Re: the midpoint

Richard Bell (
Wed, 12 May 1999 08:35:39 +1000

Further to Brian Gaines's comments:

1. Midpoint = missing data is a different category from the other two
interpretations, and can only be handled by single set representations,
that is through separate representations (cluster-trees or principal
components) of elements and constructs. Missing data could be accounted for
by the familiar 'pair-wise deletion' available in SPSS. It is not in my
programs at the moment partly because it can cause numerical problems
(stemming from the fact that the pair-wise indices of association
[correlations, distances etc] are based on different replications. Joint
representations of both elements and constructs, though unfolding,
correspondence analysis or singular-value-decomposition are not possible.
There are other strategies to deal with missing data such as EM or other
imputation approaches but I doubt there is enough data in a grid to make
these viable.

2. Where the midpoint means 'neither' a strategy involving the inclusion of
a 'phantom' construct which is a reflection of an elicited construct (i.e.
it is the elicited construct with the poles reversed) could be used to
solve the problem. As Brian noted, and my fast fading memory suggests, this
was Mildred Shaw's idea and I think I first saw it in her 1970 book 'On
becoming a personal scientist'. The element rated at the midpoint will
appear midway between the two points representing the two poles of the
construct (one from the elicited and one from the phantom). This gives
'neither' a neutral stance and makes it not different from a genuine
midpoint. Normal representations (which show only one pole) do not allow
the midpoint to easily discerned. [Putting reflected constructs into a
spatial solution tends to impose an artefactual circular configuration on
the constructs. This is okay and is known as a circumplex see eg R
Plutchick & H R Conte (eds) {1997}Circumplex models of personality and
emotions. Washington:APA]

b) Where the midpoint means 'both' I suspect you would need to include a
'phantom' element which would identical with the designated element in
ratings for each construct except the one where the element was at both
poles. In theory a spatial representation of these two elements would show
them equidistant from all the other construct pole locations except the one
representing the 'both' construct, where one version of the element would
be close to the construct pole, and the other distant. Notice however, I
said 'in theory'.

Richard C. Bell
Associate Professor
Department of Psychology
University of Melbourne
Parkville Vic 3052 Australia

ph: +61 3 9344 6364
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