Factor Analysis for Mixed Data

Compute a low‑dimensional representation of a data frame that may contain both numeric and categorical variables. The routine dispatches to FactoMineR::PCA(), FactoMineR::MCA(), or FactoMineR::FAMD() based on the variable types present.

Usage

famd(data, weights = NULL, ncp = 1L)

Arguments

data: (data.frame)
The data frame of interest. Must not contain missing values.
weights: (Scalar character or NULL)
The column name in data providing row weights. If NULL, equal weights are used.
ncp: (Scalar integer)
The number of principal dimensions to compute and return. Must be an integer where ncp >= 1 and ncp <= min(nrow(data) - 1, d), where d is the effective dimensionality of the analysis: for PCA, d equals the number of numeric variables; for MCA, d equals the total number of factor levels minus the number of factor variables; for FAMD, d is the sum of both.

Value

An object returned by the corresponding FactoMineR function, of class "FAMD", "PCA", or "MCA" depending on the input variable types.

Details

If missing values are present in your data, you must either impute them or subset to complete cases before analysis. For example,

data_cc <- data[complete.cases(data), ]

If variables with zero-variance or less than two factor levels are present in your data, you must exclude them before analysis. For example,

w <- data$weights
valid_vars <- function(x) {
  if(is.numeric(x)) {
    vclust:::weighted_var(x, w) > .Machine$double.eps
  } else if(is.factor(x) || is.character(x) || is.logical(x)) {
    nlevels(droplevels(as.factor(x))) > 1
  } else {
    FALSE
  }
}
are_valid <- vapply(data, valid_vars, logical(1))
data_valid <- data[are_valid]

Character and logical columns are coerced to factors, and factors have unused levels dropped. Observation weights are validated to be numeric, finite, non‑negative, and with positive sum.

Numeric variables are centered and standardized. Factor variables are encoded as a set of indicator variables and scaled so that the total contribution of that factor variable is comparable to a single quantitative variable. FAMD can be seen as a PCA performed on a concatenation of standardized numeric variables and properly scaled indicator variables for factor variables so that each original variable contributes equally.

Examples

#----------------------------------------------------------------------------
# famd() examples
#----------------------------------------------------------------------------
library(vclust)

# Mixed data example with weights
set.seed(123)
n <- 100
df <- data.frame(
  x1 = rnorm(n),
  x2 = rnorm(n, mean = 2),
  grp = factor(sample(letters[1:3], n, replace = TRUE)),
  w   = rexp(n)
)

res_mix <- famd(df, weights = "w", ncp = 3)
res_mix$eig
#>        eigenvalue percentage of variance cumulative percentage of variance
#> comp 1  1.3099718               32.74930                          32.74930
#> comp 2  1.0183821               25.45955                          58.20885
#> comp 3  0.9989294               24.97323                          83.18208
# individual scores
head(res_mix$ind$coord)
#>        Dim.1      Dim.2      Dim.3
#> 1 -1.4589519 -0.1398538 -0.7280949
#> 2 -0.5388565  0.2397381 -0.6289524
#> 3 -0.4271341  2.0044762 -0.2075953
#> 4  0.5977247 -0.4779488 -0.8144091
#> 5  0.1029722 -0.4497487 -0.8123913
#> 6 -0.2089503  2.1711774 -0.1658212

# Numeric‑only (PCA)
res_pca <- famd(iris[1:4], ncp = 2)
res_pca$eig
#>        eigenvalue percentage of variance cumulative percentage of variance
#> comp 1  2.9184978               72.96245                          72.96245
#> comp 2  0.9140305               22.85076                          95.81321

# Factor‑only (MCA)
toy <- data.frame(
  a = factor(sample(c("yes", "no"), 50, TRUE)),
  b = factor(sample(c("L", "M", "H"), 50, TRUE))
)
res_mca <- famd(toy, ncp = 2)
res_mca$eig
#>       eigenvalue percentage of variance cumulative percentage of variance
#> dim 1  0.5615457               37.43638                          37.43638
#> dim 2  0.5000000               33.33333                          70.76972