Understanding Society User Support

Dear Jun Wang,

Thank you for your question.
1. Selection probabilities for refreshment sample are independent of the selection probabilities for the first sample. You will know them from your design;
2. The combined probabilities are the sum of the two;
3. For the rare possible case the actual probability does not depend on whether the person appears twice or not - everyone's proability is the sum of the two probabilities.

If you could let us know which study you are working on, it would help if we can include this for our impact case.
Best wishes,
Olena

Dear Olena,

I'm working on CHARLS project. Thanks for your reply, but there is still some questions here:

According to the sample design of Innovation Panel, the inclusion probability for a respondent in Wave 1 can be written as ×(inclusion probability for address)×(inclusion probability for a household)×(adjustment for multiple dwellings and household). As [Innovation Panel, Wave 1-13: User Manual] [Sample Design part] wrote, 120 PSUs (post-sectors) are all kept fixed after they were selected as SSUs in Wave 1 sample. Refreshment sample addresses in Wave 4 were selected in those original PSUs (post-sectors) excluding addresses have already been selected as SSUs in Wave 1.

First question is, as 120 PSUs in Wave 4 refreshment sample are original PSUs in Wave 1, how to calculate inclusion probabilities for those PSUs (post-sector) for Wave 4 refreshment sample ? Are those inclusion probabilities for PSUs in Wave 4 refreshment sample the same as they were in Wave 1? Or they are recalculated by new PSUs frame in Wave 4?

Second question is, for Wave 4 refreshment sampling , those addresses have already been selected as SSUs in Wave 1 in each selected PSU (post-sector) were excluded from addresses frame first. Addresses for refreshment sample in Wave 4 were selected from the remaining addresses in each original PSU. Let B be the remaining addresses sampling frame for PSU_i, let A be the sampling frame the combining of B and those selected addresses in Wave 1 for PSU_i. Are inclusion probabilities for refreshment sample addresses in PSU_i calculated by frame B? or by frame A ?

Best wishes

Jun

Dear Olena,

I'm working on CHARLS project. Thanks for your reply, but there is still some questions here:

According to the sample design of Innovation Panel, the inclusion probability for a respondent in Wave 1 can be written as ×(inclusion probability for address)×(inclusion probability for a household)×(adjustment for multiple dwellings and household). As [Innovation Panel, Wave 1-13: User Manual] [Sample Design part] wrote, 120 PSUs (post-sectors) are all kept fixed after they were selected as SSUs in Wave 1 sample. Refreshment sample addresses in Wave 4 were selected in those original PSUs (post-sectors) excluding addresses have already been selected as SSUs in Wave 1.

First question is, as 120 PSUs in Wave 4 refreshment sample are original PSUs in Wave 1, how to calculate inclusion probabilities for those PSUs (post-sector) for Wave 4 refreshment sample ? Are those inclusion probabilities for PSUs in Wave 4 refreshment sample the same as they were in Wave 1? Or they are recalculated by new PSUs frame in Wave 4?

Second question is, for Wave 4 refreshment sampling , those addresses have already been selected as SSUs in Wave 1 in each selected PSU (post-sector) were excluded from addresses frame first. Addresses for refreshment sample in Wave 4 were selected from the remaining addresses in each original PSU. Let B be the remaining addresses sampling frame for PSU_i, let A be the sampling frame the combining of B and those selected addresses in Wave 1 for PSU_i. Are inclusion probabilities for refreshment sample addresses in PSU_i calculated by frame B? or by frame A ?

Best wishes

Jun

Jun,

Let's talk about a theoretical example.
In IP1 let's say we sample 10 people out of each PSU. If each PSU has 100 people, the selection probability is 10/100=0.1.
In IP4 let's say we again sample 10 people from the each same PSU (we exclude previous people, although this isn't theoretically necessary). For refreshment sample the selection probability is 10/100=0.1.

What you should be interested in though if you want to use original sample alongside refreshment is the joint probability. In simple terms we now have 20 people selected (either through the original sample or refreshment sample) from each PSU. So the total selection probability (for both samples) is 20/100=0.2.

Does this help?
Olena

Hi, Olena, thanks very much, the second question is solved.

For the first question, suppose there are 100 PSUs in population, we select 10 PSUs in 100 in Wave 1 by PPS, the size of population at the time of Wave 1 is 10000, the size of one selected PSU is 100, then the selection probability for this PSU can be approximated by 100*10/10000=0.1; if we select 10 people in this PSU, then the selection probability for each people in this PSU is 10/100=0.1, this is right. Then for this people, the selection probability for he/she can be calculated by (100*10/10000)*(10/100)=0.01, which is the product of (selection probability of PSU )×（selection probability of a people given PSU), selection probability here is defined as: the probability of a people in population is included to the sample.

but at the time Wave 4, the population size increase to 20000, the size of this selected PSU keep the same as it was in Wave 1 (that is 100), if we select this PSU to our sample by PPS at Wave 4, then the selection probability for this PSU should 10*100/20000=0.05 at Wave 4. However, at Wave 4, this PSU is not selected randomly, it was selected to the sample at Wave 1. as selection probability(for a people in population) equals (selection probability of PSU)×（selection probability of a people given PSU), the main issue here is how to calculate (selection probability of PSU) at Wave 4, should it be equal to 100*10/10000=0.1 (wave 1) or 10*100/20000=0.05 (wave 4)?

Best wishes
Jun

Jun,

Yes, there may be a population increase (by newborns or immigration). It depends on your longitudinal plans for renewing your sample. For us we get newborns through mums but we don't get immigrants. Immigrants between wave 1 and 4 to the country have 0 chance to be selected at wave 1 and the usual probability at wave 4. Similarly, you would need to think for each category of people whose population grows separately.

Does this help?
Olena

Jun,

Also, if people move across PSUs you are in the territory of a cross-classified design, which would need to be taken into account when analysing the data.

Hope this helps,
Olena

Olena Kaminska wrote in #note-3:

Dear Jun Wang,

Thank you for your question.
1. Selection probabilities for refreshment sample are independent of the selection probabilities for the first sample. You will know them from your design;
2. The combined probabilities are the sum of the two;
3. For the rare possible case the actual probability does not depend on whether the person appears twice or not - everyone's proability is the sum of the two probabilities.

If you could let us know which study you are working on, it would help if we can include this for our impact case.
Best wishes,
Olena

Hi, Olena,

The second you provided <2. The combined probabilities are the sum of the two> was the reply to question:

2. as IP4 addresses in refreshment sample are selected using systematic randomly amongst addresses not already selected for the IP1, how to calculate inclusion probabilities for those addresses in refreshment sample?

Refreshment sample is quite different with on-going longitudinal sample. Addresses selected at Wave 1 were followed at Wave 4, but new addresses were selected at Wave 4 for refreshment sample within each PSU selected at Wave 1.

According to Innovation panel sample design , addresses for refreshment sample at Wave 4 are selected using systematic randomly sampling excluding those addresses have already been selected at Wave1 given a selected PSU. However, for each PSU, those addresses selected at Wave 4 are not representative of all addresses within this PSU, because those addresses have been selected at Wave 1 were excluded from the sampling frame.

so for second question, I want to know, are the selection probabilities for those addresses selected at Wave 4 for refreshment sample calculated by full addresses frame information or by frame information that exclude those selected addresses have already been selected at Wave1? Can you provide some details or documents about how to calculate this inclusion probability?

We are considering add refreshment sample to our on-going sample, and now are reading technical documents on sample designs and weighting processes for refreshment sample of different longitudinal surveys, like ELSA. If you can provide some details or documents about weighting processes of Innovation Panel, you can sent it to my email jun.wang@pku.edu.cn. Thanks very much for your help.

This is the Website of CHARLS: ttp://charls.pku.edu.cn/index/en.html .

Best,
Jun

Olena Kaminska wrote in #note-8:

Jun,

Yes, there may be a population increase (by newborns or immigration). It depends on your longitudinal plans for renewing your sample. For us we get newborns through mums but we don't get immigrants. Immigrants between wave 1 and 4 to the country have 0 chance to be selected at wave 1 and the usual probability at wave 4. Similarly, you would need to think for each category of people whose population grows separately.

Does this help?
Olena

hi,Olena,

UK understanding society:*Innovation panel* add a refreshment sample at Wave 4, but PSUs (post-sectors) were the same PSUs in Wave 1. inclusion probabilities for PSUs at Wave 1 can be calculated by (number of selected PSUs) ×(size of PSU)/(total size of all population PSUs). Even though PSUs at Wave 4 were selected at Wave 1, are their selection probabilities at Wave 4 the same as they were at Wave 1? or re-calculated by the PSUs size information at Wave 4?

Best Wishes,
Jun

Jun,

Assuming no change in population size of PSUs over time, the selection probability at the PSU stage is the same in IP1 and IP4.

Hope this helps,
Olena

Olena,

Problems are solved, thanks for your help.

Best Wishes
Jun