linear_re: Main Function for fitting the random effect linear model

In pprof: Modeling, Standardization and Testing for Provider Profiling

Main Function for fitting the random effect linear model

Description

Fit a random effect linear model via lmer from the lme4 package.

Usage

linear_re(
  formula = NULL,
  data = NULL,
  Y = NULL,
  Z = NULL,
  ID = NULL,
  Y.char = NULL,
  Z.char = NULL,
  ID.char = NULL,
  ...
)

Arguments

formula	a two-sided formula object describing the model to be fitted, with the response variable on the left of a ~ operator and covariates on the right, separated by + operators. The random effect of the provider identifier is specified using (1 | ).
data	a data frame containing the variables named in the formula, or the columns specified by Y.char, Z.char, and ID.char.
Y	a numeric vector representing the response variable.
Z	a matrix or data frame representing the covariates, which can include both numeric and categorical variables.
ID	a numeric vector representing the provider identifier.
Y.char	a character string specifying the column name of the response variable in the data.
Z.char	a character vector specifying the column names of the covariates in the data.
ID.char	a character string specifying the column name of the provider identifier in the data.
...	additional arguments passed to lmer for further customization.

Details

This function is used to fit a random effect linear model of the form:

Y_{ij} = \mu + \alpha_i + \mathbf{Z}_{ij}^\top\boldsymbol\beta + \epsilon_{ij}

where Y_{ij} is the continuous outcome for individual j in provider i, \mu is the overall intercept, \alpha_i is the random effect for provider i, \mathbf{Z}_{ij} are the covariates, and \boldsymbol\beta is the vector of coefficients for the covariates.

The model is fitted by overloading the lmer function from the lme4 package. Three different input formats are accepted: a formula and dataset, where the formula is of the form response ~ covariates + (1 | provider), with provider representing the provider identifier; a dataset along with the column names of the response, covariates, and provider identifier; or the outcome vector \boldsymbol{Y}, the covariate matrix or data frame \mathbf{Z}, and the provider identifier vector.

In addition to these input formats, all arguments from the lmer function can be modified via ..., allowing for customization of model fitting options such as controlling the optimization method or adjusting convergence criteria. By default, the model is fitted using REML (restricted maximum likelihood).

If issues arise during model fitting, consider using the data_check function to perform a data quality check, which can help identify missing values, low variation in covariates, high-pairwise correlation, and multicollinearity. For datasets with missing values, this function automatically removes observations (rows) with any missing values before fitting the model.

Value

A list of objects with S3 class "random_re":

coefficient	a list containing the estimated coefficients: FE, the fixed effects for each predictor and the intercept, and RE, the random effects for each provider.
variance	a list containing the variance estimates: FE, the variance-covariance matrix of the fixed effect coefficients, and RE, the variance of the random effects.
sigma	the residual standard error.
fitted	the fitted values of each individual.
observation	the original response of each individual.
residuals	the residuals of each individual, that is response minus fitted values.
linear_pred	the linear predictor of each individual.
data_include	the data used to fit the model, sorted by the provider identifier. For categorical covariates, this includes the dummy variables created for all categories except the reference level.
char_list	a list of the character vectors representing the column names for the response variable, covariates, and provider identifier. For categorical variables, the names reflect the dummy variables created for each category.
Loglkd	the log-likelihood.
AIC	Akaike information criterion.
BIC	Bayesian information criterion.

References

Bates D, Maechler M, Bolker B, Walker S (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 1-48.

See Also

data_check

Examples

data(ExampleDataLinear)
outcome <- ExampleDataLinear$Y
covar <- ExampleDataLinear$Z
ID <- ExampleDataLinear$ID
data <- data.frame(outcome, ID, covar)
covar.char <- colnames(covar)
outcome.char <- colnames(data)[1]
ID.char <- colnames(data)[2]
formula <- as.formula(paste("outcome ~", paste(covar.char, collapse = " + "), "+ (1|ID)"))

# Fit random effect linear model using three input formats
fit_re1 <- linear_re(Y = outcome, Z = covar, ID = ID)
fit_re2 <- linear_re(data = data, Y.char = outcome.char, Z.char = covar.char, ID.char = ID.char)
fit_re3 <- linear_re(formula, data)

pprof documentation built on April 12, 2025, 1:33 a.m.