# Ordinal Model: Acceptability/alternatives to using mean and weighting factors

#### Rob_2012

##### New Member
I've been asked to validate a model created by someone else and need some help on how the final score is calculated. Have put lots of detail; apologies for the post length.

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
My queries are:
1. 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)
1. 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)
2. If using the mean is OK, is the constant rounding acceptable? I would have thought you should just round at the end.
3. Is there a better way of calculating the final score than using the mean, given the need to weight the different ordinal IVs.
1. My thought was to dispose of the hierarchical structure, and instead:
1. take the individual IV scores,
2. calculate the effective final weights for each IV (e.g. factor weight*sub-factor weight*IV weight)
3. 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..)
4. Use the point with the highest weight as the final score - like taking a weighted modal value.
Thanks
Rob