Regression model equation reconstruction with random effects

Interfaces brms
1

Hello everyone,

I ask the community for help on the following problem.
Suppose we estimate the following regression model with fixed effects Age (factor variable) and Year (factor variable) as random effects.

set.seed(123)
# Packages
library(brms)
#install.packages("rstan")
library(rstan)

# Data simulation
age <- 10:20
year <- 1990:2000
n1 <-  length(age)
n2 <-  length(year) 
n <- n1*n2
y <- rnorm(n = n,mean = 50,sd = 30 )

beta_0 <- 0.25
beta_age <- 0.25
beta_year <- - 0.85

y <-beta_0+beta_age*age+beta_year*year

# Final Dataframe
d <- data.frame(y=y,
     Age=as.factor(rep(age,n2)),
     Year=as.factor(rep(year,n1))
     )

fit <- brm(y ~ 0+Age+(1|Year), d, iter = 50, warmup = 10, chains = 1)

fixef(fit)

> fixef(fit)
Estimate Est.Error      Q2.5      Q97.5
Age10 -1.5333147 1.3878804 -3.839673  1.0539617
Age11 -0.1285437 0.9321314 -1.221775  1.9525542
Age12 -2.1895797 1.2388774 -4.829345 -1.0598727
Age13  3.7247485 2.4157734  1.408428  8.4137437
Age14 -3.0134557 2.1435395 -8.148383 -1.1134809
Age15 -0.6631218 1.2442192 -2.122722  1.8919087
Age16 -1.2382832 1.6596973 -4.145329  0.3973843
Age17  1.7116087 2.4962776 -1.389026  5.3579521
Age18 -1.1881552 1.3884096 -4.155563  0.2962675
Age19 -0.6924640 1.0659378 -1.558155  1.3804710
Age20 -0.4457888 0.6615983 -1.763389  0.8225215


ranef(fit)

$Year
, , Intercept

Estimate Est.Error       Q2.5    Q97.5
1990 -1.3702433 1.7680814 -3.2623355 0.885315
1991 -2.2592311 2.3086167 -4.6791703 1.036105
1992  1.7228745 2.5290462 -0.4616315 4.225590
1993 -0.8166271 1.2671842 -2.1690639 1.809690
1994  1.7928488 2.2368656 -0.6837609 4.464356
1995  0.7169620 1.8096562 -0.5032051 3.002480
1996 -0.1112231 0.7797995 -0.7787910 1.614591
1997  2.1406982 2.2829444 -0.2656490 4.370186
1998 -0.3399042 1.0476426 -1.3453246 2.147565
1999  1.7134314 1.9736618 -0.5384686 4.063977
2000 -0.5178907 1.0331019 -1.5312055 1.854528

Obtained the coefficients, let’s suppose to get a 5-year forecast on the Year coefficient and obtain Year_F, let’s say c(1.0342, 0.9514, 0.9234, 0.8345, 0.7863) and length (Year_F) < length (Year)
How can I reconstruct the equation: y_F ~ 0 + Age + (1 | Year_F)

Thanks for your support.
Andrea