A dual response pilot study design

[Jack]

Hi Prof Michiel,

Indeed I was estimating a single parameter for each attribute. But I was pointed out by a fellow colleague to consider specifying the continuous variables as categorical which will then allow me to obtain a design where a model can be tested for linearity. Hence I wanted to design the model which will accommodate for non-linearity across attribute levels if possible. The only issue was the FREQ attribute level '4' which only appears in SQ and not in other alternatives, which then is confounded with the SQ ASC if effects/dummy coding was applied. I found one similar design where this issue can be overcome by not specifying an ASC for SQ alternative but instead, treating SQ as another unlabelled alternative. I am not sure this is a better route given my pilot study results showed SQ ASC estimate was significant (negative). Incorporating the attribute level '4' into the design will make no sense to the respondents, hence the dilemma. How do I overcome this identification issue with attribute FREQ? Any advice much appreciated.

Jack

[Michiel Bliemer]

If you are interested in nonlinearities for continuous variables, then there is no need to use categorical variables. You can estimate functions with logarithms, exponentials, power series, etc.

e.g. you can estimate things like:
U(alt1) = b1*freq + b2*freq^2 + b3*ln(freq)

In Ngene, this could become:

;cond:
if(freq = 1, lnfreq = 0),
if(freq = 2, lnfreq = 0.69),
if(freq = 3, lnfreq = 1.09),
if(freq = 4, lnfreq = 1.39)
;model:
U(alt1) = b1*freq[1,2,3,4] + b2*freq*freq + b3*lnfreq[0,0.69,1.09,1.39]

Optimising for nonlinear transformations is not often done in experimental design, but it can be done and with a bit of creativity can be done in Ngene.

Michiel