I am trying to develop a scale for a variable, call it Z, by combining two
others, call them X and Y; whether the combination is to be addition or
multiplication is yet to be decided, although the latter has precedents
in the literature, on rational grounds. Each of X and Y are to be
assessed using the answers to questionnaires; Clinical measures for X
and Y exist that might be regarded as gold standards. However,
having devised a scoring system for both X and Y, and decided on a
gold standard for Z, call it S, I found that the correlations of both X+Y
and X*Y with S were practically identical.
However a pilot study suggested using 'factor analysis, PCA and
Rasch models' to develop suitable scales. I understand, however that
the third of these refers to binary variables (i.e. right or wrong answers
to test questions), while the other two are intended for Normally
distributed continuous variables.
Can anyone suggest references that enable categorical (ordinal)
variables to be combined into interval scores ( not yes/no diagnosis,
for someone did suggest logistic regression to me), or indeed books
that deal with factor analysis, PCA and Rasch models for ordinal
variables? I hope to obtain a stronger relationship of Z with S as well
as to be better able to decide whether additive or multiplicative
measures of Z are better. Possibly such methods could be used to
obtain an improved measure of S, as well, i.e. the gold standard
measures of X and Y could be combined in an optimal way, rather than
one that seems to use both being picked out.
Regards
Miland Joshi (Mr.)
Department of Epidemiology and Public Health
University of Leicester
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