Is the use of regression you have suggested similar to Brunswik's Lens
model which uses regression to give weights to the cues/constructs which
are used to make judgments/predict some phenomena?
The issue of using regression to analyse grid data is an interesting one.
Although possibly unrelated to the issue which has been raised, I have found
that if a regression is performed on the grid data of multiple persons,
there is a marked increase in the variance accounted for if the regression is
based on the correlations between constructs for each individual summed.
As an example assume 10 people completed a grid with 4 constructs: 'Competent,
'Intelligent', 'Wise' and 'Education' and they used 4 common elements. The
standard method of performing a regression would be to average the ratings
made by each of the 10 persons and sum them so that 4 variables would be
constructed. The correlation among these variables could be computed
and an attempt could be made to 'predict' whichever variable was the dependent
variable.
An alternative approach suggested to me by Len Dalgleish from Queensland
University, was to calculate the correlation among constructs for each
individual. Then, the 10 correlations between each pair of constructs would
be summed, e.g., between 'Competent'and 'Wise', 'Wise'and 'Education' etc.
The regression would be based on these summed correlations. This is more
difficult to do than the standard approach though is a more ideographic
approach which takes into account the importance of each individual's
construct relationships. It necessarily follows that the relationship
between constructs must be a fluid process, dependent on what is being
construed.
Regards,
Bob Green
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