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.
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] -0.003837163and 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 62984824where
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 Trumptot_votes: Total turnoutcces_pct_djt_vv: Estimated vote share,cces_totdjt_vv / cces_n_vvpct_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] -0.0086086072so 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 rowsA negative ρ means ρ = Cor(Respond, 1(Trump Supporter)) \< 0, i.e. Trump supporters were less likely to respond.