bivRegr {refreg}

Bivariate regression model

Description

This function estimates the covariates effects on the means vector, and variance covariance matrix from a bivariate variable. Non linear effects might be estimated for continuous covariates using penalized spline smoothers.

Usage

bivRegr(f = f, data = data, ace.eps = 0.01, ace.itmax = 25)

Arguments

f

A list of five formulas defining the covariates effects in both responses means, variances, and in their correlation. The formulas follow the same structure as mgcv::gam() (see example below).

data

A data frame containing the reponses, and predictor variables values.

ace.eps

A number defining the error rate in the ACE algorithm.

ace.itmax

A number defining the maximum number of ACE algorithm iterations.

Value

This function returns the covariates effect on the means, variances, and correlation of a bivariate response variable.

Examples

# Bivariate reference region for fasting plasma glucose (fpg)
# and glycated hemoglobin (hba1c) levels depending on age

dm_no <- subset(aegis, aegis$dm == "no") # select healthy patients
# 1.1) Define predictors
mu1 <- fpg ~ s(age)
mu2 <- hba1c ~ s(age)
var1 <- ~ s(age)
var2 <- ~ s(age)
rho <- ~ s(age)
f <- list(mu1, mu2, var1, var2, rho)

fit <- bivRegr(f, data = dm_no)

# 1.2) Depict the estimated covariates effects
plot(fit, eq = 1)
plot(fit, eq = 2)
plot(fit, eq = 3)
plot(fit, eq = 4)
plot(fit, eq = 5)
# 1.2.1) Depict the estimated covariates effects with CI (Not Run)

s0 <- summary_boot(fit, B = 100) # no parallelization
# s1 = summary_boot(fit,B=100,parallel=TRUE) #parallelization
plot(s0, eq = 1)


# 1.3) Obtain the reference region in the standarized residuals
region <- bivRegion(fit, tau = 0.95, shape = 2)
plot(region)

# 1.4) Identify those patients located outside the reference region
summary(region)

# 1.5) Depict the conditional reference region for two ages
plot(region,
  cond = TRUE, newdata = data.frame(age = c(20, 50)), col = "grey", pch = "*",
  reg.lwd = 2, reg.lty = 2
)