# Replicate Weights in the Current Population Survey (2023)

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## Summary

• What are replicate weights?
• Why might I want to use replicate weights?
• Does using replicate weights make any substantive difference?
• How do I obtain replicate standard errors from ASEC IPUMS-CPS data?
• Is there any way to do this automatically in major statistical packages?
• Can I simply divide the full sample into 160 random subsamples from the full sample and calculate replicate standard errors manually?
• How are the CPS replicate weights calculated?

### What are replicate weights?

Replicate weights are currently available for the 2005-Onward Annual Social and Economic Supplement (ASEC) to the Current Population Survey. In the CPS, there are 160 separate weights at the household and person levels that allow users to generate empirically derived standard error estimates. These standard errors can then be used in hypothesis testing and in the construction of confidence intervals around the sample estimate of interest.

### Why might I want to use replicate weights?

In theory, the standard error of an estimate measures the variation of a statistic across multiple samples of a given population. Thus the true standard error of any characteristic calculated from a single sample can never be known with certainty; sample standard errors are simply estimated. Replicate weights allow a single sample to simulate multiple samples, thus generating more informed standard error estimates that mimic the theoretical basis of standard errors while retaining all information about the complex sample design. These standard errors can then be used to obtain more precise confidence intervals and significance test.

### Does using replicate weights make any substantive difference?

In IPUMS testing of CPS data, replicate weights usually increase standard errors. This increase is generally not large enough to alter the significance level of coefficients, though marginally significant coefficients may become clearly nonsignificant. The more obvious effect of using replicate weights is on the width of confidence intervals, which can change substantially.

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### How do I obtain replicate standard errors from IPUMS-CPS data?

There are 3 main steps:

1. Run your analysis using the full-sample weights for ASEC (ASECWT and HASECWT are the main CPS ASEC weights). Record the statistic you are interested in (e.g., the mean income of veterans, or the coefficient describing the relationship between income and whether one has health insurance coverage).
2. Run your analysis again using each set of replicate weights. First, run the analysis using REPWTP1, then again using REPWTP2, then again using REPWTP3, and so on up to the final set of replicate weights. After each set, record the statistic you are interested in. (N.B.: If you are analyzing a household-only file, be sure to use REPWT1, REPWT2, etc.)
3. Insert the above results into the following formula: where X is the result from the analysis using the full-sample weight and Xr is the result from the analysis using the r-th set of replicate weights.

### Is there any way to do this automatically in major statistical packages?

Yes. Although the replicate standard errors contained in the IPUMS-CPS data are calculated using the a combination of the successive difference replication and modified half-sample methods, which are different from the types of replicate weights that most statistical software packages can handle, Stata can process IPUMS-CPS replicate weights automatically as of version 11.1 (released June 3, 2010).

To use IPUMS-CPS replicate weights in R, you must use the srvyr package.

``install.packages("srvyr")library("srvyr")``

Next, you'll create a survey object using the replicate weights. The `as_survey` function has other arguments you can customize if needed.

(Video) R Tutorial: What are survey weights?

``svy <- as_survey(data, weight = ASECWT, repweights = matches("REPWTP[1-160]+"))``

Any calculations you'd like to make with the replicate weights can be done with the object 'svy' instead of the object 'data'.

To use IPUMS-CPS replicate weights in Stata, you must first `svyset` the data.

``. svyset [iw=ASECWT], sdrweight(repwtp1-repwtp160) vce(sdr) mse``
• The sample should be treated as a single stratum (the weights contain the relevant information from the sample design), so no PSU should be specified.
• The full-sample weight must be specified; some replicate weights in the CPS are negative, which is why `iweight`s are specified instead of `pweight`s.
• You then specify the replicate weights in the `sdrweight()` option. Note that specifying the variable list with a wildcard character ( `repwtp*` ) rather than with a range of variables ( `repwtp1-repwtp160` ) will not produce correct results because IPUMS-CPS data contain a variable called REPWTP, which merely indicates the presence of replicate weights and is coded 1 for every case. The `fpc()` suboption should not be specified.
• You must also specify the `vce(sdr)` option.

Earlier versions of Stata can also handle successive difference replicate weights. Correspondence with StataCorp statisticians and IPUMS testing revealed that successive difference replicate weights can be treated as jackknife replicate weights if the options are specified correctly.

The `svyset` command for Stata versions 11.0 and before is slightly different:

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``. svyset [iw=ASECWT], jkrweight(repwtp1-repwtp160, multiplier(.025)) /// vce(jackknife) mse``
• As above, the sample should be treated as a single stratum (the weights contain the relevant information from the sample design), so no PSU should be specified.
• Also as above, the full-sample weight must be specified; some replicate weights in the CPS are negative, which is why `iweight`s are specified instead of `pweight`s.
• You then specify the replicate weights in the `jkrw()` option. Note that specifying the variable list with a wildcard character ( `repwtp*`) rather than with a range of variables ( `repwtp1-repwtp160` ) will not produce correct results because IPUMS-CPS data contain a variable called REPWTP, which merely indicates the presence of replicate weights and is coded 1 for every case.
• The `multiplier()` suboption gives the quotient from the above formula (4/160 = 0.025). If you are not using CPS data and have a different number of replicate weights, you will need to adjust the multiplier accordingly.
• Neither the `stratum()` nor the `fpc()`suboptions should be specified.
• You must also specify the `vce(jack)` and `mse` options.

After `svyset`ting the data, you run the command using the `svy: `prefix, which passes along the options you defined above.

``. svy: command``

Stata will execute this command using the full-sample weights and again for each set of replicate weights. There are two important things to note:

• Not all Stata commands can be run with the `svy:` prefix. Type `. help svy_estimation` to see a list of valid commands.
• If you want to limit your replicate analyses to a subset of the sample (for example, all persons aged 25-64 or all African Americans), you should not use `if `or `in`. Instead, use the `subpop()` option before the colon, as in

``. gen byte age25_64 = age>=25 & age<=64. svy, subpop(age25_64): command``

Note that you must first define the subpopulation with a dichotomous variable coded 0 for all cases that should be excluded from the analysis. See this page for a helpful discussion of `subpop()` nuances.

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As of March 2010, SAS (version 9.2) and PASW/SPSS (version 18.0) cannot handle successive difference replicate weights. SPSS does not allow for replicate-based variance estimation unless it performs the resampling itself, and SAS's jackknife procedure (available in PROC SURVEYREG and related statements) does not contain the options needed to mimic the above formula. See the Census Bureau's "Estimating ASEC Variances with Replicate Weights" document for sample SAS code that can be adapted to calculate replicate standard errors manually.

### Can I simply divide the full sample into 160 random subsamples from the full sample and calculate replicate standard errors manually?

No. Replicate weights contain full information about the complex sample design of the CPS, and this information would be lost when drawing random subsamples. Furthermore, replicate samples incorporate information from all cases in the full sample. In contrast, random subsamples would each be 1/160th the size of a single replicate subsample.

### How are the CPS replicate weights calculated?

As mentioned, replicate weights in the CPS are constructed using the successive difference replication method (for cases in self-representing strata) and the modified half-sample technique (for cases in non-self-representing strata). Both involve creating a k x k Hadamard matrix (where k is the number of replicate weights desired), assigning sample cases to rows in the matrix and calculating a replicate factor from the row values, and finally multiplying the full-sample weight by these replicate factors. The replicate samples then undergo the same weighting procedures as the full sample--adjustments for noninterivews, oversampling, and the like. For more details, see the Census Bureau's "Estimating ASEC Variances with Replicate Weights" document as well as the following:

• Fay, Robert, and George Train. 1995. "Aspects of Survey and Model-Based Postcensal Estimation of Income and Poverty Characteristics for States and Counties." Proceedings of the Section on Government Statistics, American Statistical Association, Alexandria, VA, pp. 154-159. (pdf)
• Wolter, Kirk. 2007. Introduction to Variance Estimation, 2nd ed. New York: Springer. See Chapter 3.

(Video) Analysis using Survey Weights (Dr. Ernesto Amaral)

## FAQs

### Replicate Weights in the Current Population Survey? ›

Replicate weights allow a single sample to simulate multiple samples, thus generating more informed standard error estimates that mimic the theoretical basis of standard errors while retaining all information about the complex sample design.

How do you make replicate weights? ›

This involves creating a k x k Hadamard matrix (where k is the number of replicate weights desired), assigning sample cases to rows in the matrix and calculating a replicate factor from the row values, and finally multiplying the full-sample weight by these replicate factors.

How do you calculate weights for survey data? ›

The formula for creating a weight is simple — take the percentage of your population you are trying to re-create and divide it by the percentage population in your survey.

What does it mean to weight a survey? ›

Weighting is a correction technique that is used by survey researchers. It refers to statistical adjustments that are made to survey data after they have been collected in order to improve the accuracy of the survey estimates.

What is included in the current population survey? ›

The Current Population Survey (CPS) is a monthly survey that provides current estimates and trends in employment, unemployment, earnings, and other characteristics of the general labor force, the population as a whole, and various population subgroups.

What is a replicate weight data file? ›

Replicate weights contain full information about the complex sample design of the CPS, and this information would be lost when drawing random subsamples. Furthermore, replicate samples incorporate information from all cases in the full sample.

How do you apply weights to data? ›

How to weight data
1. View the representation of the sample.
2. Calculate the weight factors.
3. Apply data weights to sample proportions.
5. Finishing your research with unbiased results.

Why do we use weights in surveys? ›

Allows for a dataset to be corrected so that results more accurately represent the population being studied. Diminishes the effects of challenges during data collection or inherent biases of the survey mode being used.

How do you find the weighted mean in a survey questionnaire? ›

The weighted mean is calculated by multiplying the weight with the quantitative outcome and adding all the products. If all the weights are equal, then the weighted mean and arithmetic mean will be the same.

How do you apply weights to survey data in Excel? ›

Using SUMPRODUCT to Calculate Weighted Average in Excel
1. Enter your data into a spreadsheet then add a column containing the weight for each data point.
2. Type =SUMPRODUCT to start the formula and enter the values.
3. Click enter to get your results.
Apr 22, 2022

### What is a survey population weight? ›

What is a Survey Weight? A value assigned to each case in the data file. g • Normally used to make statistics computed from the data more representative of the population. E.g., the value indicates how much each case will count in a statistical procedure.

How do you calculate sample weight? ›

The formula to calculate the weights is W = T / A, where "T" represents the "Target" proportion, "A" represents the "Actual" sample proportions and "W" is the "Weight" value. The weights can be easily calculated using a spreadsheet or with a calculator.

Are survey weights needed? ›

If we wish to use our sample to calculate a descriptive statistic that accurately measures the true value in the population, then we need to weight. After all, this is the original purpose of sampling weights – to reverse the distortion imposed by the differential sampling probabilities.

Do I have to answer the current population survey? ›

Welcome to the Current Population Survey (CPS) respondents' web site. If you have been selected as a CPS respondent, your participation is critical in order to obtain the most accurate U.S. labor statistics, including the national unemployment rate.

Do I have to participate in the current population survey? ›

About 59,000 households are selected for the CPS each month, and it is a voluntary survey. Participation in the CPS is important because the answers represent thousands of other addresses and people.

What is an example of a population survey? ›

An example of this is a monthly labor force survey. Typically such a survey uses a rotating design where a sampled person is interviewed a number of times.

What is a replicate in data? ›

Data replication is the process of storing the same data in multiple locations. How and where your company copies and keeps data impacts how quickly and easily you can retrieve that data when needed.

What are individual replicate measurements? ›

Repeat and replicate measurements are both multiple response measurements taken at the same combination of factor settings; but repeat measurements are taken during the same experimental run or consecutive runs, while replicate measurements are taken during identical but different experimental runs, which are often ...

How do you use CPS weights? ›

To produce an estimate of a population level, simply sum the final CPS person weights for all sample persons having the desired characteristic. To make an estimate using a continuous variable (for example, hours worked or earnings), sum the variable multiplied by the weight for the appropriate set of persons.

What type of data is weights? ›

Quantitative data is numerical. It's used to define information that can be counted. Some examples of quantitative data include distance, speed, height, length and weight.

### What are sample weights in statistics? ›

Sampling weights are the number of individuals in the population each respondent in the sample is representing. A sample weight is the inverse of the probability of selection.

How do you weight more recent data? ›

The weighted moving average (WMA) is a technical indicator that assigns a greater weighting to the most recent data points, and less weighting to data points in the distant past. The WMA is obtained by multiplying each number in the data set by a predetermined weight and summing up the resulting values.

What are weighted questions? ›

Weighted questions is a feature that allows teachers to add different point values to questions in a quiz. Teachers can adjust the weight of a question when editing an existing quiz, or creating a new quiz in the Quizzes section.

What is the difference between weighted and unweighted survey? ›

The unweighted sample size is in fact the size of the only sample selected. The weighted sample size is nothing more than the size of the population represented by the sample, which is already known or can be easily calculated from the weights.

How do you assign weights to data points? ›

How to calculate weighted average
1. Determine the weight of each data point. You determine the weight of your data points by factoring in which numbers are most important. ...
2. Multiply the weight by each value. Once you know the weight of each value, multiply the weight by each data point. ...
3. Add the results of step two together.
Mar 16, 2023

How do you normalize survey weights? ›

Simply divide the survey weight of each unit used in the analysis by the (unweighted) average of the survey weights of all the analyzed units. In the previous example, there are 6 observations and the sum of the survey weights is 24, making the average 4. Therefore, we divide each weight by 4.

What is population weighted mean? ›

Population Weighted Density (PWD) is an alternative to conventional approaches to population density that is arguably better suited to some types of research in fields of social science and epidemiology.

What is the difference between survey and population? ›

In a census, data about all individual units (e.g. people or households) are collected in the population. In a survey, data are only collected for a sub-part of the population; this part is called a sample. These data are then used to estimate the characteristics of the whole population.

What does weight sample mean? ›

Weighted Mean is an average computed by giving different weights to some of the individual values. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. It represents the average of a given data. The Weighted mean is similar to the arithmetic mean or sample mean.

When should I weight my data? ›

When data must be weighted, weight by as few variables as possible. As the number of weighting variables goes up, the greater the risk that the weighting of one variable will confuse or interact with the weighting of another variable. When data must be weighted, try to minimize the sizes of the weights.

### What is the process of weighting? ›

The process of weighting involves emphasizing the contribution of particular aspects of a phenomenon (or of a set of data) over others to an outcome or result; thereby highlighting those aspects in comparison to others in the analysis.

Who conducts the current population survey? ›

The Current Population Survey is a joint effort between the Bureau of Labor Statistics and the Census Bureau.

What happens if you don t fill out census Community survey? ›

By census law, refusal to answer all or part of the census carries a \$100 fine. The penalty goes up to \$500 for giving false answers. In 1976, Congress eliminated both the possibility of a 60-day prison sentence for noncompliance and a one-year prison term for false answers.

What is the definition of current population? ›

: the whole number of people or inhabitants in a country or region. : the total of individuals occupying an area or making up a whole.

Do I have to participate? Participation in the Census of Population and the Census of Agriculture is mandatory pursuant to the Statistics Act. All Canadian households must complete a Census of Population questionnaire.

Can you refuse to answer a census question? ›

You may decline to answer any or all questions, but each item not answered lessens the quality of the final results. The Census Bureau field representatives need to interview every home in the survey sample to get a complete picture of the housing situation across the country.

Do I have to complete survey from Statistics Canada? ›

All residents of Canada are legally required to complete the census questionnaire, according to the Statistics Act. Census staff will begin contacting households that have not completed their census questionnaire in person or by phone.

What are the 3 ways to survey a population? ›

Methods of sampling from a population
• Simple random sampling. In this case each individual is chosen entirely by chance and each member of the population has an equal chance, or probability, of being selected. ...
• Systematic sampling. ...
• Stratified sampling. ...
• Clustered sampling.

What is the meaning of population survey? ›

In a full population survey, all individuals of a population are included in a study, for example in a survey or direct questioning (e.g. all of the students of a university). There is no selection made in the form of a sample.

What are the 4 types of population? ›

They are:
• Finite Population.
• Infinite Population.
• Existent Population.
• Hypothetical Population.
Feb 19, 2020

### How do sample weights work? ›

A sample weight is the inverse of the probability of selection. For example, if my simple random sample is one tenth of the population size (i.e. my sampling fraction is 1/10), then each respondent in the sample is representing 10 people in the population.

How do you replicate an experiment? ›

A replication experiment is typically performed by obtaining test results on 20 samples of the same material and then calculating the mean, standard deviation, and coefficient of variation. The purpose is to observe the variation expected in a test result under the normal operating conditions of the laboratory.

What are negative replicate weights in ACS? ›

The negative replicate weights are due to the addition of the Group Quarters (GQ) population to the full ACS weighting process. Within a weighting cell, GQ estimates were subtracted from population totals, sometimes resulting in negative values for the cell.

When should you use survey weights? ›

If we wish to use our sample to calculate a descriptive statistic that accurately measures the true value in the population, then we need to weight. After all, this is the original purpose of sampling weights – to reverse the distortion imposed by the differential sampling probabilities.

What is an example of a sampling weight? ›

Sampling weights are often thereciprocalof the likelihood of being sampled (i.e., selection probability) of the sampling unit. For example, if you have selected 200 goldfish out of a population of 1000, the reciprocal of the likelihood of being selected is 1000/200, so the sampling weight for the goldfish would be 5.

What is a replicate measurement? ›

Repeat and replicate measurements are both multiple response measurements taken at the same combination of factor settings; but repeat measurements are taken during the same experimental run or consecutive runs, while replicate measurements are taken during identical but different experimental runs, which are often ...

What is an example of replicability in research? ›

Replicability keeps researchers honest and can give readers confidence in research. For example, if a new research paper concludes that smoking is not related to lung cancer, readers would be very skeptical because it disagrees with the weight of existing evidence.

What is replication and example? ›

It is a molecular process taking place in dividing cells by which the DNA creates a copy of itself. Another use of the word “replication” in biology is about carrying out a similar procedure. The repetition of a laboratory procedure is an example in this regard.

Is the ACS weighted? ›

The ACS includes 160 replicate weights: 80 for the analysis of individuals, and 80 for the analysis of households.

What is CPS sampling weight? ›

The CPS estimation procedure involves weighting the data from each sample person. The base weight, which is the inverse of the probability of the person being in the sample, is a rough measure of the number of actual persons that the sample person represents.

### How are weights assigned in PCA? ›

The Weight by PCA operator generates attribute weights of the given ExampleSet using a component created by the PCA. The component is specified by the component number parameter. If the normalize weights parameter is not set to true, exact values of the selected component are used as attribute weights.

How do you assign weights to features? ›

The best way to do this is: Assume you have f[1,2,.. N] and weight of particular feature is w_f[0.12,0.14... N]. First of all, you need to normalize features by any feature scaling methods and then you need to also normalize the weights of features w_f to [0-1] range and then multiply the normalized weight by f[1,2,..

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