Group Lag

Modeling
,
1

Hi,
I am trying to fit a multilevel time series with lags. This is a toy dataset I created in order to ensure I am writing my model right.

bb <- data.frame(X = rnorm(10),s = rep(1:5,2), t = rep(1:2, each = 5))
dt <- list(N_Y = 1, N_T = 2, N_I = 5, Y1 = bb$X, Subj = bb$s)

My R model using dplyr is

library(dplyr)
bb %>% 
  group_by(s) %>% 
  mutate(b = lag(X))

# A tibble: 10 x 4
# Groups:   s [5]
        X     s     t      b
    <dbl> <int> <int>  <dbl>
 1  1.12      1     1 NA    
 2  0.121     2     1 NA    
 3  0.989     3     1 NA    
 4 -1.70      4     1 NA    
 5  1.71      5     1 NA    
 6 -1.86      1     2  1.12 
 7  0.179     2     2  0.121
 8 -1.19      3     2  0.989
 9 -0.211     4     2 -1.70 
10 -2.04      5     2  1.71

In Stan, my code is

data {
  //int N_Y;
  int N_I;
  int N_T;
  real Y1[N_I*N_T];
  int Subj[N_I*N_T]
}
transformed data{
  int N;
  N = N_I*N_T;
}

generated quantities {
  vector[N] YY;
  
  for(i in 2:N){
    YY[i] = Y1[Subj[i-1]];
  }
}

with the following results

        mean se_mean sd  2.5%   25%   50%   75% 97.5% n_eff Rhat
YY[1]    NaN      NA NA    NA    NA    NA    NA    NA   NaN  NaN
YY[2]   1.12       0  0  1.12  1.12  1.12  1.12  1.12     1    1
YY[3]   0.12       0  0  0.12  0.12  0.12  0.12  0.12     1    1
YY[4]   0.99       0  0  0.99  0.99  0.99  0.99  0.99     1    1
YY[5]  -1.70       0  0 -1.70 -1.70 -1.70 -1.70 -1.70     1    1
YY[6]   1.71       0  0  1.71  1.71  1.71  1.71  1.71     1    1
YY[7]   1.12       0  0  1.12  1.12  1.12  1.12  1.12     1    1
YY[8]   0.12       0  0  0.12  0.12  0.12  0.12  0.12     1    1
YY[9]   0.99       0  0  0.99  0.99  0.99  0.99  0.99     1    1
YY[10] -1.70       0  0 -1.70 -1.70 -1.70 -1.70 -1.70     1    1
lp__    0.00     NaN  0  0.00  0.00  0.00  0.00  0.00   NaN  NaN

Thanks for your help

2

Hi Reg,

It’s not clear what your issue is, would you be able to clarify what’s going wrong here?

3

Hi andrjohns,

I am trying to model Y_{i,t} = \alpha_{i}* Y_{i,t-1}, with the lagged time points (t) nested within the individual i.

4

But what help are you trying to get? Is there part of the output that’s not what you’re expecting or are you unsure of how to write the model?

5

I’m unsure of how to write the Stan code. My Stan code doesn’t match the R code. The R code is the objective.

6

Righto, so the issue there is your indexing:

  for(i in 2:N)
    YY[i] = Y1[Subj[i-1]];

Because Subj is just the values 1 to 5 repeated twice, you’re selecting the first 5 values of Y1 twice, which is why your output isn’t lining up

7

Sorry to be a bother, but I am unsure of how to progress from here.
Even if I create a time variable t for the time points

for (i in 1:N) {
if (time[i]>1) {
YY[i] = Y1[Subj[i-1]];
}
}

I’m not sure of how to achieve an output similar to the R output.

8

The easiest way would be to pass Y1 as a matrix, rather than a vector, like:

  matrix[N_I, N_T] Y1;

Then your loop would be:

for (i in 1:N_1) {
  for(t in 1:N_t) {
    YY[i,t] = Y1[i,t]
  }
}
1 Like
9

Alright. I’ll do that. I really appreciate the help.
Thank you very much, andrjohns.