PAMS implements Profile Analysis via Multidimensional Scaling for the identification of population-level core response profiles from cross-sectional and longitudinal person-score data.
In a typical social-science dataset each row is a person profile — a vector of scores across J related subscales. PAMS decomposes each profile into two components:
PAMS then uses nonmetric multidimensional scaling (via the SMACOF algorithm) on the J × J inter-variable proximity matrix to identify a small number of core profiles — the central response patterns in the population. Because the proximity matrix is J × J rather than I × I, PAMS scales to any sample size, unlike cluster profile analysis.
The key inferential contribution of PAMS in R is the estimation of bootstrap standard errors and BCa confidence intervals for every core profile coordinate, enabling researchers to test which subscale peaks and valleys are statistically significant. This capability is not available in other profile analysis methods such as cluster profile analysis (CPA) or latent profile analysis (LPA). Both CPA and LPA also recover only level information, whereas PAMS recovers both level and pattern.
PAMS applies equally to cross-sectional and longitudinal data. For longitudinal data the input variables are the subscale scores stacked across time points, and the resulting core profiles are trajectory profiles that show how response patterns evolve over time.
# Install the CRAN release:
install.packages("pams")
# Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("sekangakim/pams")library(pams)
library(smacof)
# ---- Cross-sectional example ------------------------------------------------
# Load your data (persons x subscales)
cross_data <- read.csv("Cross-sectional.csv", header = FALSE)
colnames(cross_data) <- c("OV1","NS2","VA3","LP4","PP5","SR6","VS7","GI8",
"CF9","NR10","NP11","NW12","VA13","PR14","AS15",
"ON16","PC17","MW18")
# Step 1: inspect stress across dimensionalities to choose nprofile
smacofSym(dist(t(cross_data)), ndim = 2, type = "ordinal")$stress # 0.069
smacofSym(dist(t(cross_data)), ndim = 3, type = "ordinal")$stress # 0.047
smacofSym(dist(t(cross_data)), ndim = 4, type = "ordinal")$stress # 0.027
# Three-dimensional solution chosen (stress <= 0.05, Kruskal 1964)
# Step 2: run PAMS with 2,000 bootstrap samples
set.seed(1)
result <- BootSmacof(
testdata = cross_data,
participant = 1:10, # persons selected for individual assessment
mds = "smacof",
type = "ordinal",
distance = "euclid",
nprofile = 3,
direction = c(-1, 1, 1), # flip dimensions to aid interpretation
cl = 0.95,
nBoot = 2000,
testname = colnames(cross_data)
)
# Step 3: inspect results
summary(result)
plot(result, profiles = 1:3)
# Core profile coordinates with BCa CIs
round(result$MDSsummary[[1]], 3) # Core Profile 1
round(result$MDSsummary[[2]], 3) # Core Profile 2
round(result$MDSsummary[[3]], 3) # Core Profile 3
# Unstandardized OLS weights and partial correlations for selected persons
round(result$Weight[1:10, ], 2)
# Tidyverse-compatible tabular output (tibble is optional)
weights_tbl <- tibble::as_tibble(result$Weight, rownames = "participant")BootSmacof()The core function of the package. It fits a nonmetric MDS solution to the J × J inter-variable distance matrix of the input data, bootstraps the solution to produce empirical sampling distributions of core profile coordinates, and computes BCa confidence intervals. It also estimates person-level weights, R-squared values, and partial correlations with core profiles for all participants, with optional bootstrap CIs for a selected subset.
| Argument | Description |
|---|---|
testdata |
Data frame or matrix of persons × subscales |
participant |
Integer vector of persons for individual bootstrap assessment |
mds |
MDS algorithm: "smacof" (recommended) or
"classical" |
type |
Transformation type: "ordinal",
"interval", "ratio",
"mspline" |
distance |
Distance measure: "euclid" or
"sqeuclid" |
scale |
Logical; standardise variables before analysis |
nprofile |
Number of core profiles (dimensions) to extract |
direction |
Integer vector of 1 or −1 to flip dimension signs |
cl |
Confidence level for BCa intervals (default 0.95) |
nBoot |
Number of bootstrap samples (minimum 1000
recommended) |
testname |
Character vector of subscale names |
file |
Optional file stem for saving results as CSV |
Returns a named list with components:
| Component | Description |
|---|---|
MDS |
Original MDS fit object from smacof |
MDSsummary |
List of K data frames: coordinate, SE, BCa CI for each core profile |
MDSprofile |
List of K bootstrap coordinate matrices |
stresssummary |
Bootstrap summary (mean, SE, BCa CI) of smacof stress |
stressprofile |
Vector of 2,000 bootstrap stress values |
MDSR2 |
R² of Di regressed on other dimensions (collinearity check) |
Weight |
Unstandardized OLS weights, level, R², and partial correlations for all persons |
WeightmeanR2 |
Mean R² across all persons |
WeightB |
Bootstrap CIs for weights of selected participants |
PcorrB |
Bootstrap CIs for partial correlations of selected participants |
The bundled vignette provides a reproducible analysis using public
data. It covers preliminary dimensionality assessment, practical
direction selection, bootstrap fitting, the summary() and
plot() methods, person-level output, and conversion to a
tibble:
vignette("pams", package = "pams")MDS axis signs are arbitrary. Inspect a preliminary
smacofSym() solution and set each element of
direction to 1 or -1 so that
prespecified anchor variables appear on the desired side of the
corresponding axis. Reversing a sign does not change distances, stress,
fit, or whether a confidence interval excludes zero.
BootSmacof() performs sign alignment of resampled
dimensions to the original-sample solution. It does not perform general
rotational or dimension-permutation alignment, so coordinate-wise
inference requires care when dimensions are weak or nearly
interchangeable.
| Feature | PAMS | Cluster Profile Analysis | Latent Profile Analysis |
|---|---|---|---|
| Recovers level information | ✓ | ✓ | ✓ |
| Recovers pattern information | ✓ | ✗ | ✗ |
| Scales to any sample size | ✓ | ✗ | ✓ |
| Bootstrap CIs for coordinates | ✓ | ✗ | ✗ |
| Longitudinal extension | ✓ | Limited | Limited |
If you use PAMS in your research, please cite:
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. https://doi.org/10.20982/tqmp.20.3.p230
For the theoretical foundation of PAMS please also cite:
Davison, M. L. (1996). Multidimensional scaling interest and aptitude profiles: Idiographic dimensions, nomothetic factors. Presidential address to Division 5, American Psychological Association, Toronto.
For the SMACOF algorithm used in estimation:
de Leeuw, J., & Mair, P. (2009). Multidimensional scaling using majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1–30. https://doi.org/10.18637/jss.v031.i03
SEPA (Subprofile Extraction via Pattern Analysis) is a companion package by the same authors. While PAMS identifies population-level core profiles of response patterns, SEPA locates individual profiles in a two-dimensional SVD biplot space and quantifies each person’s alignment with cognitive ability domains via direction cosines. The two packages address complementary scientific questions and can be used together.
MIT © Se-Kang Kim & Donghoh Kim