The output (dependent) variable is ordinal scale with 5 points (i.e. 1-5) representing an assessment of risk (not risky, slightly risky etc.). The model is hierarchical; the independent variables are first grouped into subfactors, then factors, and then to the final 'score', which is the DV. The independent variables are all converted into the same 5-point ordinal scale initially.

Individual IV score --> Subfactor score --> Factor score --> Final score.

My concern is over how the individual IVs values are combined to get to the final score:

- For the individual IVs the ordinal values are weighted within the subfactor, and a weighted mean is taken [e.g. with 2 variables scoring 3 and 5, and weighted 40/60: (3*0.4)+(5*0.6)=4.2].
- To get the sub-factor score, the weighted mean is then rounded to the nearest integer, in effect returning it to the ordinal scale 4.2 --> 4
- The rounded subfactor scores within the factor are then weighted, averaged using the mean and then rounded in the same way to get the factor score.
- The factor scores are then weighted, averaged using the mean and then rounded in the same way to get the final score

- Is it wise to average ordinal variables in this way, using a mean? (Note: the IVs are NOT correlated even within sub-factors, although there will be some inter-correlations between sets of variables)
- It strikes me that, in addition to the general issue with treating an ordinal variable as if it were interval, the nature of the scale means that the two outside values, 1 & 5, are less likely to be the outcome because there is only a 'space' of 0.5 for them to be assigned within, compared to a space of 1 for the middle points (e.g. a weighted score would have to be between 1 & 1.5 to rated as a 1, whereas it can be between 1.5 and 2.5 to be rated as a 2)

- If using the mean is OK, is the constant rounding acceptable? I would have thought you should just round at the end.
- Is there a better way of calculating the final score than using the mean, given the need to weight the different ordinal IVs.
- My thought was to dispose of the hierarchical structure, and instead:
- take the individual IV scores,
- calculate the effective final weights for each IV (e.g. factor weight*sub-factor weight*IV weight)
- Sum up the weights across the IV scores, for each of the five points on the scale (e.g. all IVs scoring 1 have a weight of 15%, those scoring 2 have a weight of 12% etc..)
- Use the point with the highest weight as the final score - like taking a weighted modal value.

- My thought was to dispose of the hierarchical structure, and instead:

Rob