Weighting the data

There are 3 methods of weighting:

1) Models= model weight: Model = ?,?,..., R, model weight

2) Labels= element weight: element number = element label, anchor value, group number, element weight

3) Data= observation weight: R..,

 

These multiply to give a combined weight to each observation.

 

Weighting sub-tests: Example: Two Cases: A and B. Four aspects: Taste, Touch, Sound, Sight.

Case A Taste weight twice as important as the rest.

Case B Sound weight twice as important as the rest.

 

Labels =

1, Examinees

1-1000

*

2, Case

1=A

2=B

*

3, Aspect

1=Taste

2=Touch

3=Sound

4=Sight

*

Models=

?, 1, 1, MyScale, 2 ; Case A Taste weighted 2

?, 2, 3, MyScale, 2 ; Case B Sound weighted 2

?, ?, ?, MyScale, 1 ; everything else weighted 1

*

Rating scale = MyScale, R9, General ; this rating scale is the same for all models

 

If you want to keep the "reliabilities" and standard errors meaningful then adjust the weights:

 

Original total weights = 2 cases x 4 aspects = 8

New total weights = 2 + 2 + 6 = 10

Weight adjustment to maintain total weight is 8/10.

 

So adjusted weighting is:

Models=

?, 1, 1, MyScale, 1.6 ; Case A Taste

?, 2, 3, MyScale, 1.6 ; Case B Sound

?, ?, ?, MyScale, 0.8 ; everything else

*

 

Replication of a data point: can be specified by R and the number of replications, for instance:

R3,2,23,6,4 means that the value of 4 was observed in this context 3 times.

Fractional replication permits flexible observation-weighting:

R3.5,2,23,6,4 means that the value of 4 was observed in this context 3.5 times.

 

Weighting observations: We want to give some incorrect answers a smaller penalty than other incorrect answers. There are two ways to do this:

 

1) in the data:

 

3 facets + correct

2,3,4, 1

3 facets + incorrect

2,3,4, 0

3 facets + half-weight incorrect

R0.5, 2,3,4, 0

 

2) with a Models= specification

 

Models =

; 3 facets + dummy indicator facet + correct/incorrect

?,?,?,1,D,1   ; full weight

?,?,?,2,D,0.5   ; half weight

*

Labels=

....

*

4, Weighting, A

1 = Full weight, 0

2 = Half weight, 0

*

 

Data =

 

3 facets + indicator +correct

2,3,4, 1, 1

3 facets + indicator + incorrect

2,3,4, 1, 0

3 facets + indicator +half-weight incorrect

2,3,4,  2, 0