Sparse Factor Analysis for Learning Analytics and Content Analytics

A non-transitory memory medium storing program instructions, wherein the program instructions, when executed by a computer, cause the computer to implement:

• receiving input data that includes graded response data, wherein the graded response data includes a set of grades that have been assigned to answers provided by learners in response to a set of questions, wherein the grades are drawn from a universe of possible grades;
• computing output data based on the input data using a first latent factor model, wherein the output data includes at least:
• an association matrix that defines a set of K concepts implicit in the set of questions, wherein K is smaller than the number of questions in the set of questions, wherein, for each of the K concepts, the association matrix defines the concept by specifying strengths of association between the concept and the questions;
• and
• a learner knowledge matrix including, for each learner and each of the K concepts, an extent of the learner's knowledge of the concept;
• displaying a visual representation of at least a subset of the association strengths in the association matrix and/or at least a subset of the extents in the learner knowledge matrix.

A system comprising:

• a processor;
• and
• memory storing program instructions, wherein the program instructions, when executed by the processor, cause the processor to implement:
• receiving input data that includes graded response data, wherein the graded response data includes a set of grades that have been assigned to answers provided by learners in response to a set of questions, wherein the grades are drawn from a universe of possible grades;
• computing output data based on the input data using a first latent factor model, wherein the output data includes at least:
• an association matrix that defines a set of K concepts implicit in the set of questions, wherein K is smaller than the number of questions in the set of questions, wherein, for each of the K concepts, the association matrix defines the concept by specifying strengths of association between the concept and the questions;
• and
• a learner knowledge matrix including, for each learner and each of the K concepts, an extent of the learner's knowledge of the concept;
• displaying a visual representation of at least a subset of the association strengths in the association matrix and/or at least a subset of the extents in the learner knowledge matrix.