Hi. I have a linear mixed effects model theta_i(t) = alpha_1x + alpha_2xt + alpha_3xt^2 + u_{i0} + u_{i1}t + u_{i2}t^2 The “xt” and “xt^2” terms are highly correlated, x is a fixed covariate and t represents time. My stan code for this part is theta = alpha[1] * X + alpha[2] * X .* time + alph…

I think what you’re looking for is the the QR reparameterization trick .

Hi Mike, thank you for your advice. I apply QR Reparameterization to predictor matrix, (x, xt, xt^2). Now my code is theta = Q_ast * alpha + u[1][subject] + u[2][subject] .* time + u[3][subject] .* square(time); The pairs plot looked much better than previous one. [Rplot2] mean se_…

Presumably this is something you’re going to be running repeatedly in some sort of production environment, hence the concern for even such a short single-run time? I doubt it will make much difference, but you could pre-compute square(time) in the transformed data section instead of re-computing it…

Thank you for the reply. [image] mike-lawrence: hence the concern for even such a short single-run time? Yes, this is only for one small simulated dataset, containing about 800 data points. I plan to repeat the simulation for at least 500 times. As you suggested, I pre-computed terms like t…

[image] Gen_Y: I’ve already applied non-centered parametrization to the random effects u. But have you checked how the centered parameterization performs? I believe that there are cases (has to do with how much data you have per subject vs how many subjects you have) where one can expect cent…

Many thanks for the prompt reply. [image] mike-lawrence: But have you checked how the centered parameterization performs? I first applied centered parametrization and the running time for one chain is 200 seconds, with convergence problems (Rhat > 2). I switched it to non-centered version an…

Ah, darn, I’d forgotten about the QR stuff. I’m not sure my redundancy-reducing stuff is compatible with the QR trick. Hm, I’ll have to let this mull a bit. In the interim, could you post your full model? I might be able to see other areas where you can improve things (ex. often folks can have slow/…

Thanks for checking model code for me. data { int<lower=1> N; // Number of subjects int<lower=1> ms; // Number of longitudinal measurements int subject[ms]; // subject ID int<lower=1> K; // Number of longitudinal outcomes vector[obs] Y[K]; vector<lower=0>[ms] time; vector<lower=0>[ms]…

Oh! Do the QR stuff in the transformed data section, not transformed parameters; it only needs to be done once per data set, while putting it in the TP section means it gets done repeatedly. Also, do you genuinely have uncertainty that spans 3 orders of magnitude for all your parameters? Generally,…

Also, this bit: for (j in 1:3) u_raw[j] ~ std_normal(); Can be alternatively expressed as: to_vector(u_raw) ~ std_normal(); But I’m not sure if the latter is any faster computationally than the former, but worth a look. Also, mind editing it to remove the magic number 3? I think that some of th…

Reduce computation time with highly-correlated covariates

Modeling

mike-lawrence July 2, 2020, 8:28pm 18

Another speed-up thought for you: if you have multiple cores available, you could try out the new/experimental campfire warmup, which seems to be able to terminate warmup earlier than the standard warmup.

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Reduce computation time with highly-correlated covariates

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