Hi Andy,

If you have a measure comprised of 20 dichotomous items and you build an additive index out of them, then your response variable is most likely ordinal. In that case, you'd want an ordered logit regression. Note that since your data are discrete, not using linear regression won't result in a loss of information: there is no information about the magnitude of the difference between scores on the response scale to lose in the first place. Using an arbitrary rule (like 1 when sum(a) > 10, else 0) to run a simple logit regression would result in loss of information, though not necessarily so much as to reduce power, since your sample size is small and an ordered logit model for a 20-point response scale would be pretty cumbersome.