loglik_kappa_est

Applicable to a single latent field, or multiple latent fields if common smoothness is assumed

internal

Implements the template ICA (independent components analysis) model
proposed in Mejia et al. (2020) <doi:10.1080/01621459.2019.1679638> and the
spatial template ICA model proposed in proposed in Mejia et al. (2022)
<doi:10.1080/10618600.2022.2104289>. Both models estimate subject-level
brain as deviations from known population-level networks, which are
estimated using standard ICA algorithms. Both models employ an
expectation-maximization algorithm for estimation of the latent brain
networks and unknown model parameters. Includes direct support for 'CIFTI',
'GIFTI', and 'NIFTI' neuroimaging file formats.

Amanda Mejia

templateICAr

Estimate Brain Networks and Connectivity with ICA and Empirical
Priors

Damon Pham

Daniel Spencer

Mary Beth Nebel

loglik_kappa_est function

<dl><dt>par</dt>
<dd>Vector of length two containing values of log kappa and log residual variance at which to compute log likelihood</dd>
<dt>delta</dt>
<dd>Estimate of delta (subject effect or deviation)</dd>
<dt>D_diag</dt>
<dd>Diagonal values of D matrix (template standard deviations)</dd>
<dt>mesh</dt>
<dd>Object of class "templateICA_mesh" containing the triangular mesh (see <code>make_mesh</code>)</dd>
<dt>C1</dt>
<dd>For the unit variance case, \(\tau^2 = C1/\kappa^2\), where \(C1 = 1/(4\pi)\) when \(\alpha=2\), \(\nu=1\), \(d=2\)</dd>
<dt>Q</dt>
<dd>Equal to the number of ICs for the common smoothness model, or NULL for the IC-specific smoothness model</dd></dl>

Arguments

Kappa log-likelihood — loglik_kappa_est

<dl>

<dt>par</dt>
<dd>Vector of length two containing values of log kappa and log residual variance at which to compute log likelihood</dd>


<dt>delta</dt>
<dd>Estimate of delta (subject effect or deviation)</dd>


<dt>D_diag</dt>
<dd>Diagonal values of D matrix (template standard deviations)</dd>


<dt>mesh</dt>
<dd>Object of class "templateICA_mesh" containing the triangular mesh (see <code>make_mesh</code>)</dd>


<dt>C1</dt>
<dd>For the unit variance case, \(\tau^2 = C1/\kappa^2\), where \(C1 = 1/(4\pi)\) when \(\alpha=2\), \(\nu=1\), \(d=2\)</dd>


<dt>Q</dt>
<dd>Equal to the number of ICs for the common smoothness model, or NULL for the IC-specific smoothness model</dd>

</dl>

loglik_kappa_est: Kappa log-likelihood

Description

Usage

Value

Arguments

Details