1d:T7f0,# Bivariate regression model 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. ```r 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. ## Returns This function returns the covariates effect on the means, variances, and correlation of a bivariate response variable. ## Examples ```r # 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 ) ```

bivRegr function