You wish to fit a model to a “forced choice” binary dependent variable measuring political party preference (if you had to pick a political party, which would you select: Democratic or Republican?), and examine the relationship of parental political attitudes with the preference of the respondents. Based on the study design, there are multiple respondents measured from each of several neighborhoods, and respondents within the same neighborhood may have shared political views, but you aren’t interested in explicitly estimating between-neighborhood variance. You only wish to estimate the overall relationship of interest in the larger population, and account for possible within-neighborhood correlation in the DV.
What type of model would you fit?