GPA Introduction

Introduction

Many morphometric analyses require that the researcher perform a Generalized Procrustes Analysis (GPA) in order to extract shape variables (that is, variables that do not include information on scale, translation, or rotation) from their landmark data. A GPA can be performed in geomorph using the function gpagen. This can be done with datasets composed of anatomical (fixed) landmarks as well as those with sliding semilandmarks.

plotAllSpecimens(plethodon$land)

gpagen() (Expand for more details)

$A$: The input data to be aligned. Must be in Array format.
$curves$: An optional matrix defining which landmarks should be treated as curve semilandmarks. See below for more details.
$surfaces$: An optional input defining which landmarks should be treated as surface semilandmarks.
$print.progress$: Logical value indicating whether a progress bar should be printed to the screen.

This is a very large function with several other potential arguments which we describe in the Advanced Options tutorial. See below for a full breakdown of the, also large, output of this function.

Output

The output of this function is a large list, or gpagen object with several subsets:

$coords$: An array of Procrustes shape variables. In other words, the aligned landmark coordinates.
$Csize$: A vector of centroid sizes for each specimen.
$consensus$: The mean (consensus) configuration, or shape of the input data.
$ProcD$: A Procrustes distance matrix for all specimens.
$p$: The number of landmarks.
$k$: The number of dimensions.
$nsliders$: The number of curve semilandmarks.
$nsurf$: The number of surface semilandmarks.
$call$: The user-input code.

The following gpagen outputs are associated with arguments that are discussed elsewhere, in the Advanced Options tutorial:

$iter$: The number of GPA iterations until convergence was found.
$points.VCV$: A variance-covariance matrix among Procrustes shape variables.
$points.var$: Variances of landmark points.
$data$: Data frame with a matrix of Procrustes shape variables and centroid size.
$Q$: Final convergence criterion value.
$slide.method$: Method used to slide semilandmarks.

Each of these subsets can be accessed separately using the ‘$’ operator, like so: