16-cs02-eda

Professor Shannon Ellis

2023-11-28

CS02: Predicting Air Pollution (EDA)

Q&A

Q: I’m a bit unclear about the direction of case studies. Do just try to visualize data differently to find out the best biomarkers or do we use other methods like modeling to do so?
A: A little bit of both. If you can rule out a matrix/compound during EDA by looking at visualizations, do that. But, once you have a set of compounds that you want to include for analysis, then you would turn to sensitivity/specificity/ROC curves to help you decide. Modelling is also an option.

Q: I saw in the dataset, in some variables I think it’s the log values ( so I assumed it’s already normalized?). Why is it better to use the log data and not the raw values?
A: Great question! We’ll get to this a bit today!

Q: If the monitors are not localized at the granularity of zip code level, how do we assess the accuracy of our predictions? Seems like we can’t know the correct result.
A: We’ll get to this in the next set of notes!

Course Announcements

  • CS01 due Thursday (group work survey due Friday)
  • Lab07 due Friday
  • CS02 due next Friday
  • Final Project due Tues of Finals week (report + presentation)

Vote:

  • Option 1: Continue as planned cs01 (12.5) + cs02 (12.5) + final project (18)
  • Option 2:
    • CS01 due Thursday (17)
    • Complete either CS02 w/ external data req’d for extension OR Final Project (with final project group; due Finals week) (26)

CS02 and Final Project repos + emails went out yesterday

  • please look for your repo/make sure you have access!
  • please get in communication with your groups if you’re not already in communication

Question

Can we predict US annual average air pollution concentrations at the granularity of zip code regional levels using predictors such as data about population density, urbanization, road density, as well as, satellite pollution data and chemical modeling data?

EDA

Getting to “know” the data

The Data

pm <- readr::read_csv(here::here("OCS_data", "data","raw", "pm25_data.csv"))

skimr

skimr::skim(pm)
Data summary
Name pm
Number of rows 876
Number of columns 50
_______________________
Column type frequency:
character 3
numeric 47
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
state 0 1 4 20 0 49 0
county 0 1 3 20 0 471 0
city 0 1 4 48 0 607 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
id 0 1 26987.96 1.578761e+04 1003.00 13089.15 26132.00 39118.00 5.603910e+04 ▇▇▆▇▆
value 0 1 10.81 2.580000e+00 3.02 9.27 11.15 12.37 2.316000e+01 ▂▆▇▁▁
fips 0 1 26987.89 1.578763e+04 1003.00 13089.00 26132.00 39118.00 5.603900e+04 ▇▇▆▇▆
lat 0 1 38.48 4.620000e+00 25.47 35.03 39.30 41.66 4.840000e+01 ▁▃▅▇▂
lon 0 1 -91.74 1.496000e+01 -124.18 -99.16 -87.47 -80.69 -6.804000e+01 ▃▂▃▇▃
CMAQ 0 1 8.41 2.970000e+00 1.63 6.53 8.62 10.24 2.313000e+01 ▃▇▃▁▁
zcta 0 1 50890.29 2.778447e+04 1022.00 28788.25 48172.00 74371.00 9.920200e+04 ▅▇▇▅▇
zcta_area 0 1 183173481.91 5.425989e+08 15459.00 14204601.75 37653560.50 160041508.25 8.164821e+09 ▇▁▁▁▁
zcta_pop 0 1 24227.58 1.777216e+04 0.00 9797.00 22014.00 35004.75 9.539700e+04 ▇▇▃▁▁
imp_a500 0 1 24.72 1.934000e+01 0.00 3.70 25.12 40.22 6.961000e+01 ▇▅▆▃▂
imp_a1000 0 1 24.26 1.802000e+01 0.00 5.32 24.53 38.59 6.750000e+01 ▇▅▆▃▁
imp_a5000 0 1 19.93 1.472000e+01 0.05 6.79 19.07 30.11 7.460000e+01 ▇▆▃▁▁
imp_a10000 0 1 15.82 1.381000e+01 0.09 4.54 12.36 24.17 7.209000e+01 ▇▃▂▁▁
imp_a15000 0 1 13.43 1.312000e+01 0.11 3.24 9.67 20.55 7.110000e+01 ▇▃▁▁▁
county_area 0 1 3768701992.12 6.212830e+09 33703512.00 1116536297.50 1690826566.50 2878192209.00 5.194723e+10 ▇▁▁▁▁
county_pop 0 1 687298.44 1.293489e+06 783.00 100948.00 280730.50 743159.00 9.818605e+06 ▇▁▁▁▁
log_dist_to_prisec 0 1 6.19 1.410000e+00 -1.46 5.43 6.36 7.15 1.045000e+01 ▁▁▃▇▁
log_pri_length_5000 0 1 9.82 1.080000e+00 8.52 8.52 10.05 10.73 1.205000e+01 ▇▂▆▅▂
log_pri_length_10000 0 1 10.92 1.130000e+00 9.21 9.80 11.17 11.83 1.302000e+01 ▇▂▇▇▃
log_pri_length_15000 0 1 11.50 1.150000e+00 9.62 10.87 11.72 12.40 1.359000e+01 ▆▂▇▇▃
log_pri_length_25000 0 1 12.24 1.100000e+00 10.13 11.69 12.46 13.05 1.436000e+01 ▅▃▇▇▃
log_prisec_length_500 0 1 6.99 9.500000e-01 6.21 6.21 6.21 7.82 9.400000e+00 ▇▁▂▂▁
log_prisec_length_1000 0 1 8.56 7.900000e-01 7.60 7.60 8.66 9.20 1.047000e+01 ▇▅▆▃▁
log_prisec_length_5000 0 1 11.28 7.800000e-01 8.52 10.91 11.42 11.83 1.278000e+01 ▁▁▃▇▃
log_prisec_length_10000 0 1 12.41 7.300000e-01 9.21 11.99 12.53 12.94 1.385000e+01 ▁▁▃▇▅
log_prisec_length_15000 0 1 13.03 7.200000e-01 9.62 12.59 13.13 13.57 1.441000e+01 ▁▁▃▇▅
log_prisec_length_25000 0 1 13.82 7.000000e-01 10.13 13.38 13.92 14.35 1.523000e+01 ▁▁▃▇▆
log_nei_2008_pm25_sum_10000 0 1 3.97 2.350000e+00 0.00 2.15 4.29 5.69 9.120000e+00 ▆▅▇▆▂
log_nei_2008_pm25_sum_15000 0 1 4.72 2.250000e+00 0.00 3.47 5.00 6.35 9.420000e+00 ▃▃▇▇▂
log_nei_2008_pm25_sum_25000 0 1 5.67 2.110000e+00 0.00 4.66 5.91 7.28 9.650000e+00 ▂▂▇▇▃
log_nei_2008_pm10_sum_10000 0 1 4.35 2.320000e+00 0.00 2.69 4.62 6.07 9.340000e+00 ▅▅▇▇▂
log_nei_2008_pm10_sum_15000 0 1 5.10 2.180000e+00 0.00 3.87 5.39 6.72 9.710000e+00 ▂▃▇▇▂
log_nei_2008_pm10_sum_25000 0 1 6.07 2.010000e+00 0.00 5.10 6.37 7.52 9.880000e+00 ▁▂▆▇▃
popdens_county 0 1 551.76 1.711510e+03 0.26 40.77 156.67 510.81 2.682191e+04 ▇▁▁▁▁
popdens_zcta 0 1 1279.66 2.757490e+03 0.00 101.15 610.35 1382.52 3.041884e+04 ▇▁▁▁▁
nohs 0 1 6.99 7.210000e+00 0.00 2.70 5.10 8.80 1.000000e+02 ▇▁▁▁▁
somehs 0 1 10.17 6.200000e+00 0.00 5.90 9.40 13.90 7.220000e+01 ▇▂▁▁▁
hs 0 1 30.32 1.140000e+01 0.00 23.80 30.75 36.10 1.000000e+02 ▂▇▂▁▁
somecollege 0 1 21.58 8.600000e+00 0.00 17.50 21.30 24.70 1.000000e+02 ▆▇▁▁▁
associate 0 1 7.13 4.010000e+00 0.00 4.90 7.10 8.80 7.140000e+01 ▇▁▁▁▁
bachelor 0 1 14.90 9.710000e+00 0.00 8.80 12.95 19.22 1.000000e+02 ▇▂▁▁▁
grad 0 1 8.91 8.650000e+00 0.00 3.90 6.70 11.00 1.000000e+02 ▇▁▁▁▁
pov 0 1 14.95 1.133000e+01 0.00 6.50 12.10 21.22 6.590000e+01 ▇▅▂▁▁
hs_orless 0 1 47.48 1.675000e+01 0.00 37.92 48.65 59.10 1.000000e+02 ▁▃▇▃▁
urc2013 0 1 2.92 1.520000e+00 1.00 2.00 3.00 4.00 6.000000e+00 ▇▅▃▂▁
urc2006 0 1 2.97 1.520000e+00 1.00 2.00 3.00 4.00 6.000000e+00 ▇▅▃▂▁
aod 0 1 43.70 1.956000e+01 5.00 31.66 40.17 49.67 1.430000e+02 ▃▇▁▁▁

Why 49 “states”?

pm %>% 
  distinct(state) 
# A tibble: 49 × 1
   state               
   <chr>               
 1 Alabama             
 2 Arizona             
 3 Arkansas            
 4 California          
 5 Colorado            
 6 Connecticut         
 7 Delaware            
 8 District Of Columbia
 9 Florida             
10 Georgia             
# ℹ 39 more rows
  • DC is included
  • Alaska and Hawaii are not

Number of monitors per city?

pm %>% filter(city == "San Diego")
# A tibble: 2 × 50
     id value  fips   lat   lon state      county    city   CMAQ  zcta zcta_area
  <dbl> <dbl> <dbl> <dbl> <dbl> <chr>      <chr>     <chr> <dbl> <dbl>     <dbl>
1 6073.  11.3  6073  32.8 -117. California San Diego San …  9.68 92123  21148247
2 6073.  13.7  6073  32.7 -117. California San Diego San …  9.68 92113  13647793
# ℹ 39 more variables: zcta_pop <dbl>, imp_a500 <dbl>, imp_a1000 <dbl>,
#   imp_a5000 <dbl>, imp_a10000 <dbl>, imp_a15000 <dbl>, county_area <dbl>,
#   county_pop <dbl>, log_dist_to_prisec <dbl>, log_pri_length_5000 <dbl>,
#   log_pri_length_10000 <dbl>, log_pri_length_15000 <dbl>,
#   log_pri_length_25000 <dbl>, log_prisec_length_500 <dbl>,
#   log_prisec_length_1000 <dbl>, log_prisec_length_5000 <dbl>,
#   log_prisec_length_10000 <dbl>, log_prisec_length_15000 <dbl>, …
pm %>% filter(city == "Baltimore")
# A tibble: 5 × 50
      id value  fips   lat   lon state    county     city   CMAQ  zcta zcta_area
   <dbl> <dbl> <dbl> <dbl> <dbl> <chr>    <chr>      <chr> <dbl> <dbl>     <dbl>
1 24510.  12.2 24510  39.3 -76.6 Maryland Baltimore… Balt…  10.9 21251    461424
2 24510.  12.5 24510  39.3 -76.7 Maryland Baltimore… Balt…  10.9 21215  17645223
3 24510.  12.8 24510  39.3 -76.5 Maryland Baltimore… Balt…  10.9 21224  24539976
4 24510.  14.3 24510  39.2 -76.6 Maryland Baltimore… Balt…  10.9 21226  25718732
5 24510.  13.3 24510  39.3 -76.6 Maryland Baltimore… Balt…  10.9 21202   4111039
# ℹ 39 more variables: zcta_pop <dbl>, imp_a500 <dbl>, imp_a1000 <dbl>,
#   imp_a5000 <dbl>, imp_a10000 <dbl>, imp_a15000 <dbl>, county_area <dbl>,
#   county_pop <dbl>, log_dist_to_prisec <dbl>, log_pri_length_5000 <dbl>,
#   log_pri_length_10000 <dbl>, log_pri_length_15000 <dbl>,
#   log_pri_length_25000 <dbl>, log_prisec_length_500 <dbl>,
#   log_prisec_length_1000 <dbl>, log_prisec_length_5000 <dbl>,
#   log_prisec_length_10000 <dbl>, log_prisec_length_15000 <dbl>, …

San Diego has 2, while Baltimore has 5, despite having very similar population densities (popdens_county)…and San Diego having a much larger population (county_pop) and land area (county_area).

Feature Correlation

Why do we care if variables in our dataset are correlated?

  • we don’t want to include redundant variables
  • can add unnecessary noise to our algorithm causing a reduction in prediction accuracy
  • can cause our algorithm to be slower
  • can also make it difficult to interpret what variables are actually predictive

Taking a look at our numeric variables…

PM_cor <- cor(pm %>% dplyr::select_if(is.numeric))
corrplot::corrplot(PM_cor, tl.cex = 0.5)

  • deep blue | strongly, positively correlated
  • deep red | strongly, negatively correlated

If we don’t care about direction, but only strength…and using hierarchical clustering:

corrplot::corrplot(abs(PM_cor), order = "hclust", tl.cex = 0.5, cl.lim = c(0, 1))

Observations:

  • development variables (imp), road density (pri), and the emission (nei) variables all seem to be correlated with their group
  • none of the predictors are correlated with value (our outcome)

Development (imp)

# we used GGally in a previous set of notes
# will need to install if you haven't yet
select(pm, contains("imp")) %>%
  GGally::ggpairs()

Emmissoins (nei)

select(pm, contains("nei")) %>%
  GGally::ggpairs()

Road Density (pri)

select(pm, contains("pri")) %>%
  GGally::ggcorr(hjust = .85, size = 3,
       layout.exp=2, label = TRUE)

Warning: colors are reversed from above. If included in final report, you’d want consistency.

Are the categories correlated with one another?

pm %>%
select(log_nei_2008_pm25_sum_10000, popdens_county, 
       log_pri_length_10000, imp_a10000, county_pop) %>%
  GGally::ggpairs()

Reminder:

  • log_nei_2008_pm25_sum_10000 | Tons of emissions from major sources data base (annual data) sum of all sources within a circle with a radius of 10000 meters of distance around the monitor (Natural log)
  • popdens_county | Population density (number of people per kilometer squared area of the county)
  • log_pri_length_10000 | Count of primary road length in meters in a circle with a radius of 10000 meters around the monitor (Natural log)
    – Highways only
  • imp_a10000 | Impervious surface measure
    – Within a circle with a radius of 10000 meters around the monitor
  • county_pop | Population of the county of the monitor

Log-transforming right-skewed data

pm %>%
  mutate(log_popdens_county=log(popdens_county),
         log_pop_county = log(county_pop)) %>%
  select(log_nei_2008_pm25_sum_10000, log_popdens_county, 
       log_pri_length_10000, imp_a10000, log_pop_county) %>%
  GGally::ggpairs()

Your Turn

💪 Try to learn at least three things about the data that we haven’t yet discussed now on your own.

Outcome variable

summary(pm$value)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.024   9.268  11.153  10.808  12.369  23.161 
ggplot(pm, aes(value)) + geom_histogram()

What do we know about the monitors that have very high values?

pm |> 
  filter(value > 20) |>
  select(state) 
# A tibble: 6 × 1
  state     
  <chr>     
1 California
2 California
3 California
4 California
5 California
6 California

https://cogs137.github.io/website/