singl_log_lik

Evaluate the log-likelihood for a given set of parameters

internal

Provides functions to estimate, predict and interpolate areal
data. For estimation and prediction we assume areal data is an average
of an underlying continuous spatial process as in Moraga et
al. (2017) <doi:10.1016/j.spasta.2017.04.006>, Johnson et al. (2020)
<doi:10.1186/s12942-020-00200-w>, and Wilson and Wakefield (2020)
<doi:10.1093/biostatistics/kxy041>. The interpolation methodology is
(mostly) based on Goodchild and Lam (1980, ISSN:01652273).

Lucas da Cunha Godoy

smile

Spatial Misalignment: Interpolation, Linkage, and Estimation

singl_log_lik function

<dl><dt>theta</dt>
<dd>a <code>numeric</code> vector of size 4 (\(\mu, \sigma^2, \alpha,
\phi\)) containing the parameters associated with the model.</dd>
<dt>.dt</dt>
<dd>a <code>numeric</code> vector containing the variable \(Y\).</dd>
<dt>dists</dt>
<dd>a <code>list</code> of size distance matrices at the point level.</dd>
<dt>npix</dt>
<dd>a <code>integer vector</code> containing the number of pixels within
each polygon. (Ordered by the id variables for the polygons).</dd>
<dt>model</dt>
<dd>a <code>character</code> indicating which covariance function to
use. Possible values are <code>c("matern", "pexp", "gaussian",
 "spherical", "cs", "gw")</code>.</dd>
<dt>nu</dt>
<dd>\(\nu\) parameter. Not necessary if <code>model</code> is
<code>"gaussian"</code> or <code>"spherical"</code></dd>
<dt>kappa</dt>
<dd>\(\kappa \in \{0, \ldots, 3 \}\) parameter for the GW cov
function.</dd>
<dt>mu2</dt>
<dd>the smoothness parameter \(\mu\) for the GW function.</dd>
<dt>apply_exp</dt>
<dd>a <code>logical</code> indicating whether the exponential
transformation should be applied to variance parameters. This
facilitates the optimization process.</dd></dl>

Arguments

Evaluate log-lik — singl_log_lik

<dl>

<dt>theta</dt>
<dd>a <code>numeric</code> vector of size 4 (\(\mu, \sigma^2, \alpha,
\phi\)) containing the parameters associated with the model.</dd>


<dt>.dt</dt>
<dd>a <code>numeric</code> vector containing the variable \(Y\).</dd>


<dt>dists</dt>
<dd>a <code>list</code> of size distance matrices at the point level.</dd>


<dt>npix</dt>
<dd>a <code>integer vector</code> containing the number of pixels within
each polygon. (Ordered by the id variables for the polygons).</dd>


<dt>model</dt>
<dd>a <code>character</code> indicating which covariance function to
use. Possible values are <code>c("matern", "pexp", "gaussian",
 "spherical", "cs", "gw")</code>.</dd>


<dt>nu</dt>
<dd>\(\nu\) parameter. Not necessary if <code>model</code> is
<code>"gaussian"</code> or <code>"spherical"</code></dd>


<dt>kappa</dt>
<dd>\(\kappa \in \{0, \ldots, 3 \}\) parameter for the GW cov
function.</dd>


<dt>mu2</dt>
<dd>the smoothness parameter \(\mu\) for the GW function.</dd>


<dt>apply_exp</dt>
<dd>a <code>logical</code> indicating whether the exponential
transformation should be applied to variance parameters. This
facilitates the optimization process.</dd>

</dl>

singl_log_lik: Evaluate log-lik

Description

Usage

Value

Arguments

Details