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NAEP Assessment Weighting Procedures → Weighting Procedures for the 2009 Assessment → Computation of Full-Sample Weights for the 2009 Assessment → Student Weight Raking Adjustment for the 2009 Assessment → Raking Adjustment Factor Calculation

NAEP Technical DocumentationRaking Adjustment Factor Calculation

For assessed and excluded students in a given subject, the raking adjustment factor STU_RAKEk was computed as follows:

First, the weight for student k was intialized as follows:

STUSAWT superscript open bracket a d j open paren zero close paren close bracket subscript k equals STU underscore BWT subscript k times SCH underscore TRIM subscript k times SCH underscore NRAF subscript k times STU underscore NRAF subscript k times SUBJFAC subscript k

 where

Then, the sequence of weights for the first iteration was calculated as follows for student k in category c of dimension d:


For dimension 1:

STUSAWT superscript open bracket a d j open paren one close paren close bracket subscript k equals TOTAL subscript open bracket c open paren one close paren close bracket divided by open bracket summation with underscript open paren union of cap R subscript open bracket c open paren one close paren close bracket and cap E subscript open bracket c open paren one close paren close bracket close paren STUSAWT superscript open subbracket a d j open paren zero close paren close subbracket subscript k close bracket times STUSAWT superscript open bracket a d j open paren zero close paren close bracket subscript k

 
For dimension 2: 

STUSAWT superscript open bracket a d j open paren two close paren close bracket subscript k equals TOTAL subscript open bracket c open paren two close paren close bracket divided by open bracket summation with underscript open paren union of cap R subscript open bracket c open paren two close paren close bracket and cap E subscript open bracket c open paren two close paren close bracket close paren STUSAWT superscript open subbracket a d j open paren one close paren close subbracket subscript k close bracket times STUSAWT superscript open bracket a d j open paren one close paren close bracket subscript k


For dimension 3: 

STUSAWT superscript open bracket a d j open paren three close paren close bracket subscript k equals TOTAL subscript open bracket c open paren three close paren close bracket divided by open bracket summation with underscript open paren union of cap R subscript open bracket c open paren three close paren close bracket and cap E subscript open bracket c open paren three close paren close bracket close paren STUSAWT superscript open subbracket a d j open paren two close paren close subbracket subscript k close bracket times STUSAWT superscript open bracket a d j open paren two close paren close bracket subscript k


For dimension 4: 

STUSAWT superscript open bracket a d j open paren four close paren close bracket subscript k equals TOTAL subscript open bracket c open paren four close paren close bracket divided by open bracket summation with underscript open paren union of cap R subscript open bracket c open paren four close paren close bracket and cap E subscript open bracket c open paren four close paren close bracket close paren STUSAWT superscript open subbracket a d j open paren three close paren close subbracket subscript k close bracket times STUSAWT superscript open bracket a d j open paren three close paren close bracket subscript k

 
where

  • Rc(d) is the set of all assessed students in category c of dimension d,
  • Ec(d) is the set of all excluded students in category c of dimension d, and
  • Totalc(d) is the control total for category c of dimension d.

The process is said to converge if the maximum difference between the sum of adjusted weights and the control totals is 1.0 for each category in each dimension. If after the sequence of adjustments the maximum difference is greater than 1.0, the process continues to the next iteration cycling back to the first dimension with the initial weight for student k equalling STUSAWTkadj(4) from the previous iteration. The process continued until convergence was reached.

Once the process converged, the adjustment factor was computed as follows:

STU underscore RAKE subscript k equals STUSAWT subscript k divided by STU underscore BWT subscript k times SCH underscore NRAF subscript k times STU underscore NRAF subscript k times SCH underscore TRIM subscript k times STU underscore TRIM subscript k times SUBJFAC subscript k

where STUSAWTk  is the weight for student k after convergence.

The process was done independently for the full sample and for each replicate.

Last updated 24 September 2014 (JS)
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