class: center, middle, inverse, title-slide .title[ # Clustering ] .subtitle[ ## Part 1b ] .author[ ### Prof. Ryan 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. Application of k-means clustering --- # Clustering to Learn about MCs ``` r library(tidyverse) dat <- read_csv('../Data/H097_members.csv') glimpse(dat) ``` ``` ## Rows: 445 ## Columns: 22 ## $ congress <dbl> 97, 97, 97, 97, 97, … ## $ chamber <chr> "President", "House"… ## $ icpsr <dbl> 99907, 10717, 10721,… ## $ state_icpsr <dbl> 99, 41, 41, 41, 41, … ## $ district_code <dbl> 0, 2, 1, 4, 3, 5, 7,… ## $ state_abbrev <chr> "USA", "AL", "AL", "… ## $ party_code <dbl> 200, 200, 200, 100, … ## $ occupancy <dbl> 0, 0, 0, 0, 0, 0, 0,… ## $ last_means <dbl> 0, 1, 1, 1, 1, 1, 1,… ## $ bioname <chr> "REAGAN, Ronald Wils… ## $ bioguide_id <chr> NA, "D000326", "E000… ## $ born <dbl> 1911, 1925, 1928, 19… ## $ died <dbl> 2004, 2008, 2019, 20… ## $ nominate_dim1 <dbl> 0.692, 0.398, 0.177,… ## $ nominate_dim2 <dbl> -0.713, -0.057, 0.16… ## $ nominate_log_likelihood <dbl> -103.6031, -328.0376… ## $ nominate_geo_mean_probability <dbl> 0.74100, 0.58100, 0.… ## $ nominate_number_of_votes <dbl> 345, 605, 628, 648, … ## $ nominate_number_of_errors <dbl> 43, 134, 118, 59, 74… ## $ conditional <lgl> NA, NA, NA, NA, NA, … ## $ nokken_poole_dim1 <dbl> NA, 0.486, 0.156, -0… ## $ nokken_poole_dim2 <dbl> NA, -0.364, 0.006, 0… ``` --- # DW-NOMINATE - DW-NOMINATE is a measure of how frequently different legislators vote together -- - Often interpreted as "ideology" -- - Two-dimensions: -- 1. Standard left-right ideology (size of gov, redistribution, etc.) 2. Second dimension changes, but typically **salient social issues** -- - Can `\(k\)`-means clustering help us learn about legislators? --- # 97th Congress (1981-1983) ``` r require(scales) library(plotly) gg <- dat %>% ggplot(aes(x = nominate_dim1,y = nominate_dim2, text = bioname)) + geom_point() + labs(x = 'DW-Nominate Dimension 1', y = 'DW-Nominate Dimension 2') ``` --- # 97th Congress (1981-1983) <div class="plotly html-widget html-fill-item" id="htmlwidget-9eceb20dc2a931752ae4" style="width:648px;height:360px;"></div> <script type="application/json" 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","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> --- # Intuition Check -- - Can we see some clusters? - What do we think these are? -- - Let's try estimating `\(k\)`-means! -- - Function `kmeans(x,centers,iter.max,nstart)` -- - `x` is the data (only select the columns of interest!) - `centers` is the number of centroids - `iter.max` maximum amount of "steps" - `nstart` how many times to re-estimate --- # Clustering on Ideology - First, some light wrangling (convert numeric party code to character) ``` r datClust <- dat %>% mutate(party = ifelse(party_code == 200,'R', ifelse(party_code == 100,'D','I'))) %>% mutate(nameParty = paste0(bioname,' (',party,')')) %>% select(nominate_dim1,nominate_dim2,nameParty) %>% drop_na() ``` --- # Clustering on Ideology - Second, estimate `kmeans()` function ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 2) m ``` ``` ## K-means clustering with 2 clusters of sizes 214, 231 ## ## Cluster means: ## nominate_dim1 nominate_dim2 ## 1 0.2607991 -0.2443271 ## 2 -0.3019524 0.1529177 ## ## Clustering vector: ## [1] 1 1 1 2 2 2 2 1 1 1 2 2 2 1 2 2 1 1 2 2 1 2 2 2 1 2 1 ## [28] 2 2 1 1 2 1 1 2 2 2 2 1 2 1 2 2 1 2 2 1 1 1 2 1 1 1 1 ## [55] 1 2 1 1 2 1 2 1 2 2 1 1 2 1 1 2 1 2 2 1 2 2 2 2 2 2 1 ## [82] 1 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 1 2 2 2 1 1 1 1 2 2 2 ## [109] 1 1 2 1 1 1 1 1 2 1 2 2 2 1 1 1 1 2 1 2 1 1 1 2 2 1 2 ## [136] 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 2 2 1 2 2 1 1 2 2 2 1 2 ## [163] 1 2 1 1 1 2 1 1 2 2 1 2 2 2 2 1 2 1 2 2 1 2 2 2 2 2 1 ## [190] 2 2 2 1 2 2 2 2 2 1 1 1 2 1 2 2 1 2 1 1 1 2 2 1 1 2 1 ## [217] 2 2 2 1 1 2 2 1 1 1 2 2 2 2 1 1 1 2 1 1 1 2 2 1 2 2 2 ## [244] 2 1 1 1 2 2 1 1 2 2 1 1 1 1 2 2 2 1 2 1 1 2 2 2 1 1 1 ## [271] 2 2 1 1 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 1 1 1 1 1 2 1 2 ## [298] 1 2 2 1 2 2 2 2 1 1 2 1 1 1 1 1 1 2 2 1 1 2 1 1 1 2 2 ## [325] 2 2 1 2 1 2 1 1 1 2 2 1 2 2 2 1 1 1 2 1 2 1 2 1 2 1 1 ## [352] 1 2 2 1 1 2 1 2 1 1 2 1 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 ## [379] 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 ## [406] 1 2 1 2 2 2 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 ## [433] 2 1 1 2 2 2 2 2 1 1 1 1 1 ## ## Within cluster sum of squares by cluster: ## [1] 33.36394 48.70122 ## (between_SS / total_SS = 39.1 %) ## ## Available components: ## ## [1] "cluster" "centers" "totss" ## [4] "withinss" "tot.withinss" "betweenss" ## [7] "size" "iter" "ifault" ``` --- # Clustering on Ideology - Easier to see output with the help of `tidymodels` package ``` r require(tidymodels) tidy(m) ``` ``` ## # A tibble: 2 × 5 ## nominate_dim1 nominate_dim2 size withinss cluster ## <dbl> <dbl> <int> <dbl> <fct> ## 1 0.261 -0.244 214 33.4 1 ## 2 -0.302 0.153 231 48.7 2 ``` -- - First two columns are the **locations** of the centroids - `size` is the number of observations associated with each group - `withinss` is the **errors** each centroid makes --- # Clustering on Ideology - Third, plot points and color by cluster ``` r ggClust <- datClust %>% mutate(cluster = m$cluster) %>% # Add cluster to data ggplot(aes(x = nominate_dim1, y = nominate_dim2, color = factor(cluster), text=nameParty)) + geom_point() + labs(x = 'DW-Nominate Dimension 1', y = 'DW-Nominate Dimension 2', title="97th Congress Ideology", color = "Cluster") ``` --- # Clustering on Ideology ``` r ggplotly(ggClust,tooltip = 'text') ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-f30d7598595affc4f25a" style="width:648px;height:360px;"></div> <script type="application/json" 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More Clusters ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 3) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-b85bf888dc62471906a9" style="width:648px;height:360px;"></div> <script type="application/json" data-for="htmlwidget-b85bf888dc62471906a9">{"x":{"data":[{"x":[-0.21299999999999999,-0.042000000000000003,-0.17499999999999999,0.012999999999999999,0.42199999999999999,0.32900000000000001,-0.40999999999999998,-0.254,-0.47699999999999998,-0.41299999999999998,-0.45500000000000002,-0.087999999999999995,-0.40000000000000002,-0.42199999999999999,-0.17299999999999999,-0.23300000000000001,-0.098000000000000004,-0.0070000000000000001,-0.184,-0.193,0.014999999999999999,-0.072999999999999995,-0.217,-0.056000000000000001,-0.028000000000000001,-0.090999999999999998,-0.11600000000000001,-0.23699999999999999,-0.20200000000000001,-0.41899999999999998,-0.26900000000000002,-0.42899999999999999,-0.39000000000000001,-0.39800000000000002,-0.45100000000000001,-0.26700000000000002,-0.313,-0.28799999999999998,-0.34300000000000003,0.26000000000000001,-0.037999999999999999,-0.36799999999999999,-0.123,-0.35899999999999999,-0.0089999999999999993,0.029999999999999999,-0.024,-0.104,-0.44800000000000001,-0.25800000000000001,-0.55300000000000005,-0.161,0.017000000000000001,-0.13400000000000001,-0.25900000000000001,0.32800000000000001,-0.41599999999999998,-0.17199999999999999,-0.19600000000000001,-0.29999999999999999,-0.073999999999999996,-0.13900000000000001,-0.33900000000000002,-0.30499999999999999,-0.041000000000000002,-0.25900000000000001,-0.17799999999999999,-0.31900000000000001,-0.26400000000000001,-0.14499999999999999,-0.17499999999999999,-0.106,-0.28000000000000003,-0.095000000000000001,-0.027,-0.126,-0.112,-0.27800000000000002,-0.26500000000000001,-0.39100000000000001,-0.34699999999999998,-0.36899999999999999,-0.215,-0.246,0.17699999999999999,-0.245,0.29699999999999999,-0.058000000000000003,-0.316,-0.22800000000000001,-0.40699999999999997,-0.38300000000000001,-0.53800000000000003,-0.218,-0.255,-0.13700000000000001,-0.219,-0.19600000000000001,-0.115,0.053999999999999999,-0.316,-0.042000000000000003,0.049000000000000002,0.019,0.096000000000000002,-0.029999999999999999,0.215,0.14599999999999999,0.161,0.33300000000000002,0.318,-0.35399999999999998,-0.34899999999999998,-0.30599999999999999,-0.35499999999999998],"y":[0.97599999999999998,0.872,0.83399999999999996,0.65800000000000003,0.61099999999999999,0.94399999999999995,0.81899999999999995,0.48399999999999999,0.25600000000000001,0.34399999999999997,0.35999999999999999,0.42099999999999999,0.22900000000000001,0.35699999999999998,0.71499999999999997,0.17000000000000001,0.91600000000000004,0.73199999999999998,0.36299999999999999,0.33700000000000002,0.377,0.70099999999999996,0.84899999999999998,0.074999999999999997,0.63900000000000001,0.501,0.67800000000000005,0.19600000000000001,0.72199999999999998,0.27300000000000002,0.24299999999999999,0.34599999999999997,0.246,0.35099999999999998,0.46999999999999997,0.13600000000000001,0.17399999999999999,0.57499999999999996,0.33200000000000002,0.29799999999999999,0.47599999999999998,0.60399999999999998,0.70199999999999996,0.501,0.50700000000000001,0.56799999999999995,0.51600000000000001,0.47099999999999997,0.313,0.29399999999999998,0.30399999999999999,0.98699999999999999,1,0.70899999999999996,0.72399999999999998,0.442,0.245,0.72399999999999998,0.32900000000000001,0.45800000000000002,0.13200000000000001,0.20799999999999999,0.19700000000000001,0.28499999999999998,0.72999999999999998,0.94099999999999995,0.48099999999999998,0.57299999999999995,0.60899999999999999,0.112,0.72999999999999998,0.16600000000000001,0.155,0.44400000000000001,0.60299999999999998,0.74099999999999999,0.29899999999999999,0.39800000000000002,0.56899999999999995,0.23300000000000001,0.57299999999999995,0.44500000000000001,0.25800000000000001,0.52300000000000002,0.29399999999999998,0.82699999999999996,0.34000000000000002,0.45200000000000001,0.155,0.45500000000000002,0.72499999999999998,0.67200000000000004,0.55800000000000005,0.52300000000000002,0.75700000000000001,0.60099999999999998,0.747,0.47399999999999998,0.71099999999999997,0.93600000000000005,0.35399999999999998,0.747,0.999,1,0.995,0.92300000000000004,0.755,0.21199999999999999,0.77500000000000002,0.377,0.34599999999999997,0.192,0.58599999999999997,0.45000000000000001,0.29299999999999998],"text":["BEVILL, Tom (D)","NICHOLS, William Flynt (D)","FLIPPO, Ronnie Gene (D)","SHELBY, Richard C. 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","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> --- # More Clusters ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 4) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-88fdd2a34d502a66744b" style="width:648px;height:360px;"></div> <script type="application/json" 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More Clusters ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 5) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-8e1fe96c0688a849169a" style="width:648px;height:360px;"></div> <script type="application/json" data-for="htmlwidget-8e1fe96c0688a849169a">{"x":{"data":[{"x":[-0.63400000000000001,-0.59899999999999998,-0.51700000000000002,-0.60999999999999999,-0.64400000000000002,-0.63100000000000001,-0.41299999999999998,-0.55200000000000005,-0.47299999999999998,-0.44,-0.22500000000000001,-0.29299999999999998,-0.377,-0.35499999999999998,-0.41599999999999998,-0.49399999999999999,-0.55200000000000005,-0.39700000000000002,-0.67100000000000004,-0.48799999999999999,-0.16600000000000001,-0.23999999999999999,-0.35099999999999998,-0.52600000000000002,-0.308,-0.34300000000000003,-0.44400000000000001,-0.254,-0.51400000000000001,-0.46500000000000002,-0.499,-0.65800000000000003,-0.46300000000000002,-0.374,-0.65100000000000002,-0.34499999999999997,-0.47199999999999998,-0.51600000000000001,-0.48999999999999999,-0.435,-0.56200000000000006,-0.50900000000000001,-0.39100000000000001,-0.47799999999999998,-0.60499999999999998,-0.51400000000000001,-0.38400000000000001,-0.35299999999999998,-0.56399999999999995,-0.42899999999999999,-0.31,-0.56399999999999995,-0.55900000000000005,-0.35599999999999998,-0.57799999999999996,-0.496,-0.308,-0.24199999999999999,-0.23100000000000001,-0.311,-0.33000000000000002,-0.33400000000000002,-0.247,-0.51100000000000001,-0.59599999999999997,-0.40100000000000002,-0.51400000000000001,-0.48099999999999998],"y":[-0.30399999999999999,-0.41899999999999998,-0.36899999999999999,-0.14099999999999999,-0.64600000000000002,-0.60499999999999998,-0.78300000000000003,-0.39800000000000002,-0.34300000000000003,-0.60499999999999998,-0.97399999999999998,-0.315,-0.75600000000000001,-0.26700000000000002,-0.48599999999999999,-0.49399999999999999,-0.218,-0.224,-0.39000000000000001,-0.873,-0.28299999999999997,-0.59499999999999997,-0.54600000000000004,-0.85099999999999998,-0.216,-0.51300000000000001,-0.59299999999999997,-0.40899999999999997,-0.45900000000000002,-0.38700000000000001,-0.53400000000000003,-0.51200000000000001,-0.42699999999999999,-0.46600000000000003,-0.41399999999999998,-0.223,-0.376,-0.317,-0.872,-0.224,-0.49099999999999999,-0.48799999999999999,-0.77100000000000002,-0.34899999999999998,-0.31900000000000001,-0.34100000000000003,-0.34100000000000003,-0.22700000000000001,-0.55600000000000005,-0.25800000000000001,-0.27300000000000002,-0.70999999999999996,-0.34899999999999998,-0.41699999999999998,-0.312,-0.45700000000000002,-0.32900000000000001,-0.25800000000000001,-0.41799999999999998,-0.57799999999999996,-0.47799999999999998,-0.71799999999999997,-0.317,-0.219,-0.22800000000000001,-0.56299999999999994,-0.45200000000000001,-0.27800000000000002],"text":["BURTON, Phillip (D)","EDWARDS, William Donlon (Don) (D)","HAWKINS, Augustus Freeman (Gus) (D)","ROYBAL, Edward R. 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-- - Recall from regression that we are interested in **errors** -- - What are "errors" in the context of clustering? -- <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-17-1.png" style="display: block; margin: auto;" /> --- # How many clusters? - Recall from regression that we are interested in **errors** - What are "errors" in the context of clustering? <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-18-1.png" style="display: block; margin: auto;" /> --- # How many clusters? - Recall from regression that we are interested in **errors** - What are "errors" in the context of clustering? - Just the sum of each observation's distance from its centroid! -- - Within Sum of Squares (**WSS**) ``` r tidy(m) ``` ``` ## # A tibble: 2 × 5 ## nominate_dim1 nominate_dim2 size withinss cluster ## <dbl> <dbl> <int> <dbl> <fct> ## 1 -0.216 0.370 166 23.7 1 ## 2 0.0783 -0.281 279 58.0 2 ``` --- # So...how many?! - Want to choose a number of clusters that reduces the total **WSS** -- ``` r m.cluster <- datClust %>% select(-nameParty) %>% # Same as selecting two dimensions kmeans(centers = 3) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-21-1.png" style="display: block; margin: auto;" /> --- # So...how many?! - Want to choose a number of clusters that reduces the total **WSS** ``` r m.cluster <- datClust %>% select(-nameParty) %>% kmeans(centers = 4) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-23-1.png" style="display: block; margin: auto;" /> --- # So...how many?! - Want to choose a number of clusters that reduces the total **WSS** ``` r m.cluster <- datClust %>% select(-nameParty) %>% kmeans(centers = 5) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-25-1.png" style="display: block; margin: auto;" /> --- # So...how many?! - Want to choose a number of clusters that reduces the total **WSS** ``` r m.cluster <- datClust %>% select(-nameParty) %>% kmeans(centers = 10) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-27-1.png" style="display: block; margin: auto;" /> --- # So...how many?! - Want to choose a number of clusters that reduces the total **WSS** ``` r m.cluster <- datClust %>% select(-nameParty) %>% kmeans(centers = 30) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-29-1.png" style="display: block; margin: auto;" /> --- # So...how many?! - But there's a trade-off! -- - Accuracy versus **parsimony** -- - Simple rule: look for the "elbow" ``` r totWSS <- NULL for(k in 1:10) { m.cluster <- datClust %>% select(-nameParty) %>% kmeans(centers = k,nstart = 25) totWSS <- data.frame(totWSS = m.cluster$tot.withinss, k = k) %>% bind_rows(totWSS) } ``` --- # Looking for the "elbow" ``` r totWSS %>% ggplot(aes(x = k,y = totWSS)) + geom_line() + geom_point() + labs(x = 'Number of Clusters',y = 'Total WSS') + scale_x_continuous(breaks = 1:10) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-31-1.png" style="display: block; margin: auto;" /> --- # Clustering on Ideology - Note that we need to `set.seed()`! Centroid starting points are **random**! ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 2) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-bb3486349adfa5d821dc" style="width:648px;height:360px;"></div> <script type="application/json" 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Centroid starting points are **random**! ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 2) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-44474b3e8cd160f85a98" style="width:648px;height:360px;"></div> <script type="application/json" 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(R)","SENSENBRENNER, Frank James, Jr. (R)","PETRI, Thomas Evert (R)","GUNDERSON, Steven Craig (R)","CHENEY, Richard Bruce (R)"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(0,191,196,1)","opacity":1,"size":5.6692913385826778,"symbol":"circle","line":{"width":1.8897637795275593,"color":"rgba(0,191,196,1)"}},"hoveron":"points","name":"2","legendgroup":"2","showlegend":true,"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(235,235,235,1)","paper_bgcolor":"rgba(255,255,255,1)","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724},"title":{"text":"97th Congress Ideology","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":[-0.76345000000000007,0.96245000000000003],"tickmode":"array","ticktext":["-0.5","0.0","0.5"],"tickvals":[-0.5,0,0.50000000000000011],"categoryorder":"array","categoryarray":["-0.5","0.0","0.5"],"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":"DW-Nominate Dimension 1","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}},"hoverformat":".2f"},"yaxis":{"domain":[0,1],"automargin":true,"type":"linear","autorange":false,"range":[-1.0748,1.0988],"tickmode":"array","ticktext":["-1.0","-0.5","0.0","0.5","1.0"],"tickvals":[-1,-0.5,0,0.5,0.99999999999999978],"categoryorder":"array","categoryarray":["-1.0","-0.5","0.0","0.5","1.0"],"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":"DW-Nominate Dimension 2","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":true,"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":"Cluster","font":{"color":"rgba(0,0,0,1)","family":"","size":14.611872146118724}}},"hovermode":"closest","barmode":"relative"},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"35295252739":{"x":{},"y":{},"colour":{},"text":{},"type":"scatter"}},"cur_data":"35295252739","visdat":{"35295252739":["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> --- # Clustering on Ideology - Note that we need to `set.seed()`! Centroid starting points are **random**! ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 2) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-2514ce28ae593bde0f73" style="width:648px;height:360px;"></div> <script type="application/json" 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Centroid starting points are **random**! ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 2) ``` <div class="plotly html-widget html-fill-item" id="htmlwidget-5d05eac75555269eefd0" style="width:648px;height:360px;"></div> <script type="application/json" 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","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> --- # Clustering Randomness - Can overcome with `nstart` -- - Attempts multiple initial centroids and chooses the "best" ``` r set.seed(42) c1 <- kmeans(datClust %>% select(-nameParty),centers = 2,nstart = 25) set.seed(123) c2 <- kmeans(datClust %>% select(-nameParty),centers = 2,nstart = 25) table(c1$cluster,c2$cluster) ``` ``` ## ## 1 2 ## 1 166 0 ## 2 0 279 ``` ``` r table(c1$cluster) ``` ``` ## ## 1 2 ## 166 279 ``` ``` r table(c2$cluster) ``` ``` ## ## 1 2 ## 166 279 ``` --- # Is Polarization Increasing? - Compare 97th Congress (1981-1983) to 117th Congress (2021-2023) ``` r dat <- read_csv('../Data/H117_members.csv') datClust <- dat %>% mutate(party = ifelse(party_code == 200,'R', ifelse(party_code == 100,'D','I'))) %>% mutate(nameParty = paste0(bioname,' (',party,')')) %>% # combine name + party select(nominate_dim1,nominate_dim2,nameParty) %>% drop_na() ``` - Check for the "elbow" ``` r totWSS <- NULL for(k in 1:10) { m.cluster <- datClust %>% select(-nameParty) %>% kmeans(centers = k,nstart = 25) totWSS <- data.frame(totWSS = m.cluster$tot.withinss,k = k) %>% bind_rows(totWSS) } ``` --- # Check for the "elbow" ``` r totWSS %>% ggplot(aes(x = k,y = totWSS)) + geom_line() + geom_point() + labs(x = 'Number of Clusters',y = 'Total WSS') + scale_x_continuous(breaks = 1:10) ``` <img src="14b_ClusteringPart1_files/figure-html/unnamed-chunk-43-1.png" style="display: block; margin: auto;" /> --- # Growing polarization? ``` r m <- kmeans(x = datClust %>% select(nominate_dim1,nominate_dim2), centers = 2) ``` <div 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Theory Testing 2. Prediction 3. **Learning**