5-lca.Rmd

---
title: "Latent class analysis"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Highlights

* Latent class analysis is designed for creating clusters out of binary or categorical variables.
* It is a **model-based clustering** method based on maximum likelihood estimation.
* It provides **soft-clustering**: each observation has a probability distribution over cluster membership.
* It uses a **greedy algorithm** with performance that varies with each analysis. Therefore we often will re-run an analysis 10 or 20 times and select the iteration with the best model fit.
* It originates from the broader class of **finite mixture models**.
* Latent dirichlet allocation (LDA) is a Bayesian form of LCA.

## Load data

```{r load_data}
# From 1-clean-data.Rmd
data = rio::import("data/clean-data-imputed.RData")

names(data)
str(data)
(task = list(
  factors = names(data)[sapply(data, is.factor)]))
```

## Basic LCA

```{r run_lca}
vars = task$factors

# Specify the formula based on the variables we want to use for clustering.
(f = as.formula(paste0("cbind(", paste(vars, collapse = ", "), ") ~ 1")))

model = poLCA(f, data, nclass = 2, maxiter = 100, nrep = 10, tol = 1e-7)
```

## Compare number of classes

```{r compare_classes}
library(knitr)
library(kableExtra)

run_lca = function(data, formula, nclass = 2, nrep = 10,
                   maxiter = 5000, tolerance = 1e-7, verbose = FALSE) {
  # TODO: capture output if verbose = FALSE
  
  lca = try(poLCA(formula, data, nclass = nclass, maxiter = maxiter, nrep = reps,
                  tol = tolerance))
  
  if ("try-error" %in% class(lca)) {
    cat("Ran into error.\n")
    results = list(nclass = nclass, aic = NA, bic = NA, converged = NA, object = NULL)
  } else {
  
    converged = lca$numiter < lca$maxiter
  
    # TODO: return object.
    results = list(nclass = nclass, aic = lca$aic, bic = lca$bic, converged = converged,
                   object = lca)
  }
  
  return(results)
}

reps = 5L

results = data.frame(matrix(NA, nrow = 0, ncol = 5))
colnames = c("nclass", "aic", "bic", "converged", "description")
colnames(results) = colnames

set.seed(1)

objects = list()
outcome = NULL
# We could use nicer names for the variables here.
var_labels = vars

# Try 2 to 6 classes (clusters)
for (classes in 2:6) {
  cat("Running LCA for", classes, "classes.\n")
  
  #################### 
  # Run the latent class analysis.
  result = run_lca(data, f, nclass = classes, nrep = reps)
  
  # Extract the return object and store separately.
  object = result$object
  
  # Remove the object from the list so that we can store everything else in a dataframe.
  result$object = NULL
  
  # Could put something in here.
  result$description = ""
  
  # Use a string list name so that we don't need a null [[1]] element.
  objects[[as.character(classes)]] = object
  
  # This will be a data.frame of summary statistics, 1 row per LCA.
  results = rbind(results, result, stringsAsFactors = FALSE)
  
  # Correct colnames again.
  colnames(results) = colnames
  
  #####
  # Generate covariate table.
  
  # Currently restricting to complete cases. Could use imputed data instead possibly.
  temp_data = na.omit(data[, c(outcome, vars)])
  
  # This function is defined in R/lca-covariate-table.R
  table = lca_covariate_table(object, var_labels = var_labels,
                              outcome = NULL,
                              format = "html", # could be latex instead.
                              data = temp_data[, vars])
  
  ################
  print(kable(table, booktabs = TRUE, digits = c(rep(1, classes), 3, 3),
            col.names = linebreak(colnames(table), align = "c"),
            escape = FALSE) %>%
        kable_styling(latex_options = c("scale_down"#,
                                       # "striped"
                                        )) %>%
        row_spec(nrow(table) - 1L, hline_after = TRUE))
  
  # TODO: generate Excel export also, ideally as a separate tab within a single file.
  
}

results

```

## Resources

* Collins and Lanza. (2009). [Latent class and latent transition analysis](https://smile.amazon.com/Latent-Class-Transition-Analysis-Applications/dp/0470228393/)
* [Latent profile analysis in R](https://cran.r-project.org/web/packages/tidyLPA/vignettes/Introduction_to_tidyLPA.html)

## References

Figueroa, S. C., Kennedy, C. J., Wesseling, C., Wiemels, J. M., Morimoto, L., & Mora, A. M. (2020). Early immune stimulation and childhood acute lymphoblastic leukemia in Costa Rica: A comparison of statistical approaches. Environmental Research, 182, 109023.