class: center, middle, inverse, title-slide .title[ # Multivariate Analysis ] .subtitle[ ## Part 2b: More Visualizations! ] .author[ ### Prof. Weldzius ] .institute[ ### Villanova University ] --- <style type="text/css"> .small .remark-code { /*Change made here*/ font-size: 85% !important; } .tiny .remark-code { /*Change made here*/ font-size: 50% !important; } </style> # Agenda 1. Overtime Polls + `weighted.mean()` 2. Predicting winner with Electoral College Votes --- # 2020 polling -- - Back into the data! -- - Download and open [`Pres2020_PV.Rds`](https://github.com/rweldzius/PSC4175/raw/main/static/data/Pres2020_PV.Rds) - Wrangle to get the popular vote margin, expressed in decimals -- ``` r require(tidyverse) poll <- read_rds('https://github.com/rweldzius/PSC4175/raw/main/static/data/Pres2020_PV.Rds') poll <- poll %>% mutate(Trump = Trump/100, Biden = Biden/100, margin = Biden - Trump) ``` --- # .blue[Theory] -- - Previous results indicate that polls which predict greater support for Biden **also** predict greater support for Trump -- - Is this consistent with the theory? -- - Recall that **Biden-biased** polls should underpredict Trump support and overpredict Biden support -- - In the .red[data], this would suggest a **negative** relationship -- - But we find a **positive** relationship -- - **Inconsistent** with the theory, but raises another puzzle -- - Why do polls that underpredict support for Biden also underpredict support for Trump? -- - .blue[Third party bias?] Polls bias against 3rd party candidates -- - .blue[Timing of poll?] Fewer uncertain responses closer to election --- # Dates and More Dimensions -- - To test the .blue[timing of polls theory], let's look at how predicted support varies over time -- ``` r poll %>% select(StartDate,EndDate,DaysinField) ``` ``` ## # A tibble: 528 × 3 ## StartDate EndDate DaysinField ## <chr> <chr> <dbl> ## 1 10/31/2020 11/2/2020 3 ## 2 10/31/2020 11/2/2020 3 ## 3 10/29/2020 11/2/2020 5 ## 4 11/1/2020 11/1/2020 1 ## 5 11/1/2020 11/1/2020 1 ## 6 10/30/2020 11/1/2020 3 ## 7 10/31/2020 11/2/2020 3 ## 8 10/30/2020 11/1/2020 3 ## 9 10/29/2020 11/1/2020 4 ## 10 10/29/2020 11/1/2020 4 ## # ℹ 518 more rows ``` --- # Dates -- - Need to convert `StartDate` and `EndDate` into `date` class -- ``` r election.day <- as.Date("11/3/2020", "%m/%d/%Y") election.day ``` ``` ## [1] "2020-11-03" ``` ``` r election.day16 <- as.Date("11/8/2016", "%m/%d/%Y") election.day16 ``` ``` ## [1] "2016-11-08" ``` ``` r election.day - election.day16 ``` ``` ## Time difference of 1456 days ``` --- # Wrangling ``` r toplot <- poll %>% mutate(EndDate = as.Date(EndDate, "%m/%d/%Y"), StartDate = as.Date(StartDate, "%m/%d/%Y"), DaysToED = as.numeric(election.day - EndDate), margin = Biden - Trump) ``` -- - How many polls were conducted over time? --- ## Polls by Date (`geom_bar`) ``` r toplot %>% ggplot(aes(x = StartDate)) + geom_bar() + labs(title = 'Number of 2020 Polls by Date',x = 'Start Date of Poll',y = 'Number of Polls') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-7-1.png" style="display: block; margin: auto;" /> --- ## Polls by Date (`geom_histogram`) ``` r toplot %>% ggplot(aes(x = StartDate)) + geom_histogram(bins = 30,color = 'white') + labs(title = 'Number of 2020 Polls by Date',x = 'Start Date of Poll',y = 'Number of Polls') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-8-1.png" style="display: block; margin: auto;" /> --- ## Polls by Time to Election ``` r toplot %>% ggplot(aes(x = DaysToED)) + geom_histogram(bins = 30,color = 'white') + labs(title = 'Number of 2020 Polls Over Time',x = 'Days to Election',y = 'Number of Polls') + scale_x_reverse() ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-9-1.png" style="display: block; margin: auto;" /> --- ## Margin by Time to Election ``` r toplot %>% ggplot(aes(x = DaysToED,y = margin)) + * geom_point() + labs(title = 'Biden Margin in 2020 Polls Over Time', x = 'Days to Election',y = 'Margin: Biden - Trump') + scale_x_reverse() + geom_hline(yintercept = 0,linetype = 'dashed') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-10-1.png" style="display: block; margin: auto;" /> --- ## Margin by Time to Election ``` r toplot %>% ggplot(aes(x = DaysToED,y = margin)) + * geom_point(alpha = .3,size = 3) + labs(title = 'Biden Margin in 2020 Polls Over Time', x = 'Days to Election',y = 'Margin: Biden - Trump') + scale_x_reverse() + geom_hline(yintercept = 0,linetype = 'dashed') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-11-1.png" style="display: block; margin: auto;" /> --- ## Margin by Time to Election ``` r toplot %>% ggplot(aes(x = DaysToED,y = margin)) + * geom_jitter(height = .005) + labs(title = 'Biden Margin in 2020 Polls Over Time', x = 'Days to Election',y = 'Margin: Biden - Trump') + scale_x_reverse() + geom_hline(yintercept = 0,linetype = 'dashed') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-12-1.png" style="display: block; margin: auto;" /> --- ## Highlight Trends ``` r toplot %>% ggplot(aes(x = DaysToED,y = margin)) + * geom_point(alpha = .3) + geom_line() + labs(title = 'Biden Margin in 2020 Polls Over Time', x = 'Days to Election',y = 'Margin: Biden - Trump') + scale_x_reverse() + geom_hline(yintercept = 0,linetype = 'dashed') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-13-1.png" style="display: block; margin: auto;" /> --- ## Highlight Trends ``` r toplot %>% ggplot(aes(x = DaysToED,y = margin)) + * geom_point(alpha = .3) + geom_smooth() + labs(title = 'Biden Margin in 2020 Polls Over Time', x = 'Days to Election',y = 'Margin: Biden - Trump') + scale_x_reverse() + geom_hline(yintercept = 0,linetype = 'dashed') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-14-1.png" style="display: block; margin: auto;" /> --- ## Highlight Trends ``` r toplot %>% ggplot(aes(x = DaysToED,y = margin)) + * geom_point(alpha = .3) + geom_smooth(span = .1) + labs(title = 'Biden Margin in 2020 Polls Over Time', x = 'Days to Election',y = 'Margin: Biden - Trump') + scale_x_reverse() + geom_hline(yintercept = 0,linetype = 'dashed') ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-15-1.png" style="display: block; margin: auto;" /> --- # Multiple Variables over time -- - We can look at multiple continuous variables at the same time -- - Use `color` or `fill` to distinguish ``` r BidenTrumpplot <- toplot %>% ggplot() + geom_point(aes(x = EndDate, y = Trump), color = "red", alpha=.4) + geom_point(aes(x = EndDate, y = Biden), color = "blue", alpha=.4) + labs(title="% Support for Biden (blue) and Trump (red)", subtitle = "2020 National Popular Vote Polls Over Time", y = "Pct. Support", x = "Poll Ending Date") + scale_x_date(date_breaks = "2 week", date_labels = "%b %d") + scale_y_continuous(breaks=seq(.3,.7,by=.05), labels= scales::percent_format(accuracy = 1)) ``` --- # Multiple Variables over time ``` r BidenTrumpplot ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-17-1.png" style="display: block; margin: auto;" /> --- # Highlighting Trends ``` r BidenTrumpplot + geom_smooth(aes(x = EndDate, y = Trump), color = "red",se=T) + geom_smooth(aes(x = EndDate, y = Biden), color = "blue",se=T) ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-18-1.png" style="display: block; margin: auto;" /> --- # Let's go back to .blue[theory] -- - Evidence of **both** Biden and Trump support increasing toward election -- - Does this mean third party support waned? -- - Does this mean that undecided voters made a decision? --- # 2. Overtime Errors - Wrangling to convert character dates to `date` class -- - Plotting prediction errors over time ``` r toplot <- poll %>% mutate(EndDate = as.Date(EndDate, "%m/%d/%Y"), StartDate = as.Date(StartDate, "%m/%d/%Y"), DaysToED = as.numeric(as.Date('11/3/2020',format = '%m/%d/%Y') - EndDate), margin = Biden - Trump, * errDem = Biden - DemCertVote / 100, * errRep = Trump - RepCertVote / 100) ``` --- # Overtime Errors - Wrangling to convert character dates to `date` class - Plotting prediction errors over time ``` r pErrOverTime_Raw <- toplot %>% ggplot(aes(x = StartDate)) + geom_point(aes(y = errDem),color = 'blue') + geom_point(aes(y = errRep),color = 'red') + geom_hline(yintercept = 0,linetype = 'dashed') + geom_smooth(aes(y = errDem),color = 'blue') + geom_smooth(aes(y = errRep),color = 'red') + labs(title = 'Error Over Time',subtitle = 'Raw Prediction Error',x = 'Start Date',y = 'Prediction Error') + ylim(c(-.2,.1)) ``` --- # Overtime Errors ``` r pErrOverTime_Raw ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-21-1.png" style="display: block; margin: auto;" /> --- # Poll Quality - Polls got better -- - ...but more for Biden than for Trump -- - Poll quality: -- - Sample size - "Margin of Error" (`MoE`) --- # Weighting by Sample Size ``` r pErrOverTime_SampleSize <- toplot %>% group_by(StartDate) %>% * summarise(errDem = weighted.mean(errDem,w = SampleSize), * errRep = weighted.mean(errRep,w = SampleSize)) %>% ggplot(aes(x = StartDate)) + geom_point(aes(y = errDem),color = 'blue') + geom_point(aes(y = errRep),color = 'red') + geom_hline(yintercept = 0,linetype = 'dashed') + geom_smooth(aes(y = errDem),color = 'blue') + geom_smooth(aes(y = errRep),color = 'red') + labs(title = 'Error Over Time',subtitle = 'Sample-Weighted Prediction Error',x = 'Start Date',y = 'Prediction Error') + ylim(c(-.2,.1)) ``` --- # Weighting by Inverse of `MoE` ``` r pErrOverTime_MoE <- toplot %>% group_by(StartDate) %>% * summarise(errDem = weighted.mean(errDem,w = 1/MoE), * errRep = weighted.mean(errRep,w = 1/MoE)) %>% ggplot(aes(x = StartDate)) + geom_point(aes(y = errDem),color = 'blue') + geom_point(aes(y = errRep),color = 'red') + geom_hline(yintercept = 0,linetype = 'dashed') + geom_smooth(aes(y = errDem),color = 'blue') + geom_smooth(aes(y = errRep),color = 'red') + labs(title = 'Error Over Time',subtitle = 'MoE-Weighted Prediction Error',x = 'Start Date',y = 'Prediction Error') + ylim(c(-.2,.1)) ``` --- # Comparing ``` r require(patchwork) pErrOverTime_Raw + pErrOverTime_SampleSize + pErrOverTime_MoE ``` <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-24-1.png" style="display: block; margin: auto;" /> --- # 3. The Electoral College -- - U.S. presidents determined by the **Electoral College** (EC) -- - Each state allocated votes equal to their "congressional delegation" -- - One vote per Senator + one vote per **M**ember **o**f **t**he **H**ouse (MotH) -- - 100 Senators + 435 MotHs + 3 votes for DC = 538 total votes -- - To win the presidency, you need at least 270 EC votes -- - What does this mean for representation? -- - Population divided equally\* across 435 MotHs -- - In 2020, each MotH represented 761,179 people -- - Geographic distribution of this population is **non-uniform** --- # Assigning Districts -- - Every 10 years, U.S. takes a census of its population -- - Based on these results, congressional districts are reapportioned -- - In 2010, Florida's pop. was ~19m & average pop. per MotH was ~710k -- - How many MotHs? `ceiling(19000000 / 710000)` = `27` -- - Every state has 2 senators, so FL had 27 + 2 = 29 EC votes -- - In 2020, FL pop. was 21m &rarr; each resident had 0.00000137 of a vote -- - What about Vermont? -- - 3 EC votes / 624,340 residents = 0.00000481 -- - Vermonters have roughly 3.5 times the influence of Floridians! --- # Data Viz Misleads! <center><img src="figs/map_states.PNG" width = 60%></center> --- # Data Viz Misleads! <center><img src="figs/map_counties.png" width = 70%></center> --- # Data Viz Misleads! <center><img src="figs/map_precints.png" width = 70%></center> --- # Data Viz Misleads! <center><img src="https://www.vividmaps.com/wp-content/uploads/2019/07/Trumpland.jpg" width = 75%></center> --- # Data Viz Misleads! <center><img src="https://www.vividmaps.com/wp-content/uploads/2019/07/Clinton.jpg" width = 75%></center> --- # Correcting Maps - Fundamental challenge due to distribution of population across land <center><img src="figs/map_ec.png" width = 55%></center> --- # Correcting Maps - Fundamental challenge due to distribution of population across land <center><img src="figs/map_pop.png" width = 55%></center> --- # Introducing Data -- - We will attempt to use state polls to predict 2020 winner -- - National polls are great at predicting popular vote share... -- - ...but presidents aren't elected based on popular vote -- - With a few exceptions, states have a "winner take all" system -- - Winner of state's popular vote gets **all** of the state's EC votes -- - Thus we need good state-level polls -- - Load [`Pres2020_StatePolls.Rds`](https://github.com/rweldzius/PSC4175/raw/main/static/data/Pres2020_StatePolls.Rds) to `statePoll` object ``` r require(tidyverse) statePoll <- read_rds('https://github.com/rweldzius/PSC4175/raw/main/static/data/Pres2020_StatePolls.Rds') ``` --- # Look at the data ``` r glimpse(statePoll) ``` ``` ## Rows: 1,545 ## Columns: 19 ## $ StartDate <date> 2020-03-21, 2020-03-24, 2020-03-24… ## $ EndDate <date> 2020-03-30, 2020-04-03, 2020-03-29… ## $ DaysinField <dbl> 10, 11, 6, 2, 3, 5, 2, 2, 7, 3, 3, … ## $ MoE <dbl> 2.8, 3.0, 4.2, NA, 4.0, 1.7, 3.0, 3… ## $ Mode <chr> "Phone/Online", "Phone/Online", "Li… ## $ SampleSize <dbl> 1331, 1000, 813, 962, 602, 3244, 10… ## $ Biden <dbl> 41, 47, 48, 67, 46, 46, 46, 48, 52,… ## $ Trump <dbl> 46, 34, 45, 29, 46, 40, 48, 45, 39,… ## $ Winner <chr> "Rep", "Dem", "Dem", "Dem", "Dem", … ## $ poll.predicted <dbl> 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1,… ## $ Funded <chr> "UtahPolicy.com & KUTV 2News", "Sac… ## $ Conducted <chr> "Y2 Analytics", "GreatBlue Research… ## $ margin <dbl> -5, 13, 3, 38, 0, 6, -2, 3, 13, -7,… ## $ DaysToED <drtn> 218 days, 214 days, 219 days, 219 … ## $ StateName <chr> "Utah", "Connecticut", "Wisconsin",… ## $ EV <int> 6, 7, 10, 55, 16, 29, 16, 16, 12, 1… ## $ State <chr> "UT", "CT", "WI", "CA", "MI", "FL",… ## $ BidenCertVote <dbl> 38, 59, 49, 64, 51, 48, 50, 51, 58,… ## $ TrumpCertVote <dbl> 58, 39, 49, 34, 48, 51, 49, 48, 39,… ``` --- # .blue[Scientific] Goal: Predict Winner -- - Need to calculate predicted probability of Biden victory -- 1. Fraction of polls with Biden in the lead 2. Fraction of respondents supporting Biden 3. Fraction of twoway respondents supporting Biden -- - Wrangling time! ``` r statePoll <- statePoll %>% mutate(Biden2W = Biden / (Biden+Trump), Biden = Biden / 100, Trump = Trump/100) stateProbs <- statePoll %>% group_by(StateName,State) %>% summarise(BidenProb1 = mean(Biden > Trump), BidenProb2 = mean(Biden), BidenProb3 = mean(Biden2W), EV = mean(EV),.groups = 'drop') # This is just the value of EV ``` --- # Looking at data ``` r stateProbs ``` ``` ## # A tibble: 50 × 6 ## StateName State BidenProb1 BidenProb2 BidenProb3 EV ## <chr> <chr> <dbl> <dbl> <dbl> <dbl> ## 1 Alabama AL 0 0.389 0.407 9 ## 2 Alaska AK 0 0.442 0.466 3 ## 3 Arizona AZ 0.840 0.484 0.519 11 ## 4 Arkansas AR 0 0.381 0.395 6 ## 5 California CA 1 0.618 0.661 55 ## 6 Colorado CO 1 0.534 0.571 9 ## 7 Connecticut CT 1 0.584 0.631 7 ## 8 Delaware DE 1 0.603 0.627 3 ## 9 Florida FL 0.798 0.486 0.517 29 ## 10 Georgia GA 0.548 0.474 0.504 16 ## # ℹ 40 more rows ``` --- # Visualizing Data -- - `R` has fancy packages that allow for interactive plots (`plotly`) ``` r # install.packages('plotly') require(plotly) gg <- stateProbs %>% * ggplot(aes(x=BidenProb2, y=BidenProb3,text=paste(StateName))) + geom_point() + geom_abline(intercept=0,slope=1) + labs(x= "Probability as % Support", y = "Probability as Two-Party % Support", title = "Comparing Probability of Winning Measures") ``` --- # Visualizing Data ``` r ggplotly(gg,tooltip = 'text') %>% layout(autosize = F, width = 750, height = 450) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-b20dc2a931752ae4f30d" style="width:648px;height:360px;"></div> <script type="application/json" data-for="htmlwidget-b20dc2a931752ae4f30d">{"x":{"data":[{"x":[0.38928571428571429,0.44230769230769229,0.48415094339622639,0.38125000000000003,0.61799999999999999,0.53428571428571425,0.58444444444444443,0.60285714285714287,0.48643410852713176,0.4741095890410959,0.63428571428571434,0.38166666666666665,0.56600000000000006,0.41714285714285715,0.46619047619047621,0.424375,0.39111111111111113,0.38727272727272727,0.52833333333333332,0.63636363636363635,0.6415384615384615,0.50115384615384617,0.51068181818181824,0.40090909090909088,0.44526315789473686,0.43440000000000001,0.44400000000000001,0.49136363636363639,0.52909090909090906,0.56631578947368422,0.53545454545454552,0.61846153846153851,0.47947761194029848,0.37714285714285717,0.4653846153846154,0.36599999999999999,0.58624999999999994,0.49895104895104897,0.65400000000000003,0.44038461538461537,0.41142857142857142,0.40999999999999998,0.46369230769230768,0.3992857142857143,0.64571428571428569,0.53349999999999997,0.59307692307692306,0.35375000000000001,0.50205357142857143,0.32833333333333337],"y":[0.40696497996548259,0.46581930032762203,0.51879736341892746,0.39456407198523163,0.66108016549013837,0.57064341862963197,0.63119564660287264,0.62684067129416965,0.51673639552664608,0.5041636610284177,0.66679316894324248,0.39131509040323631,0.5889432528215327,0.44201688232547159,0.49681581253334745,0.4492683633263716,0.4118412289672253,0.40822311395405431,0.56935082794352765,0.66696769693824443,0.69076942423213772,0.5391190135878895,0.54726713099242585,0.42106312139619351,0.4646467212580116,0.45911478821711954,0.45217480931766646,0.52569038542903845,0.55300232822609408,0.60811775849763272,0.550494041773396,0.65665235364136931,0.51049271444868238,0.39320149770001478,0.49596224975874315,0.38290323831575057,0.60546937226361297,0.52920845393542826,0.66051041022469592,0.46344756475908905,0.42438478099058119,0.4248292669951656,0.49324378279804576,0.43892429795241228,0.67408835954569668,0.56452601901563448,0.6254777870302517,0.36602330001815431,0.53716607212889256,0.3380024737167594],"text":["Alabama","Alaska","Arizona","Arkansas","California","Colorado","Connecticut","Delaware","Florida","Georgia","Hawaii","Idaho","Illinois","Indiana","Iowa","Kansas","Kentucky","Louisiana","Maine","Maryland","Massachusetts","Michigan","Minnesota","Mississippi","Missouri","Montana","Nebraska","Nevada","New Hampshire","New Jersey","New Mexico","New York","North Carolina","North Dakota","Ohio","Oklahoma","Oregon","Pennsylvania","Rhode Island","South Carolina","South Dakota","Tennessee","Texas","Utah","Vermont","Virginia","Washington","West Virginia","Wisconsin","Wyoming"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(0,0,0,1)","opacity":1,"size":5.6692913385826778,"symbol":"circle","line":{"width":1.8897637795275593,"color":"rgba(0,0,0,1)"}},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.31205000000000005,0.67028333333333334],"y":[0.31205000000000005,0.67028333333333334],"text":"","type":"scatter","mode":"lines","line":{"width":1.8897637795275593,"color":"rgba(0,0,0,1)","dash":"solid"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null}],"layout":{"margin":{"t":46.684931506849317,"r":7.3059360730593621,"b":43.105022831050235,"l":43.105022831050235},"plot_bgcolor":"rgba(235,235,235,1)","paper_bgcolor":"rgba(255,255,255,1)","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724},"title":{"text":"Comparing Probability of Winning Measures","font":{"color":"rgba(0,0,0,1)","family":"","size":17.534246575342465},"x":0,"xref":"paper"},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[0.31205000000000005,0.67028333333333334],"tickmode":"array","ticktext":["0.4","0.5","0.6"],"tickvals":[0.40000000000000002,0.5,0.60000000000000009],"categoryorder":"array","categoryarray":["0.4","0.5","0.6"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.6529680365296811,"tickwidth":0.66417600664176002,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.68949771689498},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(255,255,255,1)","gridwidth":0.66417600664176002,"zeroline":false,"anchor":"y","title":{"text":"Probability as % Support","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[0.32036412619099047,0.70840777175790659],"tickmode":"array","ticktext":["0.4","0.5","0.6","0.7"],"tickvals":[0.40000000000000002,0.5,0.60000000000000009,0.70000000000000007],"categoryorder":"array","categoryarray":["0.4","0.5","0.6","0.7"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.6529680365296811,"tickwidth":0.66417600664176002,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.68949771689498},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(255,255,255,1)","gridwidth":0.66417600664176002,"zeroline":false,"anchor":"x","title":{"text":"Probability as Two-Party % Support","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":"rgba(255,255,255,1)","bordercolor":"transparent","borderwidth":1.8897637795275593,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.68949771689498}},"hovermode":"closest","barmode":"relative","autosize":false,"width":750,"height":450},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"52a223a92e9":{"x":{},"y":{},"text":{},"type":"scatter"},"52a253830023":{"intercept":{},"slope":{}}},"cur_data":"52a223a92e9","visdat":{"52a223a92e9":["function (y) ","x"],"52a253830023":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Visualizing Data -- - What about the % of polls that predict a Biden victory? -- - I.e., we know Trump won't win California or Biden won't win Tennessee ``` r gg <- stateProbs %>% * ggplot(aes(x=BidenProb2, y=BidenProb1,text=paste(StateName),color = BidenProb1)) + geom_point() + geom_abline(intercept=0,slope=1) + labs(x= "Probability as % Support", y = "Probability as % Polls Winning", title = "Comparing Probability of Winning Measures") + scale_color_gradient2(guide = 'none',low = "darkred",mid = "white",high = "darkblue",midpoint = .5) + theme_bw() ``` --- # Visualizing Data ``` r ggplotly(gg,tooltip = 'text') %>% layout(autosize = F, width = 750, height = 450) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-7598595affc4f25ab85b" style="width:648px;height:360px;"></div> <script type="application/json" data-for="htmlwidget-7598595affc4f25ab85b">{"x":{"data":[{"x":[0.38928571428571429,0.44230769230769229,0.48415094339622639,0.38125000000000003,0.61799999999999999,0.53428571428571425,0.58444444444444443,0.60285714285714287,0.48643410852713176,0.4741095890410959,0.63428571428571434,0.38166666666666665,0.56600000000000006,0.41714285714285715,0.46619047619047621,0.424375,0.39111111111111113,0.38727272727272727,0.52833333333333332,0.63636363636363635,0.6415384615384615,0.50115384615384617,0.51068181818181824,0.40090909090909088,0.44526315789473686,0.43440000000000001,0.44400000000000001,0.49136363636363639,0.52909090909090906,0.56631578947368422,0.53545454545454552,0.61846153846153851,0.47947761194029848,0.37714285714285717,0.4653846153846154,0.36599999999999999,0.58624999999999994,0.49895104895104897,0.65400000000000003,0.44038461538461537,0.41142857142857142,0.40999999999999998,0.46369230769230768,0.3992857142857143,0.64571428571428569,0.53349999999999997,0.59307692307692306,0.35375000000000001,0.50205357142857143,0.32833333333333337],"y":[0,0,0.839622641509434,0,1,1,1,1,0.79844961240310075,0.54794520547945202,1,0,1,0,0.2857142857142857,0,0,0,1,1,1,0.91538461538461535,0.97727272727272729,0,0.052631578947368418,0,0,0.95454545454545459,1,1,1,1,0.71641791044776115,0,0.38461538461538464,0,1,0.91608391608391604,1,0,0,0,0.30769230769230771,0,1,1,1,0,0.9642857142857143,0],"text":["Alabama","Alaska","Arizona","Arkansas","California","Colorado","Connecticut","Delaware","Florida","Georgia","Hawaii","Idaho","Illinois","Indiana","Iowa","Kansas","Kentucky","Louisiana","Maine","Maryland","Massachusetts","Michigan","Minnesota","Mississippi","Missouri","Montana","Nebraska","Nevada","New Hampshire","New Jersey","New Mexico","New York","North Carolina","North Dakota","Ohio","Oklahoma","Oregon","Pennsylvania","Rhode Island","South Carolina","South Dakota","Tennessee","Texas","Utah","Vermont","Virginia","Washington","West Virginia","Wisconsin","Wyoming"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":["rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(112,82,177,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(130,101,187,1)","rgba(235,229,244,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(217,154,138,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(74,46,159,1)","rgba(33,14,144,1)","rgba(139,0,0,1)","rgba(156,43,26,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(51,27,150,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(165,142,206,1)","rgba(139,0,0,1)","rgba(237,200,190,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(74,45,159,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(222,164,149,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(44,21,148,1)","rgba(139,0,0,1)"],"opacity":1,"size":5.6692913385826778,"symbol":"circle","line":{"width":1.8897637795275593,"color":["rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(112,82,177,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(130,101,187,1)","rgba(235,229,244,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(217,154,138,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(74,46,159,1)","rgba(33,14,144,1)","rgba(139,0,0,1)","rgba(156,43,26,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(51,27,150,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(165,142,206,1)","rgba(139,0,0,1)","rgba(237,200,190,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(74,45,159,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(222,164,149,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(44,21,148,1)","rgba(139,0,0,1)"]}},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.31205000000000005,0.67028333333333334],"y":[0.31205000000000005,0.67028333333333334],"text":"","type":"scatter","mode":"lines","line":{"width":1.8897637795275593,"color":"rgba(0,0,0,1)","dash":"solid"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null}],"layout":{"margin":{"t":46.684931506849317,"r":7.3059360730593621,"b":43.105022831050235,"l":48.949771689497723},"plot_bgcolor":"rgba(255,255,255,1)","paper_bgcolor":"rgba(255,255,255,1)","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724},"title":{"text":"Comparing Probability of Winning Measures","font":{"color":"rgba(0,0,0,1)","family":"","size":17.534246575342465},"x":0,"xref":"paper"},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[0.31205000000000005,0.67028333333333334],"tickmode":"array","ticktext":["0.4","0.5","0.6"],"tickvals":[0.40000000000000002,0.5,0.60000000000000009],"categoryorder":"array","categoryarray":["0.4","0.5","0.6"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.6529680365296811,"tickwidth":0.66417600664176002,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.68949771689498},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176002,"zeroline":false,"anchor":"y","title":{"text":"Probability as % Support","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-0.050000000000000003,1.05],"tickmode":"array","ticktext":["0.00","0.25","0.50","0.75","1.00"],"tickvals":[0,0.25,0.5,0.75,1],"categoryorder":"array","categoryarray":["0.00","0.25","0.50","0.75","1.00"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.6529680365296811,"tickwidth":0.66417600664176002,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.68949771689498},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176002,"zeroline":false,"anchor":"x","title":{"text":"Probability as % Polls Winning","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":"transparent","line":{"color":"rgba(51,51,51,1)","width":0.66417600664176002,"linetype":"solid"},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":"rgba(255,255,255,1)","bordercolor":"transparent","borderwidth":1.8897637795275593,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.68949771689498},"title":{"text":"","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}}},"hovermode":"closest","barmode":"relative","autosize":false,"width":750,"height":450},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"52a210fbd0b5":{"x":{},"y":{},"text":{},"colour":{},"type":"scatter"},"52a244323c9":{"intercept":{},"slope":{}}},"cur_data":"52a210fbd0b5","visdat":{"52a210fbd0b5":["function (y) ","x"],"52a244323c9":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Visualizing Data -- - Comparing to two-way ``` r gg <- stateProbs %>% * ggplot(aes(x=BidenProb3, y=BidenProb1,text=paste(StateName),color = BidenProb1)) + geom_point() + labs(x= "Probability as Two-Party % Support", y = "Probability as % Polls Winning", title = "Comparing Probability of Winning Measures") + scale_color_gradient2(guide = 'none',low = "darkred",mid = "white",high = "darkblue",midpoint = .5) + theme_bw() + geom_hline(yintercept = .5,linetype = 'dashed',alpha = .5) + geom_vline(xintercept = .5,linetype = 'dashed',alpha = .5) ``` --- # Visualizing Data ``` r ggplotly(gg,tooltip = 'text') %>% layout(autosize = F, width = 750, height = 450) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-f888dc62471906a988fd" style="width:648px;height:360px;"></div> <script type="application/json" data-for="htmlwidget-f888dc62471906a988fd">{"x":{"data":[{"x":[0.40696497996548259,0.46581930032762203,0.51879736341892746,0.39456407198523163,0.66108016549013837,0.57064341862963197,0.63119564660287264,0.62684067129416965,0.51673639552664608,0.5041636610284177,0.66679316894324248,0.39131509040323631,0.5889432528215327,0.44201688232547159,0.49681581253334745,0.4492683633263716,0.4118412289672253,0.40822311395405431,0.56935082794352765,0.66696769693824443,0.69076942423213772,0.5391190135878895,0.54726713099242585,0.42106312139619351,0.4646467212580116,0.45911478821711954,0.45217480931766646,0.52569038542903845,0.55300232822609408,0.60811775849763272,0.550494041773396,0.65665235364136931,0.51049271444868238,0.39320149770001478,0.49596224975874315,0.38290323831575057,0.60546937226361297,0.52920845393542826,0.66051041022469592,0.46344756475908905,0.42438478099058119,0.4248292669951656,0.49324378279804576,0.43892429795241228,0.67408835954569668,0.56452601901563448,0.6254777870302517,0.36602330001815431,0.53716607212889256,0.3380024737167594],"y":[0,0,0.839622641509434,0,1,1,1,1,0.79844961240310075,0.54794520547945202,1,0,1,0,0.2857142857142857,0,0,0,1,1,1,0.91538461538461535,0.97727272727272729,0,0.052631578947368418,0,0,0.95454545454545459,1,1,1,1,0.71641791044776115,0,0.38461538461538464,0,1,0.91608391608391604,1,0,0,0,0.30769230769230771,0,1,1,1,0,0.9642857142857143,0],"text":["Alabama","Alaska","Arizona","Arkansas","California","Colorado","Connecticut","Delaware","Florida","Georgia","Hawaii","Idaho","Illinois","Indiana","Iowa","Kansas","Kentucky","Louisiana","Maine","Maryland","Massachusetts","Michigan","Minnesota","Mississippi","Missouri","Montana","Nebraska","Nevada","New Hampshire","New Jersey","New Mexico","New York","North Carolina","North Dakota","Ohio","Oklahoma","Oregon","Pennsylvania","Rhode Island","South Carolina","South Dakota","Tennessee","Texas","Utah","Vermont","Virginia","Washington","West Virginia","Wisconsin","Wyoming"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":["rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(112,82,177,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(130,101,187,1)","rgba(235,229,244,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(217,154,138,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(74,46,159,1)","rgba(33,14,144,1)","rgba(139,0,0,1)","rgba(156,43,26,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(51,27,150,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(165,142,206,1)","rgba(139,0,0,1)","rgba(237,200,190,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(74,45,159,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(222,164,149,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(44,21,148,1)","rgba(139,0,0,1)"],"opacity":1,"size":5.6692913385826778,"symbol":"circle","line":{"width":1.8897637795275593,"color":["rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(112,82,177,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(130,101,187,1)","rgba(235,229,244,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(217,154,138,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(74,46,159,1)","rgba(33,14,144,1)","rgba(139,0,0,1)","rgba(156,43,26,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(51,27,150,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(165,142,206,1)","rgba(139,0,0,1)","rgba(237,200,190,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(74,45,159,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(139,0,0,1)","rgba(222,164,149,1)","rgba(139,0,0,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(0,0,139,1)","rgba(139,0,0,1)","rgba(44,21,148,1)","rgba(139,0,0,1)"]}},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.32036412619099047,0.70840777175790659],"y":[0.5,0.5],"text":"","type":"scatter","mode":"lines","line":{"width":1.8897637795275593,"color":"rgba(0,0,0,0.5)","dash":"dash"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.5,0.5],"y":[-0.050000000000000003,1.05],"text":"","type":"scatter","mode":"lines","line":{"width":1.8897637795275593,"color":"rgba(0,0,0,0.5)","dash":"dash"},"hoveron":"points","showlegend":false,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null}],"layout":{"margin":{"t":46.684931506849317,"r":7.3059360730593621,"b":43.105022831050235,"l":48.949771689497723},"plot_bgcolor":"rgba(255,255,255,1)","paper_bgcolor":"rgba(255,255,255,1)","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724},"title":{"text":"Comparing Probability of Winning Measures","font":{"color":"rgba(0,0,0,1)","family":"","size":17.534246575342465},"x":0,"xref":"paper"},"xaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[0.32036412619099047,0.70840777175790659],"tickmode":"array","ticktext":["0.4","0.5","0.6","0.7"],"tickvals":[0.40000000000000002,0.5,0.60000000000000009,0.70000000000000007],"categoryorder":"array","categoryarray":["0.4","0.5","0.6","0.7"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.6529680365296811,"tickwidth":0.66417600664176002,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.68949771689498},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176002,"zeroline":false,"anchor":"y","title":{"text":"Probability as Two-Party % Support","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-0.050000000000000003,1.05],"tickmode":"array","ticktext":["0.00","0.25","0.50","0.75","1.00"],"tickvals":[0,0.25,0.5,0.75,1],"categoryorder":"array","categoryarray":["0.00","0.25","0.50","0.75","1.00"],"nticks":null,"ticks":"outside","tickcolor":"rgba(51,51,51,1)","ticklen":3.6529680365296811,"tickwidth":0.66417600664176002,"showticklabels":true,"tickfont":{"color":"rgba(77,77,77,1)","family":"","size":11.68949771689498},"tickangle":-0,"showline":false,"linecolor":null,"linewidth":0,"showgrid":true,"gridcolor":"rgba(235,235,235,1)","gridwidth":0.66417600664176002,"zeroline":false,"anchor":"x","title":{"text":"Probability as % Polls Winning","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":"transparent","line":{"color":"rgba(51,51,51,1)","width":0.66417600664176002,"linetype":"solid"},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":"rgba(255,255,255,1)","bordercolor":"transparent","borderwidth":1.8897637795275593,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.68949771689498},"title":{"text":"","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}}},"hovermode":"closest","barmode":"relative","autosize":false,"width":750,"height":450},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"52a271d479ae":{"x":{},"y":{},"text":{},"colour":{},"type":"scatter"},"52a23480c8e4":{"yintercept":{}},"52a273050ba9":{"xintercept":{}}},"cur_data":"52a271d479ae","visdat":{"52a271d479ae":["function (y) ","x"],"52a23480c8e4":["function (y) ","x"],"52a273050ba9":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- # Translate to EC Votes -- - Start with a single state to get the idea -- - **Expected Value** (EV...could also be Expected Votes): Probability * Value ``` r stateProbs %>% filter(State == 'PA') %>% mutate(BEV1 = BidenProb1 * EV, BEV2 = BidenProb2 * EV, BEV3 = BidenProb3 * EV) %>% select(EV,matches('^B.*\\d')) ``` ``` ## # A tibble: 1 × 7 ## EV BidenProb1 BidenProb2 BidenProb3 BEV1 BEV2 BEV3 ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 20 0.916 0.499 0.529 18.3 9.98 10.6 ``` -- - Probability matters! Biden could get between 18.3 and 9.98 votes in PA! --- # Translate to EC Votes - Do this for every state ``` r stateProbs %>% mutate(BidenEV1 = BidenProb1 * EV, BidenEV2 = BidenProb2 * EV, BidenEV3 = BidenProb3 * EV, TrumpEV1 = EV - BidenEV1, TrumpEV2 = EV - BidenEV2, TrumpEV3 = EV - BidenEV3) %>% summarise_at(vars(matches('EV\\d')),sum) # Fancy shortcut! ``` ``` ## # A tibble: 1 × 6 ## BidenEV1 BidenEV2 BidenEV3 TrumpEV1 TrumpEV2 TrumpEV3 ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 345. 272. 289. 190. 263. 246. ``` -- - Overall EC votes *always* favored Biden (always above 270) -- - But none of our estimates are close to the true outcome of 306 to 232 --- # .blue[Science] Questions -- - We know that **national** polls changed closer to election -- - Can we do better if we look only at **state** polls close to election day? -- - .red[Data] limitations! ``` r pollsPerState <- statePoll %>% filter(DaysToED <= 3) %>% count(State) %>% ggplot(aes(x = n,y = reorder(State,n))) + geom_bar(stat = 'identity',alpha = .7) + labs(title = 'Number of Polls per State', subtitle = 'Last 3 Days before Election Day', x = 'Number of Polls', y = '') ``` --- # .red[Data] Limitations <img src="6_Multivariate2b_files/figure-html/unnamed-chunk-38-1.png" style="display: block; margin: auto;" /> --- # Do better with recent polls? ``` r statePoll %>% * filter(DaysToED <= 3) %>% group_by(StateName,State) %>% summarise(BidenProb1 = mean(Biden > Trump), BidenProb2 = mean(Biden), BidenProb3 = mean(Biden2W), EV = mean(EV),.groups = 'drop') %>% mutate(BidenEV1 = BidenProb1 * EV, BidenEV2 = BidenProb2 * EV, BidenEV3 = BidenProb3 * EV, TrumpEV1 = EV - BidenEV1, TrumpEV2 = EV - BidenEV2, TrumpEV3 = EV - BidenEV3) %>% summarise_at(vars(matches('EV\\d')),sum) ``` ``` ## # A tibble: 1 × 6 ## BidenEV1 BidenEV2 BidenEV3 TrumpEV1 TrumpEV2 TrumpEV3 ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 334. 277. 285. 201. 258. 250. ``` --- # Conclusion -- - Still not nailing the true votes! -- - Not even within the distributions of the bootstrapped estimates! -- - Why? -- 1. Polls have their own uncertainty (could weight by total respondents?) 2. Polls might not be representative of voters 3. Polls might not be independent of each other