New R package pams separates profile level from shape with bootstrap confidence

Statisticians who want to know not just how high a person scores across a battery of tests, but what shape their score pattern takes, now have a new tool. A December 2026 paper in SoftwareX introduces pams, an open-source R package that implements profile analysis via multidimensional scaling, or PAMS, with built-in bootstrap inference. The package, developed by S.-K. Kim and D. Kim and distributed through CRAN, bundles into a single reproducible workflow a set of steps that previously had to be programmed separately: standardizing variables, computing person levels and ipsatized patterns, building an inter-variable dissimilarity matrix, fitting and orienting a multidimensional scaling solution, running a person-level bootstrap with dimension alignment, calculating bias-corrected and accelerated confidence intervals, and regressing each person’s pattern on the retained coordinates.

The core idea behind profile analysis is that interpretation can depend on both a person’s overall elevation across measures and the deviations around that elevation. A student might score high on everything, or high on verbal tests and low on spatial ones, and these two descriptions carry different information. Common cluster-based and latent-profile workflows do not explicitly separate overall level from within-profile shape unless the variables are centered or the model is otherwise constrained. PAMS performs this decomposition directly. For each person, the level is defined as the mean of their standardized scores across the variables, and the pattern consists of the deviations of each score from that mean.

Once the patterns are extracted, the method applies nonmetric multidimensional scaling through the SMACOF algorithm to a matrix of dissimilarities between variables, rather than between people. This is a key computational feature: because the scaling step operates on the J variables rather than an I-by-I person-by-person matrix, the configuration cost depends primarily on the number of variables. The authors note that data preparation, bootstrapping, and statistical precision nevertheless remain sample-size dependent. The scaling yields a small set of core profiles, and each individual’s pattern is represented as a weighted combination of those core profiles plus a residual.

The principal function of the package is BootSmacof(), which optionally standardizes variables, forms the inter-variable distance matrix, fits the requested multidimensional scaling solution, resamples persons to estimate coordinate and stress uncertainty, and regresses each person’s pattern component on the retained core profiles to obtain weights and fit statistics. The package is distributed as a standalone package because it combines preprocessing, PAMS-specific bootstrap alignment and bias-corrected and accelerated inference, person-level projection, diagnostics, input validation, and S3 methods that are not provided by smacof, the underlying multidimensional scaling engine. Packaging these operations together also permits independent testing, documentation, and versioning.

Uncertainty quantification is central to the design. BootSmacof() resamples persons, reconstructs the dissimilarities, refits the multidimensional scaling solution, aligns the resampled dimensions with the original solution using the sign of their correlation, and calculates pointwise bias-corrected and accelerated confidence intervals for the core-profile coordinates and for stress. The default is 2,000 bootstrap samples, and the function warns when fewer than 1,000 are requested, since at least 1,000 are recommended for stable confidence-interval estimation. The returned object includes the original coordinates, bootstrap means, standard errors, percentile and bias-corrected and accelerated interval bounds, the full bootstrap distributions of the coordinates, and bootstrap stress summaries. The authors caution that these intervals are pointwise and are not adjusted for multiplicity.

To demonstrate the workflow, the paper uses the Holzinger and Swineford mental-ability data from 1939, in which 24 tests were administered to 301 seventh- and eighth-grade students at two Chicago schools. Because the tests are raw scores on heterogeneous scales, the analysis standardizes the columns, so each person’s level is the mean standardized score across the 24 tests and the pattern consists of deviations from that mean. Ordinal multidimensional scaling on the 24-by-24 inter-test Euclidean distance matrix produced stress values of .427, .185, .097, .073, and .055 for one to five dimensions. The authors retained three core profiles: the scree plot flattens after three dimensions, the three-dimensional stress of .097 is rated fair by Kruskal’s guidelines and is well below the .22 expected for random data with 24 objects, with a permutation test yielding p less than .005, and the fourth dimension adds no readily interpretable contrast.

The resulting core profiles correspond closely to the verbal, spatial, speed, and memory factors long reported for this battery. Core profile 1 shows significant positive coordinates for tests of general information, paragraph comprehension, sentence completion, word classification, word meaning, deduction, problem reasoning, and series completion, and significant negative coordinates for lozenges, counting dots, number recognition, object-number, and number-figure. Core profile 2 contrasts the spatial tests with the numerical-speed tests, and core profile 3 contrasts perceptual-speed tests with recognition-memory tests. The three profiles were nearly orthogonal, with R-squared values of each dimension regressed on the others of .04, .02, and .03. Observed three-dimensional stress was .097; across bootstrap samples the mean stress was .114 with a standard error of .010, and the 95 percent bias-corrected and accelerated interval for the population stress was [.083, .098].

Beyond the group-level profiles, the package returns person-level diagnostics. The Weight component contains, for every person, raw weights on each core profile, a level estimate, an R-squared value, and scale-free partial correlations between the person’s pattern and each core profile after controlling for the remaining profiles. In the example, the mean R-squared was .31, meaning the three core profiles reproduced about 31 percent of the variance in individual pattern components. The weights describe each person’s pattern component rather than overall level, and level correlated only .24, -.07, -.01, and .01 with the three weights and the R-squared, respectively, underscoring that level and pattern provide complementary information. The authors also present an illustrative school comparison in which Grant-White students had larger core-profile-1 weights than Pasteur students and smaller core-profile-3 weights, with no difference on core profile 2; these plug-in comparisons condition on the estimated solution and are presented as illustrations rather than a full account of uncertainty in group comparisons.

The package includes several safeguards and quality measures. It stops with an informative error if the requested number of profiles is not smaller than the number of variables, if the length of the direction vector differs from the number of profiles, or if the direction vector contains values other than 1 and -1. Automated testthat tests cover input validation, output structure, fixed-seed reproducibility, direction changes, and the plotting and summary methods, and the tests run through continuous integration using R CMD check. A worked vignette demonstrates dimensionality selection, orientation choices, bootstrap inference, plotting, and interpretation. Version 0.2.0 requires R 4.0.0 or later along with smacof 2.1.0 or later, is platform independent, and needs no compilation. The package has been available on CRAN since March 31, 2026, and the RStudio CRAN mirror recorded 854 downloads through September 10, 2026, a count of downloads rather than unique users.

The authors point to several directions where the approach may be useful. For longitudinal designs, stacked subscale scores can yield core trajectory profiles describing recurring patterns across measurement occasions, which may suit educational and developmental panel studies containing many participants and repeated multivariate measures. The computational advantage is strongest when the number of persons is large relative to the number of variables, although bootstrap time and precision still depend on sample size. The authors also flag limitations: version 0.2.0 conditions inference on the original dimension order and does not perform general rotational or permutation alignment, so weak or nearly interchangeable dimensions require caution, and interpretation should account for the pointwise rather than simultaneous nature of the intervals. The repository hosting the package contains the script that reproduces the reported analyses, figure, and tables, and the software is released under the MIT License with development open on GitHub.

Subject of Research: An R package for profile analysis via multidimensional scaling with bootstrap inference

Article Title: pams: An R package for profile analysis via multidimensional scaling

Article References: Kim, S. K., & Kim, D. (2026). pams: An R package for profile analysis via multidimensional scaling. SoftwareX, 36, Article 103160. https://doi.org/10.1016/j.softx.2026.103160

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103160

Keywords: R package, multidimensional scaling, profile analysis, bootstrap, statistics, psychometrics, SMACOF, open-source software, confidence intervals, Holzinger-Swineford, CRAN, data analysis