# Sample Weights & Clustering Adjustments

## Sample Weights & Clustering Adjustments

### Sample Weights

In each survey year a set of sampling weights is constructed. These weights provide the researcher with an estimate of how many individuals in the United States each respondent's answers represent. Weighting decisions for the NLSY79 are guided by the following principles:

- individual case weights are assigned for each year in such a way as to produce group population estimates when used in tabulations
- the assignment of individual respondent weights involves at least three types of adjustment, with additional considerations necessary for weighting of NLSY79 Child data

The interested user should consult the NLSY79 *Technical Sampling Report* (Frankel, Williams, and Spencer 1983) for a step-by-step description of the adjustment process. A cursory review of the process follows.

Adjustment One: The first weighting adjustment involves the reciprocal of the probability of selection at the first interview. Specifically, this probability of selection is a function of the probability of selection associated with the household in which the respondent was located, as well as the subsampling (if any) applied to individuals identified in screening.

Adjustment Two: This process adjusts for differential response (cooperation) rates in both the screening phase and subsequent interviews. Differential cooperation rates are computed (and adjusted) on the basis of geographic location and group membership, as well as within-group subclassification.

Adjustment Three: This weighting adjustment attempts to correct for certain types of random variation associated with sampling as well as sample "undercoverage." These ratio estimations are used to conform the sample to independently derived population totals.

**Sampling Weight Readjustments:** Sampling weights for the main survey are readjusted to account for noninterviews each survey year. The readjustments are necessitated by differential nonresponse and use base year sample parameters for their creation, employing a procedure similar to that described above. The only exception occurs in the final stage of post-stratification. Post-stratification weights in survey rounds two and above have been recomputed on the basis of completed cases in that year's sample rather than the completed cases in the base year sample.

### Custom Weights

Users looking for a simple method to correct a single year's worth of raw data for the effects of over-sampling, clustering and differential base year participation should use the weights include each round on the data release. Unfortunately, while each round of weights provides an accurate adjustment for any single year, none of the weights provide an accurate method of adjusting multiple years' worth of data. The NLS has a custom weighting program which provides the ability to create a set of customized longitudinal weights. These weights improve a researcher's ability to accurately calculate summary statistics from multiple years of data.

The custom weighting program calculates its weights by first creating a new temporary list of individuals who meet all of a researcher's criteria. This list is then weighted as if the individuals had participated in a new survey round. The weights for this temporary list are the output of the custom weighting program.

There are two options for the custom weighting program, found at http://www.nlsinfo.org/weights/nlsy79. The first option allows researchers to specify the particular rounds in which respondents participated. Researchers can also select if "The respondents are in ** all** of the selected years" or can select if "The respondents are in

**of the selected years." The second option allows users to input a list of respondent ids to get the appropriate weights for just that list. For example, this second option allows researcher to weight only those people who ever reported smoking cigarettes in any survey or weight only people who needed extra time to graduate from college.**

*any or all*Important Information About Using the Custom Weighting Program

- If you select all survey rounds available and also pick "The respondents are in
of the selected years," the weights produced are identical to round 1 survey weight. This result arises because the any selection combined with all survey rounds produces a list of every person who participated in the survey.*any or all* - The output of the custom weight program has 2 implied decimal places just like the weights found in the data release. Dividing each custom weight output value by 100 results in the number of individuals the respondent represents.

### Practical Usage of Weights

The application of sampling weights varies depending on the type of analysis being performed. If tabulating sample characteristics for a single interview year in order to describe the population being represented (that is, compute sample means, totals, or proportions), researchers should weight the observations using the weights provided. For example, to estimate the average hours worked in 1987 by persons born in 1957 through 1964, simply use the weighted average of hours worked, where weight is the 1987 sample weight. These weights are approximately correct when used in this way, with item nonresponse possibly generating small errors. Other applications for which users may wish to apply weighting, but for which the application of weights may not correspond to the intended result include:

**Samples Generated by Dropping Observations with Item Nonresponses: **Often users confine their analysis to subsamples for which respondents provided valid answers to certain questions. In this case, a weighted mean will not represent the entire population, but rather those persons in the population who would have given a valid response to the specified questions. Item nonresponse because of refusals, don't knows, or invalid skips is usually quite small, so the degree to which the weights are incorrect is probably quite small. In the event that item nonresponse constitutes only a small proportion of the data for variables under analysis, population estimates (that is, weighted sample means, medians, and proportions) would be reasonably accurate. However, population estimates based on data items that have relatively high nonresponse rates, such as family income, may not necessarily be representative of the underlying population of the cohort under analysis. For more information on item nonresponse in the NLSY79, see the Item Nonresponse section of this guide.

**Data from Multiple Waves:** Because the weights are specific to a single wave of the study, and because respondents occasionally miss an interview but are contacted in a subsequent wave, a problem similar to item nonresponse arises when the data are used longitudinally. In addition, occasionally the weights for a respondent in different years may be quite dissimilar, leaving the user uncertain as to which weight is appropriate. In principle, if a user wished to apply weights to multiple wave data, weights would have to be recomputed based upon the persons for whom complete data are available. In practice, if the sample is limited to respondents interviewed in a terminal or end point year, the weight for that year can be used (for more information on weighting see the section on clustering adjustments).

**Regression Analysis:** A common question is whether one should use the provided weights to perform weighted least squares when doing regression analysis. Such a course of action may not lead to correct estimates. If particular groups follow significantly different regression specifications, the preferred method of analysis is to estimate a separate regression for each group or to use dummy (or indicator) variables to specify group membership.

Users interested in calculating the population average effect of, for example, education upon earnings, should simply compute the weighted average of the regression coefficients obtained for each group, using the sum of the weights for the persons in each group as the weights to be applied to the coefficients. While least squares is an estimator that is linear in the dependent variable, it is nonlinear in explanatory variables, and so weighting the observations will generate different results than taking the weighted average of the regression coefficients for the groups. The process of stratifying the sample into groups thought to have different regression coefficients and then testing for equality of coefficients across groups using an F-test is described in most statistics texts.

Users uncertain about the appropriate grouping should consult a statistician or other person knowledgeable about the data set before specifying the regression model. Note that if subgroups have different regression coefficients, a regression on a random sample of the population would not be properly specified.