Table of Contents

1. About DataShop
2. Getting Data In
   1. Data Logging
   2. Data Import
3. Accessing DataShop
4. Glossary
5. Reports
   1. Dataset Info
      1. Overview
      2. Papers and Files
      3. KC Models
      4. Problem Breakdown
   2. Learning Curve
      1. Examples
      2. Algorithm
      3. Student-Step Rollup
      4. LFA Values
   3. Error Report
   4. Performance Profiler
6. Filtering Data
   1. By student, KC, and problem
   2. Sample Selector
7. Export: Getting Data Out
   1. Export Format History
8. Using Other Tools
   1. R (software)
   2. Excel PivotTables
9. Advanced
   1. Web Services Credentials
      1. User Agreement
   2. Logging Activity
   3. Metrics
10. Examples
11. Contact Us

LFA Values

The LFA Values report provides details on the results of the LFA (Learning Factors Analysis) algorithm¹, a logistic regression performed over the “error rate” Learning Curve data. (The LFA logistic regression, a standard regression bounded between 0 and 1, attempts to find the best-fit curve for error-rate data, which also ranges between 0 and 1.)

LFA is run for all datasets in DataShop, once for each knowledge component model of a dataset.

LFA values present a detailed analysis of how well, given the selected knowledge component model, the LFA statistical model fits the data. With AIC and BIC values, you can quantitatively assess how well the LFA's predictions of student correctness match the observed data.

Based on the knowledge component model and the observed data, the following LFA values are calculated:

KC Model Values

• AIC: The Akaike information criterion (AIC) is a measure of the goodness of fit of a statistical model, in this case, the LFA model. It is an operational way of trading off the complexity of the estimated model against how well the model fits the data². In this way, it penalizes the model based on its complexity (the number of parameters). A lower AIC value is better.
• BIC: The Bayesian information criterion (BIC) is also a measure of goodness of fit of the LFA model. The BIC penalizes free parameters more strongly than does the Akaike information criterion (AIC)³. A lower BIC value is better.
• Log Likelihood: a basic fit parameter used in calculating both AIC and BIC; also referred to as the log likelihood ratio. Unlike AIC and BIC, log likelihood assumes the model includes the right number of parameters; AIC and BIC take into account that the parameters of the model could be wrong both in number and value.
• Total number of parameters: The total number of parameters being fit by the LFA statistical model. This number varies with the number of knowledge components in the knowledge component model, as well as the number of students for which there is data in the dataset.

KC Values

• Intercept (logit): a parameter representing knowledge component difficulty. The higher the KC intercept, the more difficult the knowledge component.
• Intercept (probability): derived from the intercept (logit). A parameter representing knowledge component difficulty. The higher the KC intercept, the more difficult the knowledge component.
• Slope: a parameter representing of how quickly students will learn the knowledge component. The larger the KC slope, the faster the student should learn the knowledge component.

Student Values

• Intercept: a parameter representing a student's initial knowledge. The lower the student intercept, the more the student initially knew.

To view LFA values for a different knowledge component model:

1. Select a different knowledge component model from the drop-down menu under Knowledge Component Models. The LFA Values report will update to show values for that model.

Tip: If you would like to define a new knowledge component model, see KC Models.

To export LFA values:

• Click the button labeled Export LFA Values. You will be prompted to save the exported text file.

¹Is Over Practice Necessary? Improving Learning Efficiency with the Cognitive Tutor through Educational Data Mining (Cen, Koedinger, and Junker 2007).

² Akaike information criterion. (2007, February 25). In Wikipedia, The Free Encyclopedia. Retrieved 16:22, March 7, 2007, from http://en.wikipedia.org/w/index.php?title=Akaike_information_criterion&oldid=110898239

³ Bayesian information criterion. (2007, February 19). In Wikipedia, The Free Encyclopedia. Retrieved 16:29, March 7, 2007, from http://en.wikipedia.org/w/index.php?title=Bayesian_information_criterion&oldid=109323430