# Predictions from fitted DDPstar models Takes a fitted `DDPstar` object produced by `DDPstar()` and produces predictions for different functionals given a new set of values for the model covariates. ```r ## S3 method for class 'DDPstar' predict(object, what = NULL, newdata, reg.select = NULL, den.grid = NULL, quant.probs = NULL, q.value = NULL, parallel = c("no", "multicore", "snow"), ncpus = 1, cl = NULL, ...) ``` ## Arguments - `object`: An object of class `DDPstar` as produced by `DDPstar()`. - `what`: Character vector with the functionals to be obtained: ``regfun'' (regression function); ``varfun'' (variance function); ``quantfun'' (condional quantiles); ``denfun'' (conditional densities); ; ``probfun'' (conditional probabilities, i.e., probabilities of the form $P(Y \leq y^{*} \mid X = x)$). - `newdata`: Data frame containing the values of the covariates at which predictions will be computed - `reg.select`: Numeric value containing the position of the covariate effect in the DDPstar formula for which predictions are required. If NULL (and `"regfun"` is in input argument `what`), the regression function (coditional mean) is computed. - `den.grid`: Numeric vector with the response variable values at which the conditional densities should be computed. Applicable and required if ``denfun'' is in argument `what`. If required and NULL, a sequence of 100 values between the minumum and the maximum of the observed responses is considered. - `quant.probs`: Numeric vector with the quantiles at which to obtain/predict the conditional quantiles. Applicable and required if ``quantfun'' is in argument `what`. If required and NULL, the deciles are computed. - `q.value`: Numeric vector with the response variable values at which to obtain/predict the conditional probabilities. Applicable and required if ``probfun'' is in argument `what`. - `parallel`: A characters string with the type of parallel operation: either "no" (default), "multicore" (not available on Windows) or "snow". - `ncpus`: An integer with the number of processes to be used in parallel operation. Defaults to 1. - `cl`: An object inheriting from class `cluster` (from the `parallel` package), specifying an optional parallel or snow cluster if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the call. - ``...``: Further arguments passed to or from other methods. Not yet implemented. ## Returns A list with the following components (`npred` is the number of columns in `newdata` and `nsave` is the number of Gibbs sampler iterations saved) - **regfun**: Present if `"regfun"` is in input argument `what`. A matrix of dimension `npred`$\times$`nsave` with the MCMC realisations of the regression function (conditional mean) or the desired component (if `reg.select` is used). - **reg.select**: Argument `reg.select` used in the call. Present if `"regfun"` is in input argument `what`. - **varfun**: Present if `"varfun"` is in input argument `what`. A matrix of dimension `npred`$\times$`nsave` with the MCMC realisations of the conditional variance. - **quantfun**: Present if `"quantfun"` is in input argument `what`. An array of dimension `npred`$\times$`nsave`$\times$`nq` with the MCMC realisations of the conditional quantiles. Here `nq` is the length of argument `quant.probs`. - **quant.probs**: Argument `quant.probs` used in the call. Present if `"quantfun"` is in input argument `what`. - **denfun**: Present if `"denfun"` is in input argument `what`. An array of dimension `nden`$\times$`npred`$\times$`nsave` with the MCMC realisations of the conditional densities. Here `nden` is the length of argument `den.grid`. - **den.grid**: Argument `den.grid` used in the call. Present if `"denfun"` is in input argument `what`. - **probfun**: Present if `"probfun"` is in input argument `what`. An array of dimension `ny`$\times$`npred`$\times$`nsave` with the MCMC realisations of the conditional probabilities. Here `ny` is the length of argument `q.value` - **q.value**: Argument `q.value` used in the call. Present if `"probfun"` is in input argument `what`. ## See Also `DDPstar` ## Examples ```r library(DDPstar) data(dde) dde$GAD <- dde$GAD/7 # GAD in weeks set.seed(10) # For reproducibility fit_dde <- DDPstar(formula = GAD ~ f(DDE, bdeg = 3, nseg = 20, pord = 2, atau = 1, btau = 0.005), data = dde, mcmc = list(nburn = 20000, nsave = 15000, nskip = 1), prior = list(a = 2, b = 0.5, aalpha = 2, balpha = 2, L = 20), standardise = TRUE, compute.lpml = TRUE, compute.WAIC = TRUE) # Data frame for predictions (regression, variance, quartiles and probabilities functions) df_pred <- data.frame(DDE = seq(min(dde$DDE), max(dde$DDE), length = 50)) # Data frame for conditional densities # Compute the densities for 4 different DDE values df_pred_den <- data.frame(DDE = quantile(dde$DDE, c(0.1, 0.6, 0.9, 0.99))) sequenceGAD <- seq(min(dde$GAD), max(dde$GAD), length = 100) # Regression and variance function reg_var_DDE <- predict(fit_dde, newdata = df_pred, what = c("regfun", "varfun"), parallel = "multicore", ncpus = 2) # Regression function reg_m <- apply(reg_var_DDE$regfun, 1, median) reg_ql <- apply(reg_var_DDE$regfun, 1, quantile, 0.025) reg_qh <- apply(reg_var_DDE$regfun, 1, quantile, 0.975) plot(dde$DDE, dde$GAD, xlab = "DDE (mg/L)", ylab = "Gestational age at delivery (in weeks)", main = "Regression function") lines(df_pred$DDE, reg_m, lwd = 2) lines(df_pred$DDE, reg_ql, lty = 2) lines(df_pred$DDE, reg_qh, lty = 2) # Variance function var_m <- apply(reg_var_DDE$varfun, 1, median) var_ql <- apply(reg_var_DDE$varfun, 1, quantile, 0.025) var_qh <- apply(reg_var_DDE$varfun, 1, quantile, 0.975) plot(df_pred$DDE, var_m, type = "l", lwd = 2, xlab = "DDE (mg/L)", ylab = "", main = "Variance function") lines(df_pred$DDE, var_ql, lty = 2) lines(df_pred$DDE, var_qh, lty = 2) # Quartiles p <- c(0.25, 0.5, 0.75) quart_DDE <- predict(fit_dde, newdata = df_pred, what = "quantfun", quant.probs = p, parallel = "multicore", ncpus = 2) quart_m <- apply(quart_DDE$quantfun , c(1,3), median) quart_ql <- apply(quart_DDE$quantfun , c(1,3), quantile, 0.025) quart_qh <- apply(quart_DDE$quantfun , c(1,3), quantile, 0.975) plot(dde$DDE, dde$GAD, xlab = "DDE (mg/L)", ylab = "Gestational age at delivery (in weeks)", main = "Conditional quartiles") # Q1 lines(df_pred$DDE, quart_m[,1], lwd = 2, col = 2) lines(df_pred$DDE, quart_ql[,1], lty = 2, col = 2) lines(df_pred$DDE, quart_qh[,1], lty = 2, col = 2) # Median lines(df_pred$DDE, quart_m[,2], lwd = 2) lines(df_pred$DDE, quart_ql[,2], lty = 2) lines(df_pred$DDE, quart_qh[,2], lty = 2) # Q3 lines(df_pred$DDE, quart_m[,3], lwd = 2, col = 3) lines(df_pred$DDE, quart_ql[,3], lty = 2, col = 3) lines(df_pred$DDE, quart_qh[,3], lty = 2, col = 3) # Conditional densities den_DDE <- predict(fit_dde, newdata = df_pred_den, what = "denfun", den.grid = sequenceGAD, parallel = "multicore", ncpus = 2) den_m <- apply(den_DDE$denfun, c(1,2), median) den_ql <- apply(den_DDE$denfun, c(1,2), quantile, 0.025) den_qh <- apply(den_DDE$denfun, c(1,2), quantile, 0.975) op <- par(mfrow = c(2,2)) plot(sequenceGAD, den_m[,1], type = "l", lwd = 2, xlab = "DDE (mg/L)", ylab = "", main = "DDE = 12.57 (10th percentile)") lines(sequenceGAD, den_ql[,1], lty = 2) lines(sequenceGAD, den_qh[,1], lty = 2) plot(sequenceGAD, den_m[,2], type = "l", lwd = 2, xlab = "DDE (mg/L)", ylab = "", main = "DDE = 28.44 (60th percentile)") lines(sequenceGAD, den_ql[,2], lty = 2) lines(sequenceGAD, den_qh[,2], lty = 2) plot(sequenceGAD, den_m[,3], type = "l", lwd = 2, xlab = "DDE (mg/L)", ylab = "", main = "DDE = 53.72 (90th percentile)") lines(sequenceGAD, den_ql[,3], lty = 2) lines(sequenceGAD, den_qh[,3], lty = 2) plot(sequenceGAD, den_m[,4], type = "l", lwd = 2, xlab = "DDE (mg/L)", ylab = "", main = "DDE = 105.47 (99th percentile)") lines(sequenceGAD, den_ql[,4], lty = 2) lines(sequenceGAD, den_qh[,4], lty = 2) par(op) # Conditional probabilities probs_DDE <- predict(fit_dde, newdata = df_pred, what = "probfun", q.value = c(37), parallel = "multicore", ncpus = 2) prob_m <- apply(probs_DDE$probfun, c(1,2), median) prob_ql <- apply(probs_DDE$probfun, c(1,2), quantile, 0.025) prob_qh <- apply(probs_DDE$probfun, c(1,2), quantile, 0.975) plot(df_pred$DDE, prob_m, type = "l", lwd = 2, ylim = c(0, 1), xlab = "DDE (mg/L)", ylab = "P(GAD < 37 | DDE)", main = "Conditional Probabilities (premature delivery)") lines(df_pred$DDE, prob_ql, lty = 2) lines(df_pred$DDE, prob_qh, lty = 2) ```

predict.DDPstar function