Skip to contents

PUMS 1: Calculate basic summaries

pums-1-basics.Rmd

What is Census microdata?

Along with publishing summary statistics from the decennial Census or American Community Survey (ACS), the Census Bureau also makes available a subset of individual person and housing (incl. household) records, called the Public Use Microdata Sample (PUMS). These can be used to estimate models or to tabulate custom statistics unavailable in Census-published summary statistics. Partly to safeguard privacy, PUMS data is not categorized by standard Census geographies such as block, block group or tract; instead the unit is the Public Use Microdata Area (PUMA), an aggregation of tracts with total population between 100,000-200,000. In the past there were more than one set of PUMAs, corresponding to different sampling rates; that is no longer the case (PUMAs now consistently represent a 5 percent sample).

PUMS data include sampling weights in order to be extrapolated to a larger population, and replication weights in order to calculate margins of error. When PUMS is used to drill down to small subsets of the population, particular attention should be paid to the margins of error in drawing any conclusions from the data; see section below. The Census Bureau resource What ACS Public Use Microdata Sample File Users Need to Know is a helpful resource if you have further questions about PUMS itself.

Retrieve PUMS data: get_psrc_pums()

The PSRC census package makes it easy to calculate standard summary statistics by county and for the region as a whole. Data analysis with the psrccensus package involves two steps:

The first step consists of retrieving the data of interest via the get_psrc_pums() function. The arguments are:

  • span - either 1 ,3 or 5, denoting the span of the desired ACS survey (1yr from 2000-present; 3yr from 2007-13; 5yr from 2009-present)
  • dyear - aka data year (concluding year for 3- or 5-yr ACS)
  • level - the unit of analysis; “p” is equivalent to “persons”, and “h” is equivalent to “households”
  • vars - one or more PUMS variables in UPPERCASE (if multiple, as a character vector)

The result of get_psrc_pums() is a structured data object (per the srvyr package) that has sampling and replication weights built in.

get_psrc_pums() must be called separately for each combination of span - dyear - level you intend to use. For example, if you want to calculate both household statistics and population statistics from the same survey (span and year), you will still need to use get_psrc_pums() once for households (level=“h”) and a second time for persons (‘level’=“p”). This is necessary because in PUMS, households and persons are not perfectly coextensive: household-level datasets do not contain persons living in group quarters and person-level datasets are not filtered to households. (Household datasets are further filtered to remove vacant units.) When you invoke get_psrc_pums() we suggest you assign a name that helps you differentiate between whatever span - dyear - level combinations are relevant to your analysis.

Although PUMS variables are measured specific to either persons or households, either unit of analysis can be associated with all variables–persons inherit their respective household attributes (albeit missing in the case of for group quarters), and households are, per Census Bureau convention, assigned the person attributes of the adult respondent (aka “householder; this is also true of published American Community Survey estimates). Variables must be typed exactly, so it is recommended to consult a PUMS data directory, especially since some variables may differ between data years. The PUMS data dictionary from 2017- forward is captured in the R object tidycensus::pums_variables (filter by year and survey). The Census Bureau also publishes each separate data dictionary online in html, pdf or txt, which can be easily searched via web browser.

Built-in PSRC variables

In addition to variables listed in the Census PUMS data dictionary, you can also select the following custom PSRC variables:

  • PRACE - person-level race/ethnicity in which Hispanic/Latino is its own race category (non-overlapping with other races)
  • HRACE - household-level race/ethnicity considering all members; ‘Multiple Races’ category as well as Hispanic/Latino
  • NWRK - number of workers in household (from composition of persons)
  • BINCOME - household income (HINCP) grouped by standard PSRC breakpoints
  • BIN_AGE - age (AGEP) grouped by standard PSRC breakpoints
  • BIN_POVRATIO - ratio of household income to the poverty level (POVPIP) w/ PSRC breakpoints (fraction, not percent)
  • BIN_YBL - year structure was built, by current ACS breakpoints (simplified from YBL)
  • OWN_RENT - dichotomous tenure (simplified from TEN)
  • ED_ATTAIN - educational attainment (simplified from SCHL)
  • MI_JOBSECTOR - PSRC-defined Manufacturing-Industrial groups (from NAICSP)
  • LUM_JOBSECTOR - PSRC-defined land use modeling employment sector (from NAICSP)
  • SOCP3 - Standard Occupational Code (SOC) minor group (from SOCP)
  • SOCP5 - Standard Occupational Code (SOC) broad occupation (from SOCP)

If codes change (and they have in the past), it may be necessary to confirm these custom variable definitions match the new data dictionary.

DATA_YEAR, PRODUCT, UNIT, and COUNTY variables are always included in the table without you having to specify them; the first three of these can be used to identify the dataset. It is also possible to define your own variables, as described in this accompanying article.

Built-in intra-survey inflation adjustment

Because the ACS (from which the PUMS records are developed) is a rolling survey, responses are collected at different times throughout the year and the value of money may have changed slightly during that time. Published ACS estimates have a ‘baked-in’ inflation adjustment (derived from the Federal Consumer Price Index, or CPI) to account for this. Dollar amounts in the PUMS dataset, however, are provided raw–as they were reported–along with an average inflation adjustment factor. Intra-survey inflation adjustment is particularly important for multi-year (3- and 5-yr) datasets. psrccensus applies the correct adjustment for you. PUMS estimates will not match their ACS counterparts precisely, but the adjustment brings them closer. A separate adjustment is still necessary if you intend to compare between separate surveys.

Generate summary statistics

The second step in an analysis involves calculating summary statistics from the result of the prior step. Because PUMS are sampled, summary statistics must use the sampling weight in order to be expanded to the full population. Although PUMS data exists for the entire country, results of psrccensus are filtered to the 4-county PSRC region for simplicity.

There are four relevant statistical functions, along with a summary function that gives all four in the same table.

         psrc_pums_count() (also includes shares, i.e. proportions by group)
         psrc_pums_sum()
         psrc_pums_median()
         psrc_pums_mean()
         psrc_pums_summary()

The arguments for each summary function are identical:

  • so - The srvyr data object returned by get_psrc_pums()
  • stat_var - The numeric variable to be summarized.
  • group_vars - Optional grouping variable/s (if multiple, as a character vector)

Argument names can be omitted (saving keystrokes) if arguments are provided in proper sequence; you may prefer to be explicit to avoid confusing them.

All result tables make use of the srvyr::cascade feature to provide totals at each grouping level; these are “peeled off” from last-grouped to first. If you have multiple grouping variables, the order in which you specify them will control how shares psrc_pums_count() are nested, for example. For any result with COUNTY as one of the grouping variables, it will be shifted to the left-most position in the table.

psrccensus does not constrain your choice of variables, but clearly any variable to be summarized must be a number, and grouping variables should not be continuous. The stat_var argument is ignored by the count function (for which the primary variable is implicit), but is allowed since some scripting will use identical arguments (e.g. map/apply functions).

Since PUMS records are sampled rather than comprising a full census, psrccensus applies sampling weights to deliver estimates of the full population. It also provides the tabulated margin of error (MOE) for each estimate in a separately labeled ’_moe’ column.

Examples

As an example, to calculate 2019 median household income for the region you would use the following function calls:

library(psrccensus)

x <- get_psrc_pums(span = 5,                     # Denoting ACS 5-year estimates; 1-year also available
                   dyear = 2019,                 # Last data year of span
                   level = "h",                  # Unit of analysis == household ("p" used for person)
                   vars = c("HINCP","TEN"))      # PUMS household income & housing tenure variables; using tenure later. 
                                                 #  - You can choose as many variables as you need.
psrc_pums_median(x, stat_var = "HINCP")          # Median Household income (without regard to tenure)

To calculate by a subgroup category (here, housing tenure–e.g. own vs. rent), use the optional grouping variable argument.

psrc_pums_median(x,                              # the assigned result of get_psrc_pums()
                 stat_var = "HINCP",             # Summarizing household income . . .
                 group_vars = "TEN",             # . . . grouped by housing tenure
                 rr=TRUE)                        # w/ optional relative reliability measure

The count function tabulates the number people or households by grouping category, depending on the level you specified in get_psrc_pums(). The result represents the population (via weighting), not the survey sample. If you intend to count things other than people or households, such as number of bedrooms, you should use the ‘total’ function instead, which sums the target variable.

psrc_pums_count(x, group_vars=c("COUNTY","TEN"))      # If omitting stat_var argument, group_var must be labeled

The summary function provides all four statistics and their margins of error in the same table.

psrc_pums_summary(x, "HINCP", "TEN") %>% print()

Notice the statistical functions leave the data object itself unchanged, so if desired it can be used repeatedly, with various grouping variable combinations (as long as they share the same unit of analysis–i.e. persons or households). As described in the accompanying article, the recommended workflow maintains the data object whole (rather than discarding observations specific to one analysis or another).

Sample sizes, confidence, and error margins

Although psrccensus allows you to specify multiple grouping variables, you’ll need to keep in mind that there are limits to what can be usefully determined from small subsets of respondents within PUMS. To draw responsible conclusions from PUMS data, you’ll need to examine the margins of error (MOE) psrccensus calculates along with the estimate. (This is when PUMS via psrccensus really shines, since it can be laborious to calculate the MOE without dedicated statistical software.) Margins of error in the PUMS are given in the same units as the estimate (as with ACS), so it is easy to get the bounds of the 90 percent confidence interval by both adding the MOE to the estimate and subtracting the MOE from it.

If there are few respondents in a category combination, the margin of error may be beyond calculation (NaN, or ‘not a number’), or so large that the estimate itself has little practical value. In these cases, you may want to consider either switching from the 1-year to 5-year span (the latter has a larger sample), potentially analyze dimensions of the data separately rather than in combination, or potentially change the categories you are using (e.g. use dplyr::mutate to create a less disaggregate variable).

Determining difference

Is there an actual difference between two statistics generated from PUMS data? To know, you’ll need to examine the margins of error. As a rule of thumb, if there is overlap in the 90 percent confidence intervals of the two estimates, you cannot conclude the values are different. To perform a more careful test, you can calculate the Z score: \[\frac{|Est_{1} - Est_{2}|}{\sqrt{MOE_{est1}^2 + MOE_{est2}^2}}\] There is only a meaningful difference between two estimates if the Z score is greater than 1. This test can be applied between different years, or between PUMS and ACS. However, please remember Census warns against drawing comparisons between estimates generated from different spans (e.g. 1yr with 5yr), especially if they overlap (as the same observations may be exist in both).

The z_score() convenience function performs this calculation:

rs <- psrc_pums_median(x, "HINCP", "TEN")
c1 <- rs[1,(ncol(rs)-1):ncol(rs)]                # First-line estimate and its MOE (as numeric vector)
c2 <- rs[3,(ncol(rs)-1):ncol(rs)]                # Third-line estimate and its MOE (as numeric vector)
z_score(c1, c2)                                  # A true difference indicated by score > 1