I'm reading Using Weights in the Analysis of Survey Data by David R. Johnson .
When we conduct a survey, people have different likelihood to respond. For example, suppose there are 50% males and 50% females in the population, and 40% young people and 60% old people.
Suppose females are more likely to respond than males, and elders are more likely to respond than youngsters.
In the sample (the ones who answered the survey) we will have 60% of females and 80% of elders.
We need to fix this in order for the sample to be representative of the population (50% of females, and 60% of elders). To do so, we assign post-stratification weights to observations. Since we have more than one covariate (gender and age), we need to combine the 2 post-stratification weights into one.
At page 8, it provides an algorithm to combine several post-stratification weights into one by hand.
The algorithm is as follows:
Example with three characteristics A, S, E
– 1. Compute A weight (wA) and weight data by this weight
- Generate the weighted frequency table for S
– 2. Compute S weight (wS) and weight by wA*wS
- Generate the weighted frequency table for E
– 3. Compute E weight (wE) and weight by wA*wS*wE
- Generate the weighted frequency for A
– 4. Compute a second A weight(wA2) and weight by wA*wS*wE*wA’
- Generate the weighted frequency for S
– 5. Compute a second S weight (wS2) and weight by wA*wS*wE*wA2*wS2
- Generate the weighted frequency for E
– 6. Compute a second E weight (wE2) and weight by wA*wS*wE*wA2*wS2*wE2
– Continue process until the weighted frequencies and the population frequencies
don’t change. Usually converge after two or three iterations (or less)
I don't understand this algorithm. In particular, I don't know what "weighted frequency" is.
Can you provide a numerical example?
