Effects coding, utilities and probabilities

[Andrew]

Hi...

I would like to ask a few questions.

1. Suppose I use b1.effects[0.08|0.05]*[0,1,2] in utility function as I want to test for non-linearity. (0= low, 1= mild, 2=severe)
Which value do my levels contribute to utility? Is it 0.08*1 for level 1, 0.05*1 for level 2 and -1 for level 3 (reference level) using effects coding? Or would level 3 be the inverted sum * (-1) of level 1 and 2 that is -0.13?

2. How are utilities and probabilities calculated in Ngene? Could I do it manually with assumed priors?

3. How are the blocks in design output (column block) randomized?

Appreciate any help on this.

Best
Andrew

[Michiel Bliemer]

1. The last level is always the reference level, so in effects coding, level 0 will get a coefficient 0.08, level 1 will get a coefficient 0.05 and level 2 will get a coefficient -(0.08+0.05). This is the common way of effects coding. In dummy coding, it would be 0.08, 0.05, and 0.

2. You can easily calculate the utilities using the priors, the attribute levels, and your utility functions. The probability depends on your selected model, but for MNL this is simply the well-known MNL logit formula.

3. Blocks are assigned not competely random, but are optimised assuming as much orthogonality as possible with the other attribute columns. In the end this leads to a mostly attribute level balanced split within the blocks.

[Andrew]

Many thanks again.
This was very helpful.