LatentClassAnalysis.jl

A Julia package for Latent Class Analysis (LCA)

Latent Class Analysis (LCA) is a statistical method for identifying unobserved subgroups within a population based on categorical response patterns. Common applications include market segmentation, behavioral pattern identification, and psychological profiling.

This package brings LCA to the Julia ecosystem, with key features such as:

• Supports binary, string, and categorical variables
• Fit LCA models via EM algorithm
• Model diagnostics (e.g., AIC, BIC, SBIC, entropy)
• Show latent class profiles and class assignment probabilities

Installation

using Pkg
Pkg.add("LatentClassAnalysis")

Quick Example

Let's create a dataset with three response variables. LatentClassAnalysis is designed to handle dummy and categorical variables. String variables will be automatically converted to categorical ones.

using LatentClassAnalysis
using DataFrames

# Create sample data (100 observations)
df = DataFrame(
    item1 = repeat([0, 1, 0, 1, 1], 20),  # Binary responses with 0/1 coding
    item2 = categorical(repeat(["A", "B", "A", "B", "A"], 20)),  # Categorical
    item3 = repeat([1, 1, 2, 2, 1], 20)   # Binary responses with 1/2 coding
)

Step 1: prepare data.

# Prepare data
data, n_categories = prepare_data(df, :item1, :item2, :item3)

Step 2: fit models with different number of classes.

# Fit models with different numbers of classes
results = []
for k in 2:3
    model = LCAModel(k, size(data, 2), n_categories)
    ll = fit!(model, data)
    diag = diagnostics!(model, data, ll)
    push!(results, (n_classes=k, model=model, diagnostics=diag))
    
    println("Model with $k classes:")
    println("  BIC: $(round(diag.bic, digits=2))")
    println("  Entropy: $(round(diag.entropy, digits=3))")
end

Step 3: select best model and show profile.

# Select best model by BIC
best_result = argmin(r -> r.diagnostics.bic, results)
best_model = best_result.model

# Show profile
show_profiles(best_model, df, [:item1, :item2, :item3])

# Get class predictions
assignments, probabilities = predict(best_model, data)

Extended Example

See example.jl for an example with simulated data. See example_childless.jl for an example with real-world data on childlessness, replicating this research:

• Wang, Yanwen, Bussarawan Teerawichitchainan, and Christine Ho. 2024. “Diverse Pathways to Permanent Childlessness in Singapore: A Latent Class Analysis.” Advances in Life Course Research 61:100628. doi: 10.1016/j.alcr.2024.100628.