README.md

In kuriwaki/ddi: The Data Defect Index for Samples that May not be IID

ddi: The Data Defect Index for Samples that May not be iid

A simple set of functions to implement the Data Defect Index (d.d.i.), described in:

Xiao-Li Meng. 2018. “Statistical Paradises and Paradoxes in big data (I): Law of Large Populations, Big Data Paradox, and the 2016 US Presidential Election.” Annals of Applied Statistics 12:2, 685–726. doi:10.1214/18-AOAS1161SF.

(ungated version)

Install

This package is currently on CRAN (0.1.0).

install.packages("ddi")

Development versions can be downloaded via:

remotes::install_github("kuriwaki/ddi")

Usage

With a dataframe with columns for a group’s estimates and components of the formula, ddc computes the data defect correlation (ρ).

An example dataset from the 2016 US Presidential Election is included (this also serves as the replication dataset for the AOAS article). The dataset compares official election results with estimates the Cooperative Congressional Election Study (CCES), the largest political survey in the US. The CCES micro-data is fully public and accessible at its website. Here, we produce state-level estimates which are documented with help(g2016).

library(ddi)
library(tidyverse)

data(g2016)
g2016

## # A tibble: 51 x 11
##    state st    pct_djt_voters cces_totdjt_vv cces_pct_djt_vv cces_pct_djtrun…
##    <chr> <chr>          <dbl>          <dbl>           <dbl>            <dbl>
##  1 Alab… AL            0.621             159          0.408            0.428 
##  2 Alas… AK            0.513              22          0.306            0.319 
##  3 Ariz… AZ            0.487             372          0.423            0.445 
##  4 Arka… AR            0.606             117          0.416            0.434 
##  5 Cali… CA            0.316             899          0.285            0.305 
##  6 Colo… CO            0.433             232          0.350            0.371 
##  7 Conn… CT            0.409             111          0.294            0.318 
##  8 Dela… DE            0.419              50          0.329            0.349 
##  9 Dist… DC            0.0409              5          0.0575           0.0690
## 10 Flor… FL            0.490            1107          0.403            0.422 
## # … with 41 more rows, and 5 more variables: votes_djt <dbl>, tot_votes <dbl>,
## #   cces_n_vv <dbl>, vap <dbl>, vep <dbl>

We can compute the data defect correlation just by plugging in some numbers. For example

ddc(mu = 62984824/136639786, muhat = 12284/35829, N = 136639786, n = 35829)

## [1] -0.003837163

and the d.d.i. is the square of that, about 0.0000147.

we got these numbers by

select(g2016, cces_pct_djt_vv, cces_n_vv, tot_votes, votes_djt) %>%
  summarize_all(sum)

## # A tibble: 1 x 4
##   cces_pct_djt_vv cces_n_vv tot_votes votes_djt
##             <dbl>     <dbl>     <dbl>     <dbl>
## 1            17.5     35829 136639786  62984824

where

• cces_totdjt_vv: The count of Trump voters (among validated voters)
• cces_n_vv: The count of CCES validated voters (sample size)
• votes_djt: Total votes for Trump
• tot_votes: Total turnout
• cces_pct_djt_vv: Estimated vote share, cces_totdjt_vv / cces_n_vv
• pct_djt_voters: Estimated vote share, votes_djt / tot_votes

The function also takes vectors as inputs:

with(g2016, ddc(mu = pct_djt_voters,
                muhat = cces_pct_djt_vv, 
                N = tot_votes, 
                n = cces_n_vv))

##  [1] -0.0059541279 -0.0062341071 -0.0023488019 -0.0061097707 -0.0009864919
##  [6] -0.0025746344 -0.0035362241 -0.0033951165  0.0014015382 -0.0029747918
## [11] -0.0038228152 -0.0001757426 -0.0073716139 -0.0036437192 -0.0069956521
## [16] -0.0058255411 -0.0059093759 -0.0057837854 -0.0040533230 -0.0047893714
## [21] -0.0024905368 -0.0028280876 -0.0050296619 -0.0043292576 -0.0056626724
## [26] -0.0069305025 -0.0046563153 -0.0075840944 -0.0047785897 -0.0037497506
## [31] -0.0028289070 -0.0025619899 -0.0031936586 -0.0051968951 -0.0078308914
## [36] -0.0057088185 -0.0065654840 -0.0030642004 -0.0039137353 -0.0039907269
## [41] -0.0040871158 -0.0069019981 -0.0050741833 -0.0044884762 -0.0059634270
## [46] -0.0034491625 -0.0040918085 -0.0024121681 -0.0075404659 -0.0051378753
## [51] -0.0086086072

so can be implemented in a tibble as well:

transmute(g2016, st,
          ddc = ddc(mu = pct_djt_voters, 
                    muhat = cces_pct_djt_vv, 
                    N = tot_votes,
                    n = cces_n_vv))

## # A tibble: 51 x 2
##    st          ddc
##    <chr>     <dbl>
##  1 AL    -0.00595 
##  2 AK    -0.00623 
##  3 AZ    -0.00235 
##  4 AR    -0.00611 
##  5 CA    -0.000986
##  6 CO    -0.00257 
##  7 CT    -0.00354 
##  8 DE    -0.00340 
##  9 DC     0.00140 
## 10 FL    -0.00297 
## # … with 41 more rows

A negative ρ means ρ = Cor(Respond, 1(Trump Supporter)) \< 0, i.e. Trump supporters were less likely to respond.

kuriwaki/ddi documentation built on May 16, 2020, 12:47 p.m.