h_quad_form

h_quad_form_vec

h_quad_form_mat

These helpers are mainly for easier readability and slightly better efficiency
of the quadratic forms used in the Satterthwaite calculations.

internal

Mixed models for repeated measures (MMRM) are a popular
choice for analyzing longitudinal continuous outcomes in randomized
clinical trials and beyond; see Cnaan, Laird and Slasor (1997)
<doi:10.1002/(SICI)1097-0258(19971030)16:20%3C2349::AID-SIM667%3E3.0.CO;2-E>
for a tutorial and Mallinckrodt, Lane, Schnell, Peng and Mancuso
(2008) <doi:10.1177/009286150804200402> for a review. This package
implements MMRM based on the marginal linear model without random
effects using Template Model Builder ('TMB') which enables fast and
robust model fitting. Users can specify a variety of covariance
matrices, weight observations, fit models with restricted or standard
maximum likelihood inference, perform hypothesis testing with
Satterthwaite or Kenward-Roger adjustment, and extract least square
means estimates by using 'emmeans'.

Daniel Sabanes Bove

mmrm

Mixed Models for Repeated Measures

Liming Li

Julia Dedic

Doug Kelkhoff

Kevin Kunzmann

Brian Matthew Lang

Christian Stock

Ya Wang

Craig Gower-Page

Dan James

Jonathan Sidi

Daniel Leibovitz

Daniel D. Sjoberg

Lukas A. Widmer

Boehringer Ingelheim Ltd. 

Gilead Sciences, Inc. 

F. Hoffmann-La Roche AG 

Merck Sharp & Dohme, Inc. 

AstraZeneca plc 

inferential.biostatistics GmbH 

h_quad_form function

<dl><dt>vec</dt>
<dd>(<code>numeric</code>) interpreted as a row vector.</dd>
<dt>center</dt>
<dd>(<code>matrix</code>) square numeric matrix with the same dimensions as
<code>x</code> as the center of the quadratic form.</dd>
<dt>mat</dt>
<dd>(<code>matrix</code>) numeric matrix to be multiplied left and right of
<code>center</code>, therefore needs to have as many columns as there are rows and columns
in <code>center</code>.</dd></dl>

Arguments

<ul>
<li><code>h_quad_form_vec()</code>: calculates the number <code>vec %*% center %*% t(vec)</code>
as a numeric (not a matrix).</li>
<li><code>h_quad_form_mat()</code>: calculates the quadratic form <code>mat %*% center %*% t(mat)</code>
as a matrix, the result is square and has dimensions identical to the number
of rows in <code>mat</code>.</li>
</ul>

Functions

Quadratic Form Calculations — h_quad_form

<dl>

<dt>vec</dt>
<dd>(<code>numeric</code>) interpreted as a row vector.</dd>


<dt>center</dt>
<dd>(<code>matrix</code>) square numeric matrix with the same dimensions as
<code>x</code> as the center of the quadratic form.</dd>


<dt>mat</dt>
<dd>(<code>matrix</code>) numeric matrix to be multiplied left and right of
<code>center</code>, therefore needs to have as many columns as there are rows and columns
in <code>center</code>.</dd>

</dl>

Quadratic Form Calculations

h_quad_form: Quadratic Form Calculations

Description

Usage

Arguments

Functions