Package {pams}

Type:	Package
Title:	Profile Analysis via Multidimensional Scaling
Version:	0.2.0
Date:	2026-10-05
Description:	Implements Profile Analysis via Multidimensional Scaling (PAMS) for the identification of population-level core response profiles from cross-sectional and longitudinal person-score data. Each person profile is decomposed into a level component (the person mean) and a pattern component (ipsatized subscores). PAMS uses nonmetric multidimensional scaling via the SMACOF algorithm to identify a small number of core profiles that represent the central response patterns in a sample of any size. Bootstrap standard errors and bias-corrected and accelerated (BCa) confidence intervals for individual core profile coordinates are estimated, enabling significance testing of coordinates that is not available in other profile analysis methods such as cluster profile analysis or latent profile analysis. Person-level weights, R-squared values, and partial correlations with core profiles are also estimated, allowing individual profiles to be interpreted in terms of the core profile structure. PAMS can be applied to both cross-sectional data and longitudinal data, where core trajectory profiles describe how response patterns change over time. Methods are described in Kim and Kim (2024) <doi:10.20982/tqmp.20.3.p230>, de Leeuw and Mair (2009) <doi:10.18637/jss.v031.i03>, and Kruskal (1964) <doi:10.1007/BF02289565>.
License:	MIT + file LICENSE
URL:	https://github.com/sekangakim/pams
BugReports:	https://github.com/sekangakim/pams/issues
Depends:	R (≥ 4.0.0)
Imports:	smacof (≥ 2.1.0)
Suggests:	knitr, lmtest (≥ 0.9.40), rmarkdown, testthat (≥ 3.0.0), tibble
VignetteBuilder:	knitr
Encoding:	UTF-8
Config/testthat/edition:	3
NeedsCompilation:	no
Config/roxygen2/version:	8.1.0
Packaged:	2026-10-06 01:00:45 UTC; sekangkim
Author:	Se-Kang Kim [aut, cre], Donghoh Kim [aut]
Maintainer:	Se-Kang Kim <sekangandroid@gmail.com>
Repository:	CRAN
Date/Publication:	2026-10-06 22:00:09 UTC

Profile Analysis via Multidimensional Scaling

Description

Identifies population-level core response profiles from cross-sectional or longitudinal person-score data using nonmetric multidimensional scaling (SMACOF algorithm). Each person profile is decomposed into a level component (person mean) and a pattern component (ipsatized subscores). BootSmacof fits a nonmetric MDS solution to the J \times J inter-variable distance matrix, bootstraps the solution to generate empirical sampling distributions of core profile coordinates, and computes bias-corrected and accelerated (BCa) confidence intervals for each coordinate. Person-level weights, R-squared values, and partial correlations with core profiles are estimated for all participants, with optional bootstrap confidence intervals for a selected subset.

Usage

BootSmacof(
  testdata,
  participant = NULL,
  mds = c("smacof", "classical"),
  type = c("ordinal", "interval", "ratio", "mspline"),
  distance = c("euclid", "sqeuclid"),
  scale = FALSE,
  nprofile = 3,
  direction = rep(1, nprofile),
  cl = 0.95,
  nBoot = 2000,
  testname = NULL,
  file = NULL
)

Arguments

Value

A named list with the following components:

MDS

The MDS fit object for the original data. When mds = "smacof" this is the full object returned by smacofSym, including $conf (core profile coordinate matrix, J \times K) and $stress. When mds = "classical" this is a minimal list with $conf only.

MDSsummary

A list of nprofile data frames, one per core profile. Each data frame has rows corresponding to subscales and columns: Ori (original coordinate), Mean (bootstrap mean), SE (bootstrap standard error), Lower and Upper (percentile CI bounds), BCaLower and BCaUpper (BCa CI bounds). Coordinates whose pointwise BCa CI does not include zero are statistically significant at the stated coordinate-wise level; these intervals are not adjusted for multiplicity.

MDSprofile

A list of nprofile matrices, each of dimension nBoot \times J, containing the full bootstrap distribution of core profile coordinates.

stresssummary

A one-row data frame with bootstrap summary statistics for the smacof stress value: Ori, Mean, SE, Lower, Upper, BCaLower, BCaUpper. NULL when mds = "classical".

stressprofile

A numeric vector of length nBoot containing bootstrap stress values. NULL when mds = "classical".

MDSR2

A numeric vector of length nprofile containing the R-squared values from regressing each core profile dimension on the remaining dimensions. Low values confirm that the core profiles are not collinear.

Weight

A matrix of dimension I \times (2K + 2) containing, for every person: raw weights (w1, ..., wK), level estimate, R-squared value, and partial correlations with each core profile (corDim1, ..., corDimK). The raw weights are unstandardized no-intercept OLS coefficients from regressing the person's ipsatized pattern on the retained coordinate vectors. Each corDim value is the correlation between the residualized person pattern and residualized focal core profile after controlling for the other profiles. Row names are "#1", "#2", ...

WeightmeanR2

The mean R-squared value across all I persons, summarising how well the nprofile core profiles account for pattern variance in the sample.

WeightB

A matrix of bootstrap summary statistics (original estimate, mean, SE, lower and upper CI bounds) for the weights of each person in participant. NULL if participant is NULL.

PcorrB

A matrix of bootstrap summary statistics for the partial correlations of each person in participant. NULL if participant is NULL.

nprofile

The number of core profiles extracted.

nBoot

The number of bootstrap samples used.

scale

Logical; whether columns were standardised.

testname

Character vector of subscale names used.

The returned list has class "pams_fit", while retaining direct access to every component listed above.

Sign indeterminacy and alignment

MDS coordinate signs are arbitrary. For each bootstrap and jackknife sample, BootSmacof() aligns each dimension to its original-sample counterpart by its correlation sign and then reports the orientation selected through direction. This is sign alignment only: the method does not perform general rotational alignment or dimension-permutation matching. Coordinate-wise inference should therefore be interpreted cautiously when dimensions are weak or nearly interchangeable. A sign reversal changes only the reported orientation; it does not change interpoint distances, stress, model fit, or interval exclusion of zero.

References

Davison, M. L. (1996). Multidimensional scaling interest and aptitude profiles: Idiographic dimensions, nomothetic factors. Presidential address to Division 5, American Psychological Association, Toronto.

de Leeuw, J., & Mair, P. (2009). Multidimensional scaling using majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1–30. doi:10.18637/jss.v031.i03

Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall.

Kim, S.-K., & Kim, D. (2024). Utility of profile analysis via multidimensional scaling in R for the study of person response profiles in cross-sectional and longitudinal data. The Quantitative Methods for Psychology, 20(3), 230–247. doi:10.20982/tqmp.20.3.p230

Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27. doi:10.1007/BF02289565

See Also

smacofSym for the underlying MDS algorithm.

Examples

# Small toy example (runs automatically)
set.seed(42)
toy_data <- as.data.frame(matrix(rnorm(8 * 4, mean = 10, sd = 2),
                                 nrow = 8, ncol = 4))
colnames(toy_data) <- paste0("S", 1:4)

result <- suppressWarnings(BootSmacof(
  testdata    = toy_data,
  participant = NULL,
  mds         = "smacof",
  type        = "ordinal",
  distance    = "euclid",
  nprofile    = 2,
  direction   = c(1, 1),
  cl          = 0.95,
  nBoot       = 10,
  testname    = colnames(toy_data)
))
result$MDS$stress
round(result$WeightmeanR2, 2)
round(result$MDSsummary[[1]], 3)

Plot fitted PAMS core profiles

Description

Displays selected core-profile coordinates and, optionally, their pointwise percentile or BCa confidence limits.

Usage

## S3 method for class 'pams_fit'
plot(
  x,
  profiles = seq_len(x$nprofile),
  interval = c("BCa", "percentile", "none"),
  layout = NULL,
  labels = TRUE,
  label.cex = 0.75,
  type = "b",
  pch = 19,
  col = "black",
  ci.col = "steelblue",
  ci.lty = 2,
  zero.line = TRUE,
  zero.col = "grey60",
  xlab = "Variable",
  ylab = "Coordinate",
  main = NULL,
  ylim = NULL,
  xaxt = if (labels) "n" else "s",
  ...
)

Arguments

Value

The fitted object, invisibly.

Examples

set.seed(42)
x <- matrix(rnorm(32), nrow = 8, ncol = 4)
fit <- suppressWarnings(BootSmacof(x, nprofile = 2, nBoot = 10))
plot(fit, profiles = 1:2)

Summarize a fitted PAMS model

Description

Summarize a fitted PAMS model

Usage

## S3 method for class 'pams_fit'
summary(object, digits = 3L, ...)

## S3 method for class 'summary.pams_fit'
print(x, ...)

## S3 method for class 'pams_fit'
print(x, ...)

Arguments

Value

'summary.pams_fit()' returns an object of class 'summary.pams_fit' containing the analysis settings, stress, fit indices, and the number of coordinates whose pointwise BCa interval excludes zero.

Examples

set.seed(42)
x <- matrix(rnorm(32), nrow = 8, ncol = 4)
fit <- suppressWarnings(BootSmacof(x, nprofile = 2, nBoot = 10))
summary(fit)