Method for estimating examinee attribute parameters in a cognitive diagnosis model

Abstract

A method and system for determining attribute score levels from an assessment are disclosed. An assessment includes items each testing for at least one attribute. A first distribution is generated having a response propensity represented by a highest level of execution for each attribute tested by the item. An item threshold is determined for at least one score for the first distribution. Each item threshold corresponds to a level of execution corresponding to the score for which the item threshold is determined. For each attribute tested by the item, a second distribution is generated having a response propensity represented by a lowest level of execution for the attribute and the highest level of execution for all other attributes tested by the item. A mean parameter is determined for the second distribution. An attribute score level is determined for the scores based on the item thresholds and the mean parameters.

1 . A method for determining attribute score levels from an assessment, the method comprising:
 for at least one item on the assessment, wherein the item tests for at least one attribute:   generating a first distribution having a response propensity represented by a highest level of execution for each attribute tested by the item;   for at least one score, determining an item threshold for the first distribution corresponding to a level of execution corresponding to the score;   for at least one attribute tested by the item:   generating a second distribution having a response propensity represented by a lowest level of execution for the attribute and the highest level of execution for all other attributes tested by the item, and   determining a mean parameter for the second distribution; and   determining an attribute score level for at least one score based on the at least one item threshold and the at least one mean parameter.   
   
   
       2 . The method of  claim 1  wherein the first distribution comprises a standard normal distribution. 
   
   
       3 . The method of  claim 1  wherein the item threshold for a first distribution corresponding to a first score is selected from a uniform distribution defined by Unif(−5, 5). 
   
   
       4 . (canceled) 
   
   
       5 . The method of  claim 1  wherein the first distribution comprises a first distribution mean parameter, and wherein the first distribution mean parameter is greater than the mean parameter for each second distribution. 
   
   
       6 . The method of  claim 1  wherein the item threshold corresponding to a first score is greater than an item threshold corresponding to a second score if the first score is greater than the second score. 
   
   
       7 . The method of  claim 1  wherein a second distribution comprises a standard normal distribution. 
   
   
       8 . The method of  claim 1  wherein the mean parameter for a second distribution is less than 0. 
   
   
       9 . The method of  claim 1  wherein the mean parameter for a second distribution is selected from a uniform distribution defined by Unif(−10, 0). 
   
   
       10 . (canceled) 
   
   
       11 . (canceled) 
   
   
       12 . (canceled) 
   
   
       13 . A method for determining one or more examinee attribute mastery levels from an assessment, the method comprising:
 receiving a covariate vector for an examinee, wherein the covariate vector includes a value for each of one or more covariates for the examinee; and   for each of one or more attributes:   computing an examinee attribute value based on at least the covariate vector and one or more responses made by the examinee to one or more questions pertaining to the attribute on an assessment, and   assigning an examinee attribute mastery level for the examinee with respect to the attribute based on whether the examinee attribute value surpasses one or more thresholds.   
   
   
       14 . (canceled) 
   
   
       15 . (canceled) 
   
   
       16 . A system for determining attribute score levels from an assessment, the system comprising:
 a processor; and   a processor-readable storage medium in communication with the processor,   wherein the processor-readable storage medium contains one or more programming instructions for performing a method of determining attribute score levels from an assessment, the method comprising:   for at least one item on the assessment, wherein the item tests for at least one attribute:   generating a first distribution having a response propensity represented by a highest level of execution for each attribute tested by the item,   for at least one score, determining an item threshold for the first distribution corresponding to a level of execution corresponding to the score,   for at least one attribute tested by the item:   generating a second distribution having a response propensity represented by a lowest level of execution for the attribute and the highest level of execution for all other attributes tested by the item, and   determining a mean parameter for the second distribution, and   determining an attribute score level for at least one score based on the at least one item threshold and the at least one mean parameter.   
   
   
       17 . The system of  claim 16  wherein the first distribution comprises a standard normal distribution. 
   
   
       18 . The system of  claim 16  wherein the first distribution comprises a first distribution mean parameter, and wherein the first distribution mean parameter is greater than the mean parameter for each second distribution. 
   
   
       19 . The system of  claim 16  wherein the item threshold corresponding to a first score is greater than an item threshold corresponding to a second score if the first score is greater than the second score. 
   
   
       20 . The system of  claim 16  wherein a second distribution comprises a standard normal distribution. 
   
   
       21 . The system of  claim 16  wherein the mean parameter for a second distribution is less than 0. 
   
   
       22 . (canceled)