randomForest_star {countSTAR}R Documentation

Fit Random Forest STAR with EM algorithm

Description

Compute the MLEs and log-likelihood for the Random Forest STAR model. The STAR model requires a *transformation* and an *estimation function* for the conditional mean given observed data. The transformation can be known (e.g., log or sqrt) or unknown (Box-Cox or estimated nonparametrically) for greater flexibility. The estimator in this case is a random forest. Standard function calls including fitted and residuals apply.

Usage

randomForest_star(
  y,
  X,
  X.test = NULL,
  transformation = "np",
  y_max = Inf,
  sd_init = 10,
  tol = 10^-10,
  max_iters = 1000,
  ntree = 500,
  mtry = max(floor(ncol(X)/3), 1),
  nodesize = 5
)

Arguments

y

n x 1 vector of observed counts

X

n x p matrix of predictors

X.test

m x p matrix of out-of-sample predictors

transformation

transformation to use for the latent data; must be one of

  • "identity" (identity transformation)

  • "log" (log transformation)

  • "sqrt" (square root transformation)

  • "np" (nonparametric transformation estimated from empirical CDF)

  • "pois" (transformation for moment-matched marginal Poisson CDF)

  • "neg-bin" (transformation for moment-matched marginal Negative Binomial CDF)

  • "box-cox" (box-cox transformation with learned parameter)

y_max

a fixed and known upper bound for all observations; default is Inf

sd_init

add random noise for EM algorithm initialization scaled by sd_init times the Gaussian MLE standard deviation; default is 10

tol

tolerance for stopping the EM algorithm; default is 10^-10;

max_iters

maximum number of EM iterations before stopping; default is 1000

ntree

Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets predicted at least a few times. Default is 500.

mtry

Number of variables randomly sampled as candidates at each split. Default is p/3.

nodesize

Minimum size of terminal nodes. Setting this number larger causes smaller trees to be grown (and thus take less time). Default is 5.

Details

STAR defines a count-valued probability model by (1) specifying a Gaussian model for continuous *latent* data and (2) connecting the latent data to the observed data via a *transformation and rounding* operation.

The expectation-maximization (EM) algorithm is used to produce maximum likelihood estimators (MLEs) for the parameters defined in the The fitted values are computed using out-of-bag samples. As a result, the log-likelihood is based on out-of-bag prediction, and it is similarly straightforward to compute out-of-bag squared and absolute errors.

Value

a list with the following elements:

Note

Since the random forest produces random predictions, the EM algorithm will never converge exactly.

Infinite latent data values may occur when the transformed Gaussian model is highly inadequate. In that case, the function returns the *indices* of the data points with infinite latent values, which are significant outliers under the model. Deletion of these indices and re-running the model is one option, but care must be taken to ensure that (i) it is appropriate to treat these observations as outliers and (ii) the model is adequate for the remaining data points.

References

Kowal, D. R., & Wu, B. (2021). Semiparametric count data regression for self‐reported mental health. Biometrics. doi:10.1111/biom.13617

Examples


# Simulate data with count-valued response y:
sim_dat = simulate_nb_friedman(n = 100, p = 10)
y = sim_dat$y; X = sim_dat$X

# EM algorithm for STAR (using the log-link)
fit_em = randomForest_star(y = y, X = X,
                 transformation = 'log',
                 max_iters = 100)

# Fitted values (out-of-bag)
y_hat = fitted(fit_em)
plot(y_hat, y);

# Residuals:
plot(residuals(fit_em))
qqnorm(residuals(fit_em)); qqline(residuals(fit_em))

# Log-likelihood at MLEs (out-of-bag):
fit_em$logLik



[Package countSTAR version 1.0.2 Index]