I want to compare different attributes of a population and see if one is more indicative of an outcome measurement than the other.
In a general case, suppose I want to examine $k$ attributes. Each attribute is binary, meaning that each individual either has this attribute or doesn't. At the first time point, I sample a large number $n$ (>1 million) from the whole population and obtain outcome measurement values, $v_{1,1}$ ...$v_{1,n}$. I also obtain all attributes for each individual. At the second time point, I sample another large number $m$ (>1 million) from the whole population and obtain outcome measurement values, $v_{2,1}$ ...$v_{2,m}$. I again obtain all attributes for each individual. Let's assume the the population is so large that I don't have any overlap in the members that I sample at two different time points. I want to see if one attribute is more indicative of changes in the outcome measurement between two time points, and perform a suitable statistical test.
Here is an example:
At the first time point, I sampled a large group of people at age 15 and measured their height. I recorded if each one of them 1) eats meat or 2) eats fruit or 3) eats vegetable. Let's assume no one in the whole population changes diet ever. After a year, I sampled another large group of people at age 16 (not the same people as those a year ago) and measured their height. I also recorded if each one of them 1) eats meat or 2) eats fruit or 3) eats vegetable. So I want to see if eating meat is more helpful than eating fruit or eating vegetable in gaining height.
Does anyone have any suggestions on what kind of statistical test I should use here?
Thank you!