Extensible Data Structures for Multivariate Analysis

Provides a set of basic and extensible data structures and functions for multivariate analysis, including dimensionality reduction techniques, projection methods, and preprocessing functions. The aim of this package is to offer a flexible and user-friendly framework for multivariate analysis that can be easily extended for custom requirements and specific data analysis tasks.

multivarious

This package is intended to provide some basic abstractions and default implementations of basic computational infrastructure for multivariate component-based modeling such as principal components analysis.

The main idea is to model multivariate decompositions as involving projections from an input data space to a lower dimensional component space. This idea is encapsulated by the projector class and the project function. Support for two-way mapping (row projection and column projection) is provided by the derived class bi-projector. Generic functions for common operations are included:

• project for mapping from input space into (usually) reduced-dimensional output space
• partial_project for mapping a subset of input space into output space
• project_vars for mapping new variables (“supplementary variables”) to output space
• reconstruct for reconstructing input data from its low-dimensional representation
• residuals for extracting residuals of a fit with n components.

The package now also includes a mixed-model path for operator-valued ANOVA. With mixed_regress(), each named fixed-effect term in a repeated-measures design can be extracted as an effect_operator, then analyzed with the same core verbs:

• effect for named term extraction
• components and scores for interpretable effect axes
• reconstruct for effect contributions in original variable space
• perm_test for omnibus and rank inference
• bootstrap for subject-level stability

The broader calibration harness for this path lives at experimental/mixed_effect_operator_calibration.R, with batch outputs saved under experimental/results/ when you run the simulation grid locally.

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("bbuchsbaum/multivarious")

Example

This is a basic example which shows you how to solve a common problem:

library(multivarious)
#> 
#> Attaching package: 'multivarious'
#> The following objects are masked from 'package:stats':
#> 
#>     residuals, screeplot
#> The following objects are masked from 'package:base':
#> 
#>     transform, truncate
## basic example code

Mixed effect operators

set.seed(1)

design <- expand.grid(
  subject = factor(seq_len(6)),
  level = factor(c("low", "mid", "high"), levels = c("low", "mid", "high")),
  KEEP.OUT.ATTRS = FALSE
)
design$group <- factor(rep(c("A", "B"), each = 9))

level_num <- c(low = -1, mid = 0, high = 1)[as.character(design$level)]
group_num <- ifelse(design$group == "B", 1, 0)
subj_idx <- as.integer(design$subject)
b0 <- rnorm(6, sd = 0.5)

Y <- cbind(
  b0[subj_idx] + level_num + rnorm(nrow(design), sd = 0.15),
  group_num + rnorm(nrow(design), sd = 0.15),
  level_num * group_num + rnorm(nrow(design), sd = 0.15),
  rnorm(nrow(design), sd = 0.15)
)

fit <- mixed_regress(
  Y,
  design = design,
  fixed = ~ group * level,
  random = ~ 1 | subject,
  basis = shared_pca(3),
  preproc = pass()
)

E <- effect(fit, "group:level")
pt <- perm_test(E, nperm = 19, alpha = 0.10)

ncomp(E)
#> [1] 0
ncomp(pt)
#> [1] 0

Albers theme

This package uses the albersdown theme. Vignettes are styled with vignettes/albers.css and a local vignettes/albers.js; the palette family is provided via params$family (default ‘red’). The pkgdown site uses template: { package: albersdown }.