design with interactions

[mpburton]

I would like some feedback on a design with interactions.

This is based on the proposal by
Marcel F. Jonker, Bas Donkers,
Interaction Effects in Health State Valuation Studies: An Optimal Scaling Approach,
Value in Health, Volume 26, Issue 4, 2023.

to parsimoniously identify interaction effects between health attributes, using the EQ5D framework. Essentially, it assumes dummy coded effects for the 5 levels that each attribute (m,s,a,u,p) can take, but then codes those as a continuous variable to allow for interaction effects (avoiding the need for interactions between each of the levels of each of the 5 attributes). In the design below, the 5 levels of (dis)health are assumed to vary on a linear scale (1,0.75,0.5,0.25,0), but those priors could be changed to any values. The choice facing respondents is decreased health in alt1 (at least some values of m,s,a,u,p are larger than 0) or full health (m,s,a,u,p=0) at a cost (alt2)

What’s surprising is that the implied sample size required is large (about 225, each doing a full set of 100 questions), and the coefficients that are problematic are the 10 interaction coefficients. Given these are essentially continuous variables (conditional upon the priors used) I would have thought that these would be easily retrieved. Any insights on why this is the case/errors made/suggestions for improvement?

thanks

Michael


Design
;alts=alt1, alt2
;rows=100
;block=6
;eff=(mnl,s)
;model:
U(alt1)=mb.dummy[-1|-0.75|-0.5|-0.25]*m[1,0.75,0.5,0.25,0]+sb.dummy[-1|-0.75|-0.5|-0.25]*s[1,0.75,0.5,0.25,0]+ab.dummy[-1|-0.75|-0.5|-0.25]*a[1,0.75,0.5,0.25,0]+ub.dummy[-1|-0.75|-0.5|-0.25]*u[1,0.75,0.5,0.25,0]+pb.dummy[-1|-0.75|-0.5|-0.25]*p[1,0.75,0.5,0.25,0]+

mub[0.2]*m[1,0.75,0.5,0.25,0]*u[1,0.75,0.5,0.25,0]+
msb[0.2]*m[1,0.75,0.5,0.25,0]*s[1,0.75,0.5,0.25,0]+
mpb[0.2]*m[1,0.75,0.5,0.25,0]*p[1,0.75,0.5,0.25,0]+
mab[0.2]*m[1,0.75,0.5,0.25,0]*a[1,0.75,0.5,0.25,0]+
usb[0.2]*u[1,0.75,0.5,0.25,0]*s[1,0.75,0.5,0.25,0]+
upb[0.2]*u[1,0.75,0.5,0.25,0]*p[1,0.75,0.5,0.25,0]+
uab[0.2]*u[1,0.75,0.5,0.25,0]*a[1,0.75,0.5,0.25,0]+
spb[0.2]*s[1,0.75,0.5,0.25,0]*p[1,0.75,0.5,0.25,0]+
sab[0.2]*s[1,0.75,0.5,0.25,0]*a[1,0.75,0.5,0.25,0]+
pab[0.2]*p[1,0.75,0.5,0.25,0]*a[1,0.75,0.5,0.25,0]
/
U(alt2)=cost[-0.1]*cost[5,10,20,40,50]
$

[Michiel Bliemer]

Your priors 0.2 indicate that each interaction effect only plays a very small role in choice behaviour, so that means you will need a large sample size to estimate the parameter of a minor effect. If your prior would have been 0.4 or larger, the sample size would by definition be much smaller. Sample size estimates are heavily dependent on prior values and should be ignored if the prior values are unknown (in your case you set them all arbitrarily to 0.2).

Note that I would generally always generate a D-efficient design, an S-efficient design only optimises for the most difficult to estimate parameters and ignores the rest.

Michiel