# Prediction Method for `BayesSIM` Generate predictions from a fitted Bayesian single-index model. ```r ## S3 method for class 'bsim' predict( object, newdata = NULL, se.fit = FALSE, type = c("response", "latent", "index"), method = c("mean", "median"), interval = c("none", "credible"), level = 0.95, ... ) ``` ## Arguments - `object`: A fitted object of `BayesSIM` or individual model. - `newdata`: Optional data frame for which predictions should be made. If `NULL`, predictions are returned for the training data. - `se.fit`: A logical value indicating whether standard errors are required. Default is `FALSE`. - `type`: Character string specifying the type of prediction. `"response"` is the default. - **`"response"`**: Posterior predictive summaries of the response $Y$. This corresponds to draws from the posterior predictive distribution $Y^{(m)} \sim N(f(X'\theta^{(m)}), \sigma^{2(m)})$ and therefore incorporates both the uncertainty in the link function and the variability of the error term for each $m^{th}$ MCMC sample. - **`"latent"`**: Posterior summaries of the latent mean structure $E(Y \mid X) = f^{(m)}(t^{(m)})$, where $t^{(m)} = X'\theta^{(m)}$. Unlike `"response"`, it excludes the noise term and calculated by $f^{(m)}(X'\theta^{(m)})$ for each $m^{th}$ MCMC sample of $\theta$. - **`"index"`**: Posterior summaries of the single index $t^{(m)} = X'\theta^{(m)}$. - `method`: Character string determining the posterior summary used for point predictions. Options are `"mean"` or `"median"`. Default is `"mean"`. - `interval`: Character string indicating whether a credible interval should be returned. Default is `"none"`. - **`"none"`**: Return only point predictions. - **`"credible"`**: Return a $100 \times \text{level}\%$ credible interval. - `level`: Numeric value between 0 and 1 specifying the credible level. `level = 0.95` yields a 95% credible interval. Default is `0.95`. - `...`: Additional arguments. ## Returns A list containing at least the following components: - **`fitted`**: Posterior mean or median predictions. If `se.fit = TRUE` or `interval = "credible"`, standard error and lower, upper bounds of the credible interval is also included. - **`truey`**: True response value of test data. When true response value is not available, `NULL` is saved. - **`idxValue`**: Linear index value is saved where $\theta$ is estimated by `method`. - **`level`**: Credible level. ## Details This method extracts MCMC posterior samples stored in a BayesSIM object and computes posterior summaries of: * the posterior predictive response $Y \mid X$ (type `"response"`), * the latent link function evaluation $E(Y \mid X) = f(X'\theta)$ (type `"latent"`), or * the single index $X'\theta$ (type `"index"`). The key distinction is that `"response"` incorporates the posterior variability of the error term $\epsilon$, whereas `"latent"` represents the noiseless conditional expectation $E(Y \mid X)$ computed directly from the link function and the posterior draws of $\theta$. When `interval = "credible"`, the returned object includes lower and upper credible bounds computed via posterior quantiles for the chosen prediction scale. If `newdata` is supplied, predictions are evaluated at the new covariate values by computing the corresponding posterior index $t = X'\theta$ and applying the link function. ## Examples ```r simdata2 <- data.frame(DATA1$X, y = DATA1$y) # 1. One tool version fit_one <- BayesSIM(y ~ ., data = simdata2, niter = 5000, nburnin = 1000, nchain = 1) # Check median index vector estimates with standard errors coef(fit_one, method = "median", se = TRUE) # Fitted index values of median prediction fitted(fit_one, type = "linpred", method = "median") # Residuals of median prediction residuals(fit_one, method = "median") # Summary of the model summary(fit_one) # Convergence diagnostics nimTraceplot(fit_one) # Goodness of fit GOF(fit_one) # Fitted plot plot(fit_one) # Prediction with 95% credible interval at new data newx <- data.frame(X1 = rnorm(10), X2 = rnorm(10), X3 = rnorm(10), X4 = rnorm(10)) pred <- predict(fit_one, newdata = newx, interval = "credible", level = 0.95) plot(pred) # 2. Split version models <- BayesSIM_setup(y ~ ., data = simdata2) Ccompile <- compileModelAndMCMC(models) nimSampler <- get_sampler(Ccompile) initList <- getInit(models) mcmc.out <- runMCMC(nimSampler, niter = 5000, nburnin = 1000, thin = 1, nchains = 1, setSeed = TRUE, inits = initList, summary = TRUE, samplesAsCodaMCMC = TRUE) # "fit_split" becomes exactly the same as the class of "fit_one" object and apply generic functions. fit_split <- as_bsim(models, mcmc.out) ```

predict.bsim function