关于美国ASEC调查中Replicate weights使用方法的技术咨询

Great question—ASEC's replicate weights are critical for getting accurate variance estimates, and it’s easy to get tripped up on the exact workflow. Let’s break this down step by step, starting with core application rules, then diving into the technical variance math.

Core Application Rules #

First, let’s nail down the non-negotiable steps for using ASEC’s 160 replicate weights correctly:

• Start with the main weight estimate: Always calculate your target statistic (e.g., median income, employment rate, regression coefficient) using the main survey weight (usually labeled ASECWT in the microdata) first. This is your point estimate—all replicate calculations will reference this value.
• Recalculate with each replicate weight independently: For every replicate weight column (typically named REPWGT1 through REPWGT160), rerun the exact same statistic calculation, replacing the main weight with that single replicate weight. You’ll end up with 160 separate replicate estimates of your metric.
• Mirror the main calculation exactly: If your main estimate uses weighted percentiles, weighted least squares, or any other weighted computation, the replicate estimates must follow that exact logic. Even tiny deviations (like rounding differences or changing how you handle tied values) will skew your variance results.
• Never mix weights: Don’t combine the main weight with any replicate weight in a single calculation—each replicate estimate should rely solely on one replicate weight, just like the main estimate uses only the main weight.

Variance Calculation Technical Details #

Once you have your main estimate (θ̂) and 160 replicate estimates (θ̂_r for r=1 to 160), ASEC uses the Balanced Repeated Replication (BRR) method to compute variance. Here’s the exact formula you’ll use:

Var(θ̂) = (1/160) * Σ(θ̂_r - θ̂)²

Key Notes on the Math: #

• Scaling factor: Unlike some other survey designs, ASEC’s replicate weights are pre-adjusted so you don’t need an extra scaling factor here—dividing by 160 (the number of replicates) is all you need.
• Standard error conversion: If you need the standard error (instead of variance), just take the square root of the variance result:

  SE(θ̂) = sqrt(Var(θ̂))
  

• Why this works: Each replicate weight corresponds to a half-sample of the original ASEC survey. By recalculating your statistic across these half-samples, you’re simulating the variability you’d see if you ran the survey 160 times—this gives you a robust estimate of the true sampling variance.

Quick Example #

Let’s say your main estimate of median household income (using ASECWT) is $70,000. You recalculate the median with each of the 160 replicate weights, getting values from $68,500 to $71,200. You compute the squared difference between each replicate median and $70k, sum all those squares, then divide by 160. That’s your variance. The square root of that number is your standard error for the median income estimate.

内容的提问来源于stack exchange，提问作者andrewH