Help trying to program a regression with random walk

Modeling
1

I am trying to program (in Rstan) a regression with time-varying intercept and constant slope. After the first time-step (data point) the intercept may undergo a random walk. Here are the files: file TestRW1.stan:
data {
int<lower=1>N;
real S[N];
real R[N];
}
transformed data{
real<lower=0>hlogamn;//mean of the normal prior on log alpha
real<lower=0>hlogasd;//std dev of the normal prior on log alpha
hlogamn=1.5078;
hlogasd=0.3486;
}
parameters {
real logalpha[N];
real walk[N]; //annual random walk error ~N(0, sigmaw).
real<lower=1000, upper=30000>beta; //population-specific slope (capacity) parameters
real<lower=0, upper=2.0>sigmaw; //standard error of the annual random walk
real<lower=0,upper = 2.0>sigma; //population-specific process error of the weight-length relationship.
}
model {
logalpha[1]~normal(hlogamn, hlogasd) T[-4.60, 2.89];
log(R[1]/S[1]) ~ normal(logalpha[1] - S[1]/beta, sigma);
for (i in 2:N) {
walk[i]~normal(0,sigmaw);
logalpha[i] = logalpha[i-1]+walk[i];
log(R[i]/S[i]) ~ normal(logalpha[i] - S[i]/beta, sigma);
}
}
file: TestRW1.R:
Skagit <- read.table(“TestRWdata1.txt”, header = TRUE)
N<-nrow(Skagit)
S<-Skagit$Spawners
R <-Skagit$Recruits
stanDat<- list(“S”,“R”, “N”)

fit<-stan(file = ‘TestRW1.stan’, data = stanDat, iter = 100, chains = 1)

traceplot(fit,“sigma”)
print(fit)

When I run “fit…” I receive the following error message:
SYNTAX ERROR, MESSAGE(S) FROM PARSER:

attempt to assign variable in wrong block. left-hand-side variable origin=parameter
error in ‘model15346f4f170c_TestRW1’ at line 25, column 25

23:         for (i in 2:N) {
24:         walk[i]~normal(0,sigmaw);
25: 		    logalpha[i] = logalpha[i-1]+walk[i];
                            ^
26: 		    log(R[i]/S[i]) ~ normal(logalpha[i] - S[i]/beta, sigma);

PARSER EXPECTED:
Error in stanc(file = file, model_code = model_code, model_name = model_name, :
failed to parse Stan model ‘TestRW1’ due to the above error.
In addition: Warning message:
In readLines(file, warn = TRUE) :
incomplete final line found on 'C:\Stan\Stock_Recruit\Tests\TestRW1.stan’
Data set:
#Test spawner and recruit
#data for BYs 1 to 12
"Spawners" "Recruits"
7448 7107
7870 5038
3780 6073
4584 5529
5394 5154
6818 2429
7332 3702
6382 2494
6757 6174
4242 6093
4887 5814
2502 8627

The idea is pretty simple. After the initial time-step (where the intercept parameter ‘logalpha’ is drawn from a normal random distribution, the values of logalpha in each subsequent timestep is expected to be equal to logalpha(t-1) plus a normal random (‘walk’) that has a zero mean. So, it seems that after calculating the posterior (for log(R(t)/S(t)), logalpha needs to be updated for the next time-step by adding w(t) to logalpha(t-1). It would seem that this must be done in the model block. But the error indicates that this is illegal???
What is the correct way to program this? What am I failing to understand.

2

Statements like a ~ normal(b, c); aren’t actually drawing random numbers from distributions and assigning them to the left hand side.

Internally, something like that increments the log density of the model, which the HMC algorithm uses to explore parameter space.

Something like this:

target += normal_lpdf(a | b, c);

It’s not possible to assign parameter values in Stan, those come from HMC, and this is where your error is at.

It would be valid Stan code to write (edited the code to fix glaring mistake):

for (i in 2:N) {
  logalpha[i] ~ normal(logalpha[i-1], sigmaw);
  ...
}

Which is equivalent to saying logalpha[i] is normally distributed about the previous logalpha[i - 1] with some noise. Not sure that’s what you’re going for though.

3

Thank you. What you describe is what I am going for. I will give your suggestion a try.

4

I just re-read what I wrote and feel like a bit of a goof.

Don’t say (what I originally wrote):

logalpha[i] ~ logalpha[i-1] + normal(0, sigmaw);

Say (what I corrected it to):

logalpha[i] ~ normal(logalpha[i-1], sigmaw);

I’m not sure what the first thing means, and it definitely isn’t valid code ~~.