Using Weighted Data

1
Using Weighted Data

• Donald Miller
• Population Research Institute
• 812 Oswald Tower, 3-3155
• miller_at_pop.psu.edu
• December 2008

2
Review of David Johnsons Presentation

• A population weight (pweight) is a variable which
  indicates how many people (in the population of
  interest) an observation will count in a
  statistical procedure. This is different from a
  frequency weight (fweight), which indicates a row
  of a dataset actually represents more than one
  observation.
• Weights can be used to correct for design (over-
  and under- sampling), and for non-response bias.
• Most software packages treat pweights properly (a
  notable exception is SPSS outside of complex
  survey package).
• To create a pweight, use either a raking-type
  algorithm, or a logistic regression.

3
How to use Population Weights

• SAS
• Use the weight statement in procedures this
  is a population weight
• proc logistic datamydata descending
• model finishedage cs_educ sex
  race_white a1b a2b a3b a4b a5b a6b
• weight pwgt_variable
• run
• Stata
• Use the pweight option (you can use pw)
• regress y x1 x2 x3 pweightpwgt_variable

4
Raking 1 Select Census Data

• Choose a census dataset (CPS, ACS, etc.), and
  which variables you will use in your raking
  model. These are usually demographics variables
  (age, race, education, gender).
• You will need to recode your survey variables
  and/or the census variables so the response
  categories match. This might require grouping
  some values together.
• Match the year of the survey with the census
  data. If you have 2006 survey data, use the 2006
  census data.
• Match the physical area as closely as possible.
  For example, the ACS uses PUMA codes (basically
  county-level data). Select only the PUMA codes
  of the area of interest.
• You should probably do some simple descriptives /
  frequencies to compare survey to census.
  Remember the ACS already has a weight (PWGTP).

5
Raking 2 Frequencies (Census data)

• Construct 1-way frequency counts for every
  variable in the raking model. You need a dataset
  for each variable, with mrgtotal being the
  counts. SAS code example (do this for
  gender, race, etc.)
• proc freq dataacs.acs_myarea_recoded
• table cs_educ /list missing outcs_educ
• weight PWGTP
• run
• data cs_educ
• set cs_educ
• rename COUNTmrgtotal
• run

6
Raking 3 Raking Macro (SAS)

• Izrael, etc. has provided a SAS Macro (RAKINGE)
  to do the main raking procudure. This is
  introduced in Paper 258-25, from SAS SUGI 25.
  This is available online from SAS at
• http//www2.sas.com/proceedings/sugi25/25/st/2
  5p258.pdf
• Various improvements were made to macro and
  introduced in Paper 207-29, from SAS SUGI 29.
  This is available online from SAS at
• http//www2.sas.com/proceedings/sugi29/207-29.
  pdf
• I uploaded the (corrected version of the) RAKINGE
  macro here
• http//help.pop.psu.edu/help-by-statistical-m
  ethod/weighting

7
Raking 4 Raking Macro (SAS)

• You will need to save this macro, edit it
  slightly, and run it. The vast majority of the
  code you will never touch. Towards the top of
  the program you will need to change these lines
• macro rakinge (indsINPUTDATASETNAME,
• outdsOUTPUTDATASETNAME,
• ...
• outwtNEW_PWEIGHT_VARIABLE_NAME,
• ...
• varlistLIST OF VARIABLES IN RAKING MODEL,
• numvar4,

8
Normalized Weight

• If the raking macro does not converge, look at
  the frequencies (for census and survey) again.
  You may need to collapse some categories, or
  change the convergence criterion in the raking
  macro (you can control this with the TRMPCT and
  NUMITER options in the macro).
• You may wish to normalize the weight, so the
  sum of the weights for the dataset equal to a
  predetermined number N (either sample size or the
  areas total population). To do this, calculate
• SW the sum of the weights
• then multiply each weight value by N/SW.

9
Non-Response Bias 1

• The probability to survey completion may differ
  with people of different characteristics
  (demographics, chronic conditions, etc.). To
  address this non-response bias, estimate a
  logistic regression model such as the following
• FINISH ß0 ß1AGE ß2EDUCATION
• ß3FEMALE ß4WHITE ß5OTHER e
• Where FINISH is 1 if they finished the survey (0
  otherwise). The next four values are from the
  raking model. The next value (OTHER, there can
  be more than one of these) are other variables
  which might explain non-response bias.

10
Non-Response Bias 2

• For each respondent, the non-response bias weight
  is the reciprocal of the predicted probability of
  survey completion. It is treated as a weight,
  and should be multiplied with the raking weight
  to create a total weight.
• Sample SAS code (continued next slide)
• proc logistic dataarea_weighted descending
• class finish
• model finishage cs_educ sex race_white a1b
• output outlogitresults pp
• weight pwgt
• run / check output to see if significant /

11
Non-Response Bias 3

• (SAS code continued)
• proc sort datalogitresults
• by ID
• run
• data area_weighted2 / merge in pred. prob.
  /
• merge area_weighted logitresults
• by ID
• run
• data area_weighted2 / calculate non-resp
  wgt /
• set area_weighted2
• nonresp_wgt1/p
• total_wgtpwgtnonresp_wgt
• run

12
Stata / R

• I personally havent tried either of these yet,
  but raking packages exist for Stata and R
• Stata
• survwgt - you can get and install this using
  findit
• survwgt rake pw , by(varlist_raking_model)
• totvars(varlist_totals) generate(pwgt)
  replace
• R
• Rake package
• sraked_data lt- simpleRake(unraked_data,
  pop_totals, rake_var1, rakevar2, ...,
• TRUE)