# as.carCM: Convert weights vector to parameters of 'dcar_proper'... In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

 as.carCM R Documentation

## Convert weights vector to parameters of `dcar_proper` distributio

### Description

Convert weights vector to `C` and `M` parameters of `dcar_proper` distribution

### Usage

```as.carCM(adj, weights, num)
```

### Arguments

 `adj` vector of indices of the adjacent locations (neighbors) of each spatial location. This is a sparse representation of the full adjacency matrix. `weights` vector of symmetric unnormalized weights associated with each pair of adjacent locations, of the same length as adj. This is a sparse representation of the full (unnormalized) weight matrix. `num` vector giving the number of neighbors of each spatial location, with length equal to the total number of locations.

### Details

Given a symmetric matrix of unnormalized weights, this function will calculate corresponding values for the `C` and `M` arguments suitable for use in the `dcar_proper` distribution. This function can be used to transition between usage of `dcar_normal` and `dcar_proper`, since `dcar_normal` uses the `adj`, `weights`, and `num` arguments, while `dcar_proper` requires `adj`, `num`, and also the `C` and `M` as returned by this function.

Here, `C` is a sparse vector representation of the row-normalized adjacency matrix, and `M` is a vector containing the conditional variance for each region. The resulting values of `C` and `M` are guaranteed to satisfy the symmetry constraint imposed on C and M, that M^{-1} C is symmetric, where M is a diagonal matrix and C is the row-normalized adjacency matrix.

### Value

A named list with elements `C` and `M`. These may be used as the `C` and `M` arguments to the `dcar_proper` distribution.

### Author(s)

Daniel Turek

`CAR-Normal`, `CAR-Proper`