I am creating a new measurement scale for withdrawal from cannabis, and have daily withdrawal data from 50 people for 1 week before abstinence (baseline smoking as usual) and then for 2 weeks of abstinence. There are 26 items on this new scale, and essentially what I want to is to rank the items by the amount that they increase above baseline during the withdrawal phase...I am calling this "validity" - and it can be conceptualized as taking the integral (area under the curve) between the average baseline score and the score given on each day of abstinence - for every item on the scale.

I did exactly this - i.e. calculated the integral between the mean daily withdrawal score and the average baseline score for the week of smoking as usual - and used that single value to rank the scale items.

All well and good, but what I really need is to put some stats next to the items - that somehow reflect my "integral" approach (I.E. parameter values that also reflect a descending order inline with the sorted integral values). In theory this should be possible.

However I am having a lot of difficulty making my stats match the ranking given by the integral...

Because I have such repeated measures data - I am using Generalized Estimating Equations - to allow for the within person correlations in their answers. I build 26 models (1 for each item on the scale) - with withdrawal score as the dependent variable, and time (days in abstinence) as the independent. Actually because withdrawal tends to increase at first and then decrease, I am adding time squared - to get a quadratic effect - which is most always significant. I also include the baseline score as the covariate in this model.

So I get a bunch of parameters out - i.e. slope parameters and wald chi square statistics - for each item - and I want to use these parameters or stats to describe the trajectory of withdrawal through abstinence - ultimately describing which items are most valid (i.e. respond more to abstinence)..... does anybody have any ideas for why non of my wald stats or slope values are matching my original integration ranking of the items? Also, I can get my stats program (SPSS) to output predicted mean values for each item.....when I take the integral of these predicted values and rank the items - they rank differently to the original integral ranking on the original raw values....any ideas why this is?

I realise that I am going "off road" with my approach to stats here - not using the traditional approaches and perspectives - so..

Thanks for any body who can give any alternative perspectives on this,

Dave