How to calculate weights?

[Dan Su]

Hi experts!

If for the sub sample(total number=n), black is 50% and whites is 50%; and for the full sample(total number=N), black is 75% and white is 25%. So in the full sample, the probability(p) for black is 0.75 and the p for white is 0.25. How can I calculate the weights(wt) that I want to include as [pweight=wt] when I run the regression model for the subsample?

Let's say Pi is the probability for each participant in the sub sample (0.75 or 0.25 in this case), is the weight= (Pi / sum of Pi) *N? N is the total number of the full sample. Thanks everyone!

[Dan Su]

I know if

NB = # blacks in population
nb = # blacks in subsample
NW = # whites in population
nb = # whites in subsample

then
weight for blacks = NB/nb
weight for whites = NW/nw

In this simple example, it should work out to be a weight of 1.5 for blacks and .5 for whites.

However, since I still need to use other covariates such as age, gender, etc. besides race to predict the probability being selected for the subsample, I can't simply calculated the weights like that. If I already use "logistic" to predict the weights for each person in the subsample, what's the formula to calculate the weights?

[Dan Su]

Steve Samuels Hi Steve, can you help me with this? Thanks!

[Marcos Almeida]

This "formula" is correct.

That said, this text may be helpful to you.

Sampling weights: There are several types of weights that can be associated with a survey. Perhaps the most common is the sampling weight. A sampling weight is a probability weight that has had one or more adjustments made to it. Both a sampling weight and a probability weight are used to weight the sample back to the population from which the sample was drawn. By definition, a probability weight is the inverse of the probability of being included in the sample due to the sampling design (except for a certainty PSU, see below). The probability weight, called a pweight in Stata, is calculated as N/n, where N = the number of elements in the population and n = the number of elements in the sample.For example, if a population has 10 elements and 3 are sampled at random with replacement, then the probability weight would be 10/3 = 3.33.

[Dan Su]

This "formula" is correct.

That said, this text may be helpful to you.

Thanks Marcos! Just want to make sure, the weight for each participant: weight= (Pi / sum of Pi) *N is correct? N is the total number of the full sample. Pi is the probability for each participant being selected for the sub sample. Thanks!

[Marcos Almeida]

Hello Dan,

The core principle is: n or percentage for a given level of a variable in the population and n or percentage for the very same level of a given variable in the sample.

There are examples of weights in this text, relying on one or more variables.

I believe they apply exactly to your needs.