Hello:

First time posting, but I’ve been visiting this forum fairly regularly.

R has been my primary programming language, but I have been wanting to learn generative modeling using `rethinking`

and `Stan`

.

I was hoping if anyone can assist me with the mathematical notations needed to estimate the simple changes from pre- to post-time points.

For your reference, I am posting a sample script that I ran using R:

```
df<- data.frame(
ID <- c(1,1, 2,2,3,3,4,4,5,5,6,6), #ID
GRP <- c(1,1,1,1,2,2,1,1,2,2,2,2),
BMI <- c(30.4, 29.9, 41.6, 38.5, 43.4, 43.5, 36.4, 34.3, 32.3, 31.6, 40.1, 37.5),
BMI_BS<- c(30.4, 30.4, 41.6, 41.6, 43.4, 43.4, 36.4, 36.4, 32.3, 32.3, 40.1, 40.1), #baseline
TIMEPTS<- c(1,2, 1,2, 1,2, 1,2, 1,2, 1,2)) #1-baseline; 2-post-treatment
df$TIMEPTS<- factor (df$TIMEPTS)
df$GRP <- factor (df$GRP)
library(nlme)
fit.1<- lme (BMI ~ GRP: TIMEPTS + GRP + BMI_BS,
correlation = corCAR1 (form =~ 1 |ID),
random = list (ID=~1),
method="REML", data= df)
```

To convert the formula above into Stan, I attempted to write them into mathematical notations; however, I got stuck on what to write for interaction of two dichotomous categorical variable.

## Likelihood

BMI_i ~ \beta_0 +\beta_1*GRP + b_1GRP*TIMEPTS + b_2*BMIBS + \sigma^2_e)

## Priors:

\beta_o ~ Normal (25,45)

\beta_1 ~ normal (1,2)

b_1 ~ ??

b_2 ~ normal (25,45)

\sigma_e ~ halfcauchy (0,0.5)??

Once I have these notations set, I can use rethinking’s Ulam function to fit the model and compare the results.

Any guidance would be much appreciated.