How to speed up the construction of the random effects in joint models?

Modeling
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1

Hi all,

Does anyone have better ideas to speed up the matrix construction of the random effects in the mixed effect model or joint models? As shown below, I currently wrote my Stan function by calling the random effect per observation per subject. This is really time-consuming in the computation upon the total number of subject and observation. The R package lme4 actually introduced to utilize the block diagonal matrix and Khatri-Rao2 (Khatri and Rao 1968) and Kronecker products for calculation. See the attachment lmer.pdf (518.0 KB) . Thus, no loop is needed. I guess it should run faster compared to loop. However, I am not sure whether Stan currently have similar functions for this kind of product operators. If anyone knows this, feel free to share. Thank you for your help in advance.


functions {
    vector evaluate_eta(matrix randMat, matrix randeff, int[ ] sub_ind)
     {                   
        int N = rows(randMat);
        vector[N] eta;
  
        for (n in 1:N)
            {eta[n] = randMat[n,] * randeff[,sub_ind[n]] ;}
      
        return eta;
    } 

}

Yan

2

Have you profiled if this is really a bottleneck in your program? Cmdstan 2.26 has new profiling support which should tell you easily what takes long.

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3

You can replace this function with:

rows_dot_product(randMat, randeff[,sub_ind]');
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4

Also, check out the trick here.

5

I haven’t check recently, but a while ago I benchmarked rows_dot_product and didn’t find it faster than the equivalent loop.

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6

Hi Andrew,

Thank you for your suggestion. I tried this function. However, the speed was not improved significantly.

7

Good to know that new features. I used Rstan which is 2.21 version now. I will try to see this to detect the reasons.

8

Hi Mike,

You made a good point. The function rows_dot_product did not beat loop in my codes. I will check the website you mentioned.

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