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.
In Facets, all the weights (in Models=, in Labels= or R.... at the observation level) are applied as replications of the observation. So for instance:
Models=?,?,?, 2 ; weight of two
or
Labels=*
1, Facet 1
1, element 1, , , 2 ; weight of two
or
R2, 1,1,1, 3 ; weight of two
are all processed internally to mean the same as
1,1,1, 3
1,1,1, 3
Fractional weights are allowed.
If two or more weights apply to the same observation, then the weights are multiplied.
Reliability Index: The true reliability of the measures is from the unweighted analysis. Weighting introduces an arbitrariness into the analysis. One solution is to adjust the weights to maintain the unweighted reliability = Ru. The reliability of the weighted analysis, using an initial set of weights, = Rw. We can then scale the weights using the Spearman-Brown Prophecy Formula: S = Ru * (1-Rw) / ((1-Ru)*Rw)). Multiply the initial set of weights by S. Then the weighted and unweighted reliabilities should be the same.
Weighting using Models=: 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
*
Weighting using Labels=: individual elements can be weighted
element number = element label, anchor value, group number, element weight
Labels=
...
*
3, facet name
1 = first element, , , 0.8 ; all observations with this element weighted 0.8
....
*
Weighting of a data point using R.... weights: can be specified by R (or another replication character) 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.
Example: We want to construct response data according to the known probabilities of being observed:
Person 3 has a 60% probability of succeeding on item 4:
Person 7 has a 25% probability of succeeding on item 11:
Data=
R0.60, 3, 4, 1 ; 60% probability of success
R0.40, 3, 4, 0 ; 40% probability of failure
R0.25, 7, 11, 1 ; 25% probability of success
R0.75, 7, 11, 0 ; 75% probability of failure
Weighting summaries using element weights and R.... weights:
Example: for 25 people scoring 32, there was 0.57 success on item 4:
Facets=2
Models= ?,?,D
Labels=
1, Raw Scores
....
32=32, , , 25 ; weight by number of people at score
.....
*
2, item
1-9
*
Data=
....
R0.57 , 32,4, 1 ; weight correct answer by its probability
R0.43 , 32,4, 0 ; weight incorrect answer by it probability
....
Weighting specific 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 and a weighting facets
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
3) with a Labels= specification and a weighting facets
Models =
; 3 facets + dummy indicator facet + correct/incorrect
?,?,?,?,D
*
Labels=
....
*
4, Weighting, A
1 = Full weight, 0, , 1 ; element weight
2 = Half weight, 0, , 0.5
*
