# What to do when results vary wildly based on coding the predictors as counts or frequencies?

I don't want to explain my real data, but I will make up an example that is equivalent.

Let's say people are judging the quality of paintings and can say "like" or "dislike". Paintings can have five colours in them: red, yellow, blue, green and/or orange. The paintings can be any size.

Count Approach

Let's say I categorize each square cm based on its colour (and that in this example each square cm can only be one colour). Because paintings can be of different sizes, the totals will differ across paintings. I create a model that is the number of square cms that are each colour.

So my model is: Liked = TotalRed + TotalYellow + TotalBlue + TotalGreen + TotalOrange

Analyzed like this, my results are something like this:

Term B
Intercept .8*
TotalRed -.2
TotalYellow .04
TotalBlue -.5
TotalGreen -.5*
TotalOrange -.3*

*= p < .05

Proportion Approach

Let's say for each painting I calculate the proportion of the painting that is each colour. This time I leave out blue because it is the least frequent and I want to avoid perfect redundancy among my predictors.

So my model is: Liked = PropRed + PropYellow + PropGreen + PropOrange

Analyzed like this, my results are something like this:

Term B
Intercept -.4
PropRed 1
PropYellow 1.5*
PropGreen -.01
PropOrange -.15

*= p < .05

Some predictors change signs, different predictors are significant, and my intercept changes.

How do I know which one is "more right"?

Edit:

To give some more detail, this is a logistic regression, with multiple predictors. I have about 450 observations.