PSweight (version 2.1.1)

OUTmethod_SW: Fitting potential outcome regression with different methods in survey observational data

Description

The function OUTmethod_SW is an internal function to estimate the potential outcomes given a specified model through formula. It is built into function PSweight, and is used for constructing the augmented estimators.

Usage

OUTmethod_SW(
  out.formula = out.formula,
  out.weights = NULL,
  y = y,
  out.method = "glm",
  family = "gaussian",
  datain = datain,
  dataout = dataout,
  out.control = list()
)

Value

m.est

a vector of predicted outcome on the dataout.

gamma.h

estimated coefficient of the outcome model when method = "glm".

Arguments

out.formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the outcome model to be fitted.

out.weights

A numeric vector of weights to be used in the weighted regression estimator. For the moment estimator(MOM) and clever covariates estimator(CVR), this parameter defaults to NULL; however, in the weighted regression estimator(WET) it should be set to the balancing weights used for the weighted outcome regression model.

y

a vector of the observed outcome in the training data (datain).

out.method

a character to specify the method for estimating the outcome regression model. "glm" is default, and "gbm" and "SuperLearner" are also allowed.

family

a description of the error distribution and link function to be used in the outcome model. Supported distributional families include "gaussian" (link = identity), "binomial" (link = logit) and "poisson" (link = log). Default is "gaussian".

datain

The training data for the outcome model. In the context of PSweight, it refers to the data observed for each treatment group.

dataout

The prediction data for the outcome model. In the context of PSweight, it refers to the full data.

out.control

a list to specify additional options when out.method is set to "gbm" or "SuperLearner".

Details

A typical form for out.formula is y ~ terms where y is the outcome variable and terms is a series of terms which specifies linear predictors (on the link function scale). out.formula by default specifies generalized linear model given the gaussian error through the default arguments method = "glm" and family = "gaussian". It fits the logistic regression when family = "binomal",and poisson regression when family = "poisson". The argument out.method allows user to choose model other than glm to fit the outcome regression models for constructing the augmented estimator. We have included gbm and SuperLearner as alternative machine learning estimators. Additional argument in them can be supplied through the ... argument. Please refer to the user manual of the gbm and SuperLearner packages for all the allowed arguments.

When out.weights is provided, weighted regression is applied in all supported methods. In "glm", weighted least squares is used for Gaussian outcomes, and weighted likelihood for binomial or Poisson outcomes. If family = "poisson" and non-integer outcomes are detected (due to continuous-valued responses or weighting effects), the function automatically switches to "gaussian" to ensure numerical stability. In "gbm", outcome weights are passed via the weights argument, and if non-integer outcomes exist under family = "poisson", the model switches to "gaussian". For "SuperLearner", weighted estimation is supported through the obsWeights argument. Since "SuperLearner" does not support Poisson regression, a warning is issued, and the model defaults to "gaussian". These adjustments ensure compatibility and stability across different estimation approaches.

Examples

# Load example datasets
data("psdata")
data("psdata_bin_prospective_fp")
data("psdata_bin_retrospective_fp")

# Define the outcome model formula.
out.formula <- Y ~ cov1 + cov2 + cov3 + cov4 + cov5 + cov6

# Extract the outcome vector from the retrospective data.
y <- psdata_bin_retrospective_fp$Y

# Use only the observations in treatment group 1 as the training data.
datain <- psdata_bin_retrospective_fp[psdata_bin_retrospective_fp$trt == 1, ]

# Fit the outcome regression model via OUTmethod_SW.
# By default, out.method = "glm" and family = "gaussian" are used.
outfit <- OUTmethod_SW(out.formula = out.formula, y = y, datain = datain,
                       dataout = psdata_bin_retrospective_fp)

# Print the predicted outcome vector on dataout.
cat("Predicted outcomes (first 10 values):\n")
print(head(outfit$m.est, 10))

# Print the estimated coefficient vector from the GLM.
cat("\nEstimated coefficients (gamma.h):\n")
print(outfit$gamma.h)