{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"(conditional_autoregressive_priors)=\n",
"# Conditional Autoregressive (CAR) Models for Spatial Data\n",
"\n",
":::{post} Jul 29, 2022 \n",
":tags: spatial, autoregressive, count data\n",
":category: beginner, tutorial\n",
":author: Conor Hassan, Daniel Saunders\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import os\n",
"\n",
"import arviz as az\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import pymc as pm\n",
"import pytensor.tensor as pt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
":::{include} ../extra_installs.md\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# THESE ARE THE LIBRARIES THAT ARE NOT DEPENDENCIES ON PYMC\n",
"import libpysal\n",
"\n",
"from geopandas import read_file"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"RANDOM_SEED = 8927\n",
"rng = np.random.default_rng(RANDOM_SEED)\n",
"az.style.use(\"arviz-darkgrid\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Conditional Autoregressive (CAR) model\n",
"\n",
"A *conditional autoregressive CAR prior* on a set of random effects $\\{\\phi_i\\}_{i=1}^N$ models the random effect $\\phi_i$ as having a mean, that is the weighted average the random effects of observation $i$'s adjacent neighbours. Mathematically, this can be expressed as \n",
"\n",
"$$\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i} \\sim \\text{Normal} \\bigg( \\alpha \\frac{ \\sum_{j=1}^{n_i}w_{ij} \\phi_j}{n_i}, \\sigma_{i}^2\\bigg)$$\n",
"\n",
"where ${j \\sim i}$ indicates the set of adjacent neighbours to observation $i$, $n_i$ denotes the number of adjacent neighbours that observation $i$ has, $w_{ij}$ is the weighting of the spatial relationship between observation $i$ and $j$. If $i$ and $j$ are not adjacent, then $w_{ij}=0$. Lastly, $\\sigma_i^2$ is a spatially varying variance parameter for each area. Note that information such as an adjacency matrix, indicating the neighbour relationships, and a weight matrix $\\textbf{w}$, indicating the weights of the spatial relationships, is required as input data. The parameters that we infer are $\\{\\phi\\}_{i=1}^N, \\{\\sigma_i\\}_{i=1}^N$, and $\\alpha$. \n",
"\n",
"## Model specification \n",
"\n",
"Here we will demonstrate the implementation of a CAR model using a canonical example: the lip cancer risk data in Scotland between 1975 and 1980. The original data is from [1]. This dataset includes observed lip cancer case counts $\\{y_i\\}_{i=1}^N$ at $N=56$ spatial units in Scotland, with the expected number of cases $\\{E_i\\}_{i=1}^N$ as an offset term, an intercept parameter, and and a parameter for an area-specific continuous variable for the proportion of the population employed in agriculture, fishing, or forestry, denoted by $\\{x_i\\}_{i=1}^N$. We want to model how the lip cancer rates relate to the distribution of employment among industries, as exposure to sunlight is a risk factor. Mathematically, the model is \n",
"\\begin{align*} \n",
"y_i &\\sim \\text{Poisson}\\big (\\lambda_i),\\\\\n",
"\\log \\lambda_i &= \\beta_0+\\beta_1x_i + \\phi_i + \\log E_i,\\\\\n",
"\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i}&\\sim\\text{Normal}\\big(\\alpha\\sum_{j=1}^{n_i}w_{ij}\\phi_j, \\sigma_{i}^2\\big ), \\\\\n",
"\\beta_0, \\beta_1 &\\sim \\text{Normal}\\big (0, a\\big ),\n",
"\\end{align*}\n",
"where $a$ is the some chosen hyperparameter for the variance of the prior distribution of the regression coefficients. \n",
"\n",
"## Preparing the data \n",
"\n",
"We need to load in the dataset to access the variables $\\{y_i, x_i, E_i\\}_{i=1}^N$. But more unique to the use of CAR models, is the creation of the necessary spatial adjacency matrix. For the models that we fit, all neighbours are weighted as $1$, circumventing the need for a weight matrix."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"try:\n",
" df_scot_cancer = pd.read_csv(os.path.join(\"..\", \"data\", \"scotland_lips_cancer.csv\"))\n",
"except FileNotFoundError:\n",
" df_scot_cancer = pd.read_csv(pm.get_data(\"scotland_lips_cancer.csv\"))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [
{
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" CODENO NAME CANCER CEXP AFF ADJ \\\n",
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"\n",
" WEIGHTS \n",
"0 [1, 1, 1, 1] \n",
"1 [1, 1] \n",
"2 [1, 1] \n",
"3 [1, 1, 1] \n",
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"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_scot_cancer.head()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# observed cancer counts\n",
"y = df_scot_cancer[\"CANCER\"].values\n",
"\n",
"# number of observations\n",
"N = len(y)\n",
"\n",
"# expected cancer counts E for each county: this is calculated using age-standardized rates of the local population\n",
"E = df_scot_cancer[\"CEXP\"].values\n",
"logE = np.log(E)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# proportion of the population engaged in agriculture, forestry, or fishing\n",
"x = df_scot_cancer[\"AFF\"].values / 10.0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below are the steps that we take to create the necessary adjacency matrix, where the entry $i,j$ of the matrix is $1$ if observations $i$ and $j$ are considered neighbours, and $0$ otherwise."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# spatial adjacency information: column `ADJ` contains list entries which are preprocessed to obtain adj as a list of lists\n",
"adj = (\n",
" df_scot_cancer[\"ADJ\"].apply(lambda x: [int(val) for val in x.strip(\"][\").split(\",\")]).to_list()\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# change to Python indexing (i.e. -1)\n",
"for i in range(len(adj)):\n",
" for j in range(len(adj[i])):\n",
" adj[i][j] = adj[i][j] - 1"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# storing the adjacency matrix as a two-dimensional np.array\n",
"adj_matrix = np.zeros((N, N), dtype=\"int32\")\n",
"\n",
"for area in range(N):\n",
" adj_matrix[area, adj[area]] = 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualizing the data \n",
"\n",
"An important aspect of modelling spatial data is the ability to effectively visualize the spatial nature of the data, and whether the model that you have chosen captures this spatial dependency. \n",
"\n",
"We load in an alternate version of the *Scottish lip cancer* dataset, from the `libpysal` package, to use for plotting."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
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"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"_ = libpysal.examples.load_example(\"Scotlip\")\n",
"pth = libpysal.examples.get_path(\"scotlip.shp\")\n",
"spat_df = read_file(pth)\n",
"spat_df[\"PROP\"] = spat_df[\"CANCER\"] / np.exp(spat_df[\"CEXP\"])\n",
"spat_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We initially plot the observed number of cancer counts over the expected number of cancer counts for each area. The spatial dependency that we observe in this plot indicates that we may need to consider a spatial model for the data."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"scotland_map = spat_df.plot(\n",
" column=\"PROP\",\n",
" scheme=\"QUANTILES\",\n",
" k=4,\n",
" cmap=\"BuPu\",\n",
" legend=True,\n",
" legend_kwds={\"loc\": \"center left\", \"bbox_to_anchor\": (1, 0.5)},\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Writing some models in **PyMC**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Our first model: an *independent* random effects model\n",
"We begin by fitting an independent random effect's model. We are not modelling any *spatial dependency* between the areas. This model is equivalent to a Poisson regression model with a normal random effect, and mathematically looks like\n",
"\\begin{align*} \n",
"y_i &\\sim \\text{Poisson}\\big (\\lambda_i),\\\\\n",
"\\log \\lambda_i &= \\beta_0+\\beta_1x_i + \\theta_i + \\log E_i,\\\\\n",
"\\theta_i &\\sim\\text{Normal}\\big(\\mu=0, \\tau=\\tau_{\\text{ind}}\\big ), \\\\\n",
"\\beta_0, \\beta_1 &\\sim \\text{Normal}\\big (\\mu=0, \\tau = 1e^{-5}\\big ), \\\\\n",
"\\tau_{\\text{ind}} &\\sim \\text{Gamma}\\big (\\alpha=3.2761, \\beta=1.81\\big),\n",
"\\end{align*} \n",
"where $\\tau_\\text{ind}$ is an unknown parameter for the precision of the independent random effects. The values for the $\\text{Gamma}$ prior are chosen specific to our second model and thus we will delay explaining our choice until then."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [beta0, beta1, tau_ind, theta]\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"
\n",
" "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 4 chains for 2_000 tune and 2_000 draw iterations (8_000 + 8_000 draws total) took 32 seconds.\n"
]
}
],
"source": [
"with pm.Model(coords={\"area_idx\": np.arange(N)}) as independent_model:\n",
" beta0 = pm.Normal(\"beta0\", mu=0.0, tau=1.0e-5)\n",
" beta1 = pm.Normal(\"beta1\", mu=0.0, tau=1.0e-5)\n",
" # variance parameter of the independent random effect\n",
" tau_ind = pm.Gamma(\"tau_ind\", alpha=3.2761, beta=1.81)\n",
"\n",
" # independent random effect\n",
" theta = pm.Normal(\"theta\", mu=0, tau=tau_ind, dims=\"area_idx\")\n",
"\n",
" # exponential of the linear predictor -> the mean of the likelihood\n",
" mu = pm.Deterministic(\"mu\", pt.exp(logE + beta0 + beta1 * x + theta), dims=\"area_idx\")\n",
"\n",
" # likelihood of the observed data\n",
" y_i = pm.Poisson(\"y_i\", mu=mu, observed=y, dims=\"area_idx\")\n",
"\n",
" # saving the residual between the observation and the mean response for the area\n",
" res = pm.Deterministic(\"res\", y - mu, dims=\"area_idx\")\n",
"\n",
" # sampling the model\n",
" independent_idata = pm.sample(2000, tune=2000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can plot the residuals of this first model."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"spat_df[\"INDEPENDENT_RES\"] = independent_idata[\"posterior\"][\"res\"].mean(dim=[\"chain\", \"draw\"])"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"independent_map = spat_df.plot(\n",
" column=\"INDEPENDENT_RES\",\n",
" scheme=\"QUANTILES\",\n",
" k=5,\n",
" cmap=\"BuPu\",\n",
" legend=True,\n",
" legend_kwds={\"loc\": \"center left\", \"bbox_to_anchor\": (1, 0.5)},\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The mean of the residuals for the areas appear spatially correlated. This leads us to explore the addition of a spatially dependent random effect, by using a **conditional autoregressive (CAR)** prior.\n",
"\n",
"### Our second model: a *spatial* random effects model (with fixed spatial dependence)\n",
"Let us fit a model that has two random effects for each area: an *independent* random effect, and a *spatial* random effect first. This models looks\n",
"\\begin{align*} \n",
"y_i &\\sim \\text{Poisson}\\big (\\lambda_i),\\\\\n",
"\\log \\lambda_i &= \\beta_0+\\beta_1x_i + \\theta_i + \\phi_i + \\log E_i,\\\\\n",
"\\theta_i &\\sim\\text{Normal}\\big(\\mu=0, \\tau=\\tau_{\\text{ind}}\\big ), \\\\\n",
"\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i} &\\sim \\text{Normal}\\big(\\mu=\\alpha\\sum_{j=1}^{n_i}\\phi_j, \\tau=\\tau_{\\text{spat}}\\big ),\\\\\n",
"\\beta_0, \\beta_1 &\\sim \\text{Normal}\\big (\\mu = 0, \\tau = 1e^{-5}\\big), \\\\\n",
"\\tau_{\\text{ind}} &\\sim \\text{Gamma}\\big (\\alpha=3.2761, \\beta=1.81\\big), \\\\\n",
"\\tau_{\\text{spat}} &\\sim \\text{Gamma}\\big (\\alpha=1, \\beta=1\\big ),\n",
"\\end{align*} \n",
"where the line $\\phi_i \\big | \\mathbf{\\phi}_{j\\sim i} \\sim \\text{Normal}\\big(\\mu=\\alpha\\sum_{j=1}^{n_i}\\phi_j, \\tau=\\tau_{\\text{spat}}\\big )$ denotes the CAR prior, $\\tau_\\text{spat}$ is an unknown parameter for the precision of the spatial random effects, and $\\alpha$ captures the degree of spatial dependence between the areas. In this instance, we fix $\\alpha=0.95$. \n",
"\n",
"*Side note:* Here we explain the prior's used for the precision of the two random effect terms. As we have two random effects $\\theta_i$ and $\\phi_i$ for each $i$, they are independently unidentifiable, but the sum $\\theta_i + \\phi_i$ is identifiable. However, by scaling the priors of this precision in this manner, one may be able to interpret the proportion of variance explained by each of the random effects."
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"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [beta0, beta1, tau_ind, tau_spat, theta, phi]\n"
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