# Credible interval estimation for curve correlation based on posterior simulation Inputs raw data representing two curves, and computes a credible interval for the curve correlation between them simulating from the approximate posterior distribution of the joint spline coefficient vector. ```r ccor_posim( y, time, curve = NULL, method, k = 15, conf = 0.95, ndraw = 999, min.overlap = 0 ) ``` ## Arguments - `y, time, curve, k, min.overlap`: see `ccor` - `method`: `"indep"` (curves fitted independently) or `"mvn"` (curves fitted together, with error correlation estimated based on multivariate normal likelihood) - `conf`: confidence level - `ndraw`: number of draws from posterior distribution of spline coefficient vector ## Returns A list with components - **cor**: curve correlation - **model**: the model for the two curves (if `method=="mvn"`), or a list of the two curves' models (if `method=="indep"`) - **bsb**: B-spline basis (from package `fda`) used for the curves - **Vc.fda**: corrected posterior covariance matrix for the coefficients with respect to the B-spline basis `bsb` (see the component `$Vc` in `gamObject`) - **sims**: curve correlations for the `ndraw` draws from the posterior distribution - **ci**: credible interval for the curve correlation ## Examples ```r ## Not run: if (interactive () && requireNamespace("wbwdi", quietly = TRUE) && requireNamespace("ggplot2", quietly = TRUE) && requireNamespace("dplyr", quietly = TRUE)) { # Curve correlation of per capita GDP and fertility rate in Paraguay wdi_dat <- wbwdi::wdi_get(entities = c("PRY"), start_year=1960, end_year=2023, indicators = c("NY.GDP.PCAP.KD","SP.DYN.TFRT.IN"), format="wide") |> dplyr::rename(percapitaGDP = NY.GDP.PCAP.KD, fertility = SP.DYN.TFRT.IN) ggplot2::ggplot(wdi_dat, aes(percapitaGDP, fertility, color=year)) + geom_point() y <- as.matrix(wdi_dat[ , c("percapitaGDP", "fertility")]) set.seed(345) ci <- list() ci[[1]] <- ccor_posim(y=y, time=wdi_dat$year, method="indep") ci[[2]] <- ccor_posim(y=y, time=wdi_dat$year, method="mvn") ci[[3]] <- ccor_boot(y=y, time=wdi_dat$year, ndraw=399) tabl <- matrix(NA, 3, 3) for (k in 1:3) tabl[k, ] <- c(ci[[k]]$cor, ci[[k]]$ci) dimnames(tabl) <- list(c("Posim_indep", "Posim_MVN", "Bootstrap"), c("Est","Lower95","Upper95")) round(tabl, 4) } ## End(Not run) ``` ## See Also `ccor`, `ccor_boot`, `mvn` ## Author(s) Philip Tzvi Reiss , Noemi Foa, Dror Arbiv and Biplab Paul

ccor_posim function