Question: For a simple example of a multinomial model, we consider a sample survey question with three possible responses. In late October, 1988, a survey was

For a simple example of a multinomial model, we consider a sample survey question with three possible responses. In late October, 1988, a survey was conducted by CBS News of 1447 adults in the United States to find out their preferences in the upcoming presidential election. Out of 1447 persons, y 1 = 727 supported George Bush, y 2 = 583 supported Michael Dukakis, and y 3 137 supported other candidates or expressed no opinion. Assuming no other information on the respondents, the 1447 observations are exchangeable. If we also assume simple random sampling (that is, 1447 names 'drawn out of a hat'), then the data (y 1 , y 2 , y 3 ) follow a multinomial distribution, with parameters ( 1 , 2 , 3 ), the proportions of Bush supporters, Dukakis supporters, and those with no opinion in the survey population. An estimand of interest is 1 2 , the population difference in support for the two major candidates.

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