Rasch model and covariate adjustment

Modeling
1

Hi, I am reading and learning from a tutorial on Rasch model.

Within, there is a function to adjust covariates.

functions {
  matrix obtain_adjustments(matrix W) {
    real min_w;
    real max_w;
    int minmax_count;
    matrix[2, cols(W)] adj;
    adj[1, 1] = 0;
    adj[2, 1] = 1;
    if(cols(W) > 1) {
      for(k in 2:cols(W)) {                       // remaining columns
        min_w = min(W[1:rows(W), k]);
        max_w = max(W[1:rows(W), k]);
        minmax_count = 0;
        for(j in 1:rows(W))
          minmax_count = minmax_count + W[j,k] == min_w || W[j,k] == max_w;
        if(minmax_count == rows(W)) {       // if column takes only 2 values
          adj[1, k] = mean(W[1:rows(W), k]);
          adj[2, k] = (max_w - min_w);
        } else {                            // if column takes > 2 values
          adj[1, k] = mean(W[1:rows(W), k]);
          adj[2, k] = sd(W[1:rows(W), k]) * 2;
        }
      }
    }
    return adj;
  }
}

The tutorial provides an explanation on what is going on. But I am baffled by one line:

adj[2, k] = sd(W[1:rows(W), k]) * 2;

My understanding is that this line calculates the standard deviation and then later is used in the denominator for standardization. But how come it is SD*2?

Thank you.

2

I think it comes from the advice in http://www.stat.columbia.edu/~gelman/research/unpublished/standardizing.pdf

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