{
  "alt": "Scatter plot of sampled tracts on two principal components, colored by neighborhood type. The colors form a fan from left to right along the resource score, with the high-poverty, single-parent type at the far left and high-income owners at the far right. Adjacent colors overlap along the horizontal axis, and the vertical axis separates dense, renting places such as dense, college-educated renters from older, low-density, owner-occupied places such as low-density owners and older owners.",
  "caption": "Look for colors that shade into one another along the horizontal axis, a combined resource score: neighboring types overlap, which suggests a continuum. The first component captures {fact:pc1_evr} of the variance in the inputs and the second {fact:pc2_evr}. Each dot is a tract in the plotted sample of {fact:n_sample}, and each labeled dot is a type's population-weighted centroid. The share of tracts nearer another type comes from a separate sample of {fact:sil_sample} tracts.",
  "data": [],
  "id": "pca_continuum",
  "notes": [
    "The dots are a random sample of {fact:n_sample} of the typed tracts drawn with a fixed seed (replicates and seed in the methods note); the components, the types and the centroids use every typed tract. Components are in standardized units, and their signs are set so that log income and log density rise with the first and second component.",
    "The first component weights income, college share, homeownership and the share of older adults positively and poverty and the single-parent share negatively. The second component weights density and college share positively and homeownership and the share of older adults negatively."
  ],
  "source": "k-means types of tracts on seven ACS 2019-2023 measures and 2020 land area; principal components of the standardized inputs; unweighted sample of tracts, centroids population-weighted",
  "spec": {
    "colors": {
      "Dense, college-educated renters": "cat5",
      "High-income owners": "cat1",
      "High-poverty, single-parent": "cat8",
      "Low-density owners": "cat4",
      "Lower-income renters": "cat7",
      "Middle-income owners": "cat3",
      "Moderate-income, mixed-tenure": "cat6",
      "Older owners": "cat2"
    },
    "group": "group",
    "highlight": [
      "High-income owners",
      "Older owners",
      "Middle-income owners",
      "Low-density owners",
      "Dense, college-educated renters",
      "Moderate-income, mixed-tenure",
      "Lower-income renters",
      "High-poverty, single-parent"
    ],
    "label": "label",
    "payload": "pca_continuum.json",
    "x": "x",
    "xDomain": [
      -10,
      5
    ],
    "xFormat": {
      "digits": 0
    },
    "xLabel": "First principal component: resource score (standardized units)",
    "y": "y",
    "yDomain": [
      -7,
      5
    ],
    "yFormat": {
      "digits": 0
    },
    "yLabel": "Second principal component: denser, younger, more renting (standardized units)"
  },
  "subtitle": "A random sample of tracts on the first two principal components of the {fact:n_features} standardized inputs, colored by type, with each type's centroid labeled",
  "title": "Neighboring types overlap along the first component, and {fact:sil_neg_share} of {fact:sil_sample} sampled tracts sit nearer another type than their own",
  "type": "scatter",
  "width": "wide"
}