary area of research in psychometrics for half a century =-=[2]-=-. The dominant theory at the time was that intelligence was univariate (g-theory). However, some data simply did not match the proposed model. Utilizing then-new techniques for calculating correlation... |

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Citation Context ...ertainty groups underlying the precision-recall curves, and describe those that readers may be unfamiliar with. 4.2.1. Clustering We are evaluating k-means [7], spectral clustering [8] single-linkage =-=[9]-=-, completelinkage [10], and average-linkage [11] algorithms. All of these can give an ordering on which questions are most certainly grouped by sorting the questions by the distance to their cluster c... |

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Citation Context ...lying the precision-recall curves, and describe those that readers may be unfamiliar with. 4.2.1. Clustering We are evaluating k-means [7], spectral clustering [8] single-linkage [9], completelinkage =-=[10]-=-, and average-linkage [11] algorithms. All of these can give an ordering on which questions are most certainly grouped by sorting the questions by the distance to their cluster center. Another set of ... |

38 |
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Citation Context ...actors in CFA are assumed to be the topics of the various questions. Other branches of psychometrics such as Item-Response Theory (IRT) have similar assumptions about the dominant importance of topic =-=[3]-=-. This paper is an attempt to verify the CFA assumption that the underlying factors in the generative model for a score matrix are the topics of the questions being tested. 3. Datasets Each of the dat... |

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Citation Context ... are also investigating two methods from educational statistics in this study: Common Factor Analysis [2], which we are using as the major point of comparison for educational statistics, and Q-Matrix =-=[15]-=-. Both of these have been specifically suggested by researchers in education for this problem. Q-Matrix is another method of capturing the underlying factors and abilities that give rise to a matrix o... |

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Citation Context ...ed to produce the certainty groups underlying the precision-recall curves, and describe those that readers may be unfamiliar with. 4.2.1. Clustering We are evaluating k-means [7], spectral clustering =-=[8]-=- single-linkage [9], completelinkage [10], and average-linkage [11] algorithms. All of these can give an ordering on which questions are most certainly grouped by sorting the questions by the distance... |

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Citation Context ...5 FR PC 153 O. S. 66 34 MC,FR Binary,PC 164 Networks 23 72 MC,FR Binary,PC Academic Online 267 40 FR Binary Trivia Online 467 40 FR Binary latent quantities of knowledge and ability in the human mind =-=[1]-=-. These are difficult values to quantify, as there is no direct way to measure them and no implicit units or dimensionality to such a measurement. One of the most important developments in psychometri... |

6 |
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Citation Context ...mensionality Reduction Dimensionality reduction algorithms can also be used to find the underlying structure of the data. For dimensionality reduction, we evaluated Singular Value Decomposition (SVD) =-=[12]-=-, Independent Component Analysis (ICA) [13], and a non-negative matrix factorization (NNMF) [14]. We also evaluate slight alterations of SVD and ICA. In the base versions of these algorithms group mem... |

3 |
Educational Data Mining: Collection and Analysis of Score Matrices for Outcomes-Based Assessment
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Citation Context ... we performed several experiments on this data, due to space constraints we only present results for unsupervised clustering. Interested readers are invited to seek additional details on this work in =-=[6]-=-. This unsupervised clustering experiment is in some4 T. Winters et al. / Factors of Score Matrices thing we have labelled topic clustering: given S and the human-generated groups, is there an unsupe... |

1 |
subject tests. http://www.collegeboard.com/student/testing/sat/about/SATII.html
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Citation Context ...opic. To this end we built two additional datasets, one derived from trivia questions from the popular game Trivial Pursuit [4], and one derived from questions from study guides for SAT Subject Tests =-=[5]-=-. Both quizzes are forty questions drawn from four topics, with ten questions in each topic. The trivia quiz draws questions from Sports and Leisure, Science and Nature, Arts and Entertainment, and Li... |