I am using the Howell1 dataset from rethinking package.

```
require(cmdstanr)
require(brms)
require(tidybayes)
data("Howell1")
d <- Howell1
d2 <- d[d$age > 18,]
d2$hs <- (d2$height - mean(d2$height))/ sd(d2$height)
d2$ws <- (d2$weight - mean(d2$weight))/ sd(d2$weight)
```

Building a simple brms model using one numeric and one categorical predictor

```
priors <- c(prior(normal(0,2), class = "Intercept"),
prior(normal(0,2), class = 'b'),
prior(cauchy(0,2), class = "sigma"))
m4.4 <- brm(formula = hs ~ 1 + ws + male, data = d2, family = gaussian,
backend = "cmdstanr", prior = priors
iter = 2000, warmup = 1000, chains = 4, cores = 4)
```

I am trying to understand how add_fitted_draws and add_predicted_draws work.

Considering add_fitted_draws:

```
i <- 4 # looking at the results for a particular row of the input dataset
y <- posterior_epred(m4.4)
x <- d2 %>% add_fitted_draws(model = m4.4, value = "epred")
x %>% as_tibble() %>% filter(.row ==i) %>% dplyr::select(epred) %>% cbind(fitdr = y[,i]) %>% mutate(diff = fitdr - epred)
```

Based on the documentation add_fitted_draw internally uses posterior_epred or its equivalent in brms and the results exactly match.

Now when I move on to do exactly the same between add_predicted_draws and posterior_predict, the results don’t match

```
yp <- posterior_predict(m4.4)
xp <- d2 %>% add_predicted_draws(model = m4.4, prediction = "pred")
xp %>% as_tibble() %>% filter(.row ==i) %>% dplyr::select(pred) %>% cbind(preddr = yp[,i]) %>% mutate(diff = preddr - pred)
```

I am pretty sure there is a gap in my understanding, please advice.

The sessioninfo is as follows:

…

R version 4.0.3 (2020-10-10)

Platform: x86_64-pc-linux-gnu (64-bit)

Running under: Ubuntu 20.04.1 LTS

Matrix products: default

BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0

LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

other attached packages:

[1] stringr_1.4.0 readr_1.4.0 tibble_3.0.4 tidyverse_1.3.0 MASS_7.3-53 bayesplot_1.8.0 cmdstanr_0.1.3 rethinking_2.13

[9] loo_2.4.1 gganimate_1.0.7 RColorBrewer_1.1-2 ggrepel_0.9.0 brms_2.14.4 Rcpp_1.0.5 rstan_2.21.2 StanHeaders_2.21.0-7

[17] cowplot_1.1.1 ggplot2_3.3.3 tidybayes_2.3.1 ggdist_2.4.0 modelr_0.1.8 tidyr_1.1.2 forcats_0.5.0 purrr_0.3.4

[25] dplyr_1.0.2 magrittr_2.0.1