Bayesian Regression Techniques for Determining True Measurements

• US 20140038155A1
• Filed: 06/20/2013
• Published: 02/06/2014
• Est. Priority Date: 08/25/2006
• Status: Active Grant

• Current Assignee: Ronald Weitzman
• Original Assignee: Ronald Weitzman
• Inventors: Weitzman, Ronald
• Granted Patent: US 10,198,961 B2
• Time in Patent Office: Days
• US Class Current: 434/350
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G09B 19/00 Teaching not covered by other main groups of this subclass teaching or practice apparatus for gun-aiming or gun-laying F41G3/26

Abstract

Techniques for estimating a true measurement from a Bayesian regression on an observed measurement of received responses.

Claims

1. A method comprising:

receiving responses to a multi-item test by a sample of respondents representing a population; and

estimating a true measurement from a Bayesian regression on an observed measurement from the received responses.

2. The method according to claim 1, wherein estimating the true measurement from the Bayesian regression on the observed measurement comprises:

estimating a probability of a correct response to a given item by a particular person from the Bayesian regression on a response of the particular person to the given item of a multi-item test taken by a plurality of test-takers.

3. The method according to claim 2, further comprising:

determining a logit of the Bayeseian estimated probability of the correct response; and

estimating a difficulty of an item as a function of average of the logit over the plurality of test-takers.

4. The method according to claim 3, further comprising estimating the particular person'"'"'s ability as a function of the average logit and an average of the difficulty over the number of test items.

5. The method according to claim 1, wherein a value of the response is 1 if the response is correct and 0 if the response is incorrect.

6. A method comprising:

receiving a correct or incorrect response for each item and each test-taker, and a total score for each test-taker to a multi-item test taken by a plurality of test-takers; and

estimating a probability of a correct response to a given item by a particular person from a Bayesian regression on a response of the particular person to the given item using a correlation between the response to each item and the total test score over the plurality of test takers.

7. The method according to claim 6, further comprising:

determining a logit of the Bayeseian estimated probability of the correct response; and

estimating a difficulty of an item as a function of average of the logit over the plurality of test-takers.

8. The method according to claim 7, further comprising estimating the particular person'"'"'s ability as a function of the average logit and an average of the difficulty over the number of test items.

9. The method according to claim 7, wherein estimating the given test-taker'"'"'s ability comprises a sum of the average difficulty of the item and the average logit over the plurality of items.

10. The method according to claim 7, further comprising iteratively performing the processes of:

estimating the probability of the correct response;

determining the logit;

estimating the difficulty; and

estimating the test-taker'"'"'s ability.

12. The method according to claim 10, wherein the process is iteratively performed until the change in the given test-taker'"'"'s ability is less than a predetermined amount.

13. The method according to claim 9, further comprising:

estimating a new difficulty for each item using a Rasch model; and

substituting the average of the new Rasch difficulties for the average difficulty to obtain a new ability estimate for each test-taker.

14. A non-transitory media which performs a process comprising:

receiving an observed measurement of responses to a multi-item test by a test taker, and

estimating a true measurement from a Bayesian regression on the observed measurement of the received responses.