# Simulating with vcov

**URL:** <https://discourse.pumas.ai/t/simulating-with-vcov/575>\
**Category:** Simulation\
**Created:** [January 15, 2022, 1:13pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575 "2022-01-15T13:13:01Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![donaldlee3](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/donaldlee3/32/165_2.png) [@donaldlee3](https://discourse.pumas.ai/u/donaldlee3)\
**Post date:** [January 15, 2022, 1:13pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/1 "2022-01-15T13:13:01Z")

</div>

Hello,

I am trying to simulate with vcov. However, I’m getting an error. Could I get some help with this?

```auto
julia> test_sims = simobs(model_fit, vcov(model_fit), samples=2)
Progress: 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:00
ERROR: MethodError: no method matching PDMats.PDMat(::Pumas.CovarianceEstimate{Float64, Matrix{Float64}})
Closest candidates are:
  PDMats.PDMat(::AbstractMatrix{T} where T, ::LinearAlgebra.Cholesky{T, S}) where {T, S} at /builds/PumasAI/PumasSystemImages-jl/.julia/packages/PDMats/vgpB7/src/pdmat.jl:12
  PDMats.PDMat(::LinearAlgebra.Cholesky) at /builds/PumasAI/PumasSystemImages-jl/.julia/packages/PDMats/vgpB7/src/pdmat.jl:21
  PDMats.PDMat(::Symmetric) at /builds/PumasAI/PumasSystemImages-jl/.julia/packages/PDMats/vgpB7/src/pdmat.jl:20
  ...
Stacktrace:
 [1] MvNormal(μ::Vector{Float64}, Σ::Pumas.CovarianceEstimate{Float64, Matrix{Float64}})
   @ Distributions /builds/PumasAI/PumasSystemImages-jl/.julia/packages/Distributions/Xrm9e/src/multivariate/mvnormal.jl:211
 [2] simobs(fpm::Pumas.FittedPumasModel{PumasModel{ParamSet{NamedTuple{(:tvtr_ratio, :tvCL, :tvVc, :tvDuration, :ωtr_ratio, :ωCL, :ωVc, :σ_add, :σ_prop), NTuple{9, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#39#55", var"#40#56", var"#42#58", var"#44#60", Pumas.LinearODE, var"#45#61", var"#50#66", ModelingToolkit.ODESystem}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantCovar{NamedTuple{(:rep, :params_num, :NSubj, :occ, :period, :sequence, :seq_n, :formulation, :isT, :input_tr_ratio), Tuple{Int64, Int64, Int64, Int64, Int64, String, Int64, String, Int64, Float64}}}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Optim.MultivariateOptimizationResults{Optim.BFGS{LineSearches.InitialStatic{Float64}, LineSearches.BackTracking{Float64, Int64}, Nothing, Float64, Optim.Flat}, Float64, Vector{Float64}, Float64, Float64, Vector{Optim.OptimizationState{Float64, Optim.BFGS{LineSearches.InitialStatic{Float64}, LineSearches.BackTracking{Float64, Int64}, Nothing, Float64, Optim.Flat}}}, Bool, NamedTuple{(:f_limit_reached, :g_limit_reached, :h_limit_reached, :time_limit, :callback, :f_increased), NTuple{6, Bool}}}, Pumas.FOCE, Vector{Vector{Float64}}, NamedTuple{(:optimize_fn, :constantcoef, :omegas, :ensemblealg, :diffeq_options), Tuple{Pumas.DefaultOptimizeFN{Nothing, NamedTuple{(:show_trace, :store_trace, :extended_trace, :g_tol, :allow_f_increases), Tuple{Bool, Bool, Bool, Float64, Bool}}}, NamedTuple{(), Tuple{}}, Tuple{}, EnsembleThreads, NamedTuple{(), Tuple{}}}}, ParamSet{NamedTuple{(:tvtr_ratio, :tvCL, :tvVc, :tvDuration, :ωtr_ratio, :ωCL, :ωVc, :σ_add, :σ_prop), NTuple{9, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}}, population::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantCovar{NamedTuple{(:rep, :params_num, :NSubj, :occ, :period, :sequence, :seq_n, :formulation, :isT, :input_tr_ratio), Tuple{Int64, Int64, Int64, Int64, Int64, String, Int64, String, Int64, Float64}}}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, vcov::Pumas.CovarianceEstimate{Float64, Matrix{Float64}}, randeffs::Nothing; samples::Int64, rng::MersenneTwister)
   @ Pumas /builds/PumasAI/PumasSystemImages-jl/.julia/packages/Pumas/HDuXQ/src/estimation/inference.jl:630
 [3] simobs(fpm::Pumas.FittedPumasModel{PumasModel{ParamSet{NamedTuple{(:tvtr_ratio, :tvCL, :tvVc, :tvDuration, :ωtr_ratio, :ωCL, :ωVc, :σ_add, :σ_prop), NTuple{9, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#39#55", var"#40#56", var"#42#58", var"#44#60", Pumas.LinearODE, var"#45#61", var"#50#66", ModelingToolkit.ODESystem}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantCovar{NamedTuple{(:rep, :params_num, :NSubj, :occ, :period, :sequence, :seq_n, :formulation, :isT, :input_tr_ratio), Tuple{Int64, Int64, Int64, Int64, Int64, String, Int64, String, Int64, Float64}}}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Optim.MultivariateOptimizationResults{Optim.BFGS{LineSearches.InitialStatic{Float64}, LineSearches.BackTracking{Float64, Int64}, Nothing, Float64, Optim.Flat}, Float64, Vector{Float64}, Float64, Float64, Vector{Optim.OptimizationState{Float64, Optim.BFGS{LineSearches.InitialStatic{Float64}, LineSearches.BackTracking{Float64, Int64}, Nothing, Float64, Optim.Flat}}}, Bool, NamedTuple{(:f_limit_reached, :g_limit_reached, :h_limit_reached, :time_limit, :callback, :f_increased), NTuple{6, Bool}}}, Pumas.FOCE, Vector{Vector{Float64}}, NamedTuple{(:optimize_fn, :constantcoef, :omegas, :ensemblealg, :diffeq_options), Tuple{Pumas.DefaultOptimizeFN{Nothing, NamedTuple{(:show_trace, :store_trace, :extended_trace, :g_tol, :allow_f_increases), Tuple{Bool, Bool, Bool, Float64, Bool}}}, NamedTuple{(), Tuple{}}, Tuple{}, EnsembleThreads, NamedTuple{(), Tuple{}}}}, ParamSet{NamedTuple{(:tvtr_ratio, :tvCL, :tvVc, :tvDuration, :ωtr_ratio, :ωCL, :ωVc, :σ_add, :σ_prop), NTuple{9, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}}, vcov::Pumas.CovarianceEstimate{Float64, Matrix{Float64}}, randeffs::Nothing; samples::Int64, rng::MersenneTwister)
   @ Pumas /builds/PumasAI/PumasSystemImages-jl/.julia/packages/Pumas/HDuXQ/src/estimation/inference.jl:616
 [4] top-level scope
   @ REPL[75]:1

```

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 17, 2022, 11:46am UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/2 "2022-01-17T11:46:57Z")

</div>

Hello Donald,

Can you please try the following instead?

```auto
test_sims = simobs(model_fit, vcov(model_fit).Σ, samples=2)

```

---

<div class="post-metadata">

**Author:** ![donaldlee3](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/donaldlee3/32/165_2.png) [@donaldlee3](https://discourse.pumas.ai/u/donaldlee3)\
**Post date:** [January 17, 2022, 7:27pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/3 "2022-01-17T19:27:06Z")

</div>

Hi Mohamed,

I tried that and got the following error msg:

```auto
Progress: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:01:21
ERROR: PosDefException: matrix is not Hermitian; Cholesky factorization failed.
Stacktrace:
 [1] checkpositivedefinite(info::Int64)
   @ LinearAlgebra /usr/local/julia/share/julia/stdlib/v1.6/LinearAlgebra/src/factorization.jl:18
 [2] cholesky!(A::Matrix{Float64}, ::Val{false}; check::Bool)
   @ LinearAlgebra /usr/local/julia/share/julia/stdlib/v1.6/LinearAlgebra/src/cholesky.jl:282
 [3] #cholesky#130
   @ /usr/local/julia/share/julia/stdlib/v1.6/LinearAlgebra/src/cholesky.jl:378 [inlined]
 [4] cholesky (repeats 2 times)
   @ /usr/local/julia/share/julia/stdlib/v1.6/LinearAlgebra/src/cholesky.jl:378 [inlined]
 [5] PDMat
   @ /builds/PumasAI/PumasSystemImages-jl/.julia/packages/PDMats/vgpB7/src/pdmat.jl:19 [inlined]
 [6] MvNormal(μ::Vector{Float64}, Σ::Matrix{Float64})
   @ Distributions /builds/PumasAI/PumasSystemImages-jl/.julia/packages/Distributions/Xrm9e/src/multivariate/mvnormal.jl:211
 [7] simobs(fpm::Pumas.FittedPumasModel{PumasModel{ParamSet{NamedTuple{(:tvtr_ratio, :tvCL, :tvVc, :tvDuration, :ωtr_ratio, :ωCL, :ωVc, :σ_add, :σ_prop), NTuple{9, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}, var"#39#55", var"#40#56", var"#42#58", var"#44#60", Pumas.LinearODE, var"#45#61", var"#50#66", ModelingToolkit.ODESystem}, Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantCovar{NamedTuple{(:rep, :params_num, :NSubj, :occ, :period, :sequence, :seq_n, :formulation, :isT, :input_tr_ratio), Tuple{Int64, Int64, Int64, Int64, Int64, String, Int64, String, Int64, Float64}}}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, Optim.MultivariateOptimizationResults{Optim.BFGS{LineSearches.InitialStatic{Float64}, LineSearches.BackTracking{Float64, Int64}, Nothing, Float64, Optim.Flat}, Float64, Vector{Float64}, Float64, Float64, Vector{Optim.OptimizationState{Float64, Optim.BFGS{LineSearches.InitialStatic{Float64}, LineSearches.BackTracking{Float64, Int64}, Nothing, Float64, Optim.Flat}}}, Bool, NamedTuple{(:f_limit_reached, :g_limit_reached, :h_limit_reached, :time_limit, :callback, :f_increased), NTuple{6, Bool}}}, Pumas.FOCE, Vector{Vector{Float64}}, NamedTuple{(:optimize_fn, :constantcoef, :omegas, :ensemblealg, :diffeq_options), Tuple{Pumas.DefaultOptimizeFN{Nothing, NamedTuple{(:show_trace, :store_trace, :extended_trace, :g_tol, :allow_f_increases), Tuple{Bool, Bool, Bool, Float64, Bool}}}, NamedTuple{(), Tuple{}}, Tuple{}, EnsembleThreads, NamedTuple{(), Tuple{}}}}, ParamSet{NamedTuple{(:tvtr_ratio, :tvCL, :tvVc, :tvDuration, :ωtr_ratio, :ωCL, :ωVc, :σ_add, :σ_prop), NTuple{9, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}}}}}, population::Vector{Subject{NamedTuple{(:dv,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantCovar{NamedTuple{(:rep, :params_num, :NSubj, :occ, :period, :sequence, :seq_n, :formulation, :isT, :input_tr_ratio), Tuple{Int64, Int64, Int64, Int64, Int64, String, Int64, String, Int64, Float64}}}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, vcov::Matrix{Float64}, randeffs::Nothing; samples::Int64, rng::MersenneTwister)
   @ Pumas /builds/PumasAI/PumasSystemImages-jl/.julia/packages/Pumas/HDuXQ/src/estimation/inference.jl:630
 [8] #simobs#634
   @ /builds/PumasAI/PumasSystemImages-jl/.julia/packages/Pumas/HDuXQ/src/estimation/inference.jl:616 [inlined]
 [9] top-level scope
   @ REPL[96]:1

```

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 17, 2022, 8:35pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/4 "2022-01-17T20:35:50Z")

</div>

Could you please display the matrix here? It is possible that the matrix is slightly not symmetric due to numerical error. If that’s the only issue,

```auto
test_sims = simobs(model_fit, Symmetric(vcov(model_fit).Σ), samples=2)

```

should run fine (note I added `Symmetric` above).

---

<div class="post-metadata">

**Author:** ![donaldlee3](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/donaldlee3/32/165_2.png) [@donaldlee3](https://discourse.pumas.ai/u/donaldlee3)\
**Post date:** [January 17, 2022, 8:52pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/5 "2022-01-17T20:52:29Z")

</div>

Thanks, Mohamed! Looks like adding `Symmetric` fixed it.

This is the vcov matrix:

```auto
9×9 Pumas.CovarianceEstimate{Float64, Matrix{Float64}}:
   0.0129921 3.4533 602.888 -0.000103089 0.00126979 -0.00336832 7.22671e-5 -4.44173e-6 3.23847e-5
   3.4533 7898.16 47458.3 0.0570391 -3.00166 3.07869 0.264192 0.0657525 -0.0180367
 602.888 47458.3 1.01233e8 -33.397 213.61 -346.286 232.472 -3.27684 5.01936
  -0.000103089 0.0570391 -33.397 3.19186e-5 -5.42398e-5 6.51985e-5 6.85552e-5 1.80607e-6 -1.81526e-6
   0.00126979 -3.00166 213.61 -5.42398e-5 0.0342586 -0.0113754 -0.00108963 -0.000136951 7.22875e-6
  -0.00336832 3.07869 -346.286 6.51985e-5 -0.0113754 0.010411 -1.68559e-5 0.000110317 -5.04867e-5
   7.22671e-5 0.264192 232.472 6.85552e-5 -0.00108963 -1.68559e-5 0.00407851 8.05854e-6 -1.85646e-5
  -4.44173e-6 0.0657525 -3.27684 1.80607e-6 -0.000136951 0.000110317 8.05854e-6 1.6085e-6 -7.38658e-7
   3.23847e-5 -0.0180367 5.01936 -1.81526e-6 7.22875e-6 -5.04867e-5 -1.85646e-5 -7.38658e-7 3.99894e-6

```

---

<div class="post-metadata">

**Author:** ![bobbrown](https://avatars.discourse-cdn.com/v4/letter/b/c2a13f/32.png) [@bobbrown](https://discourse.pumas.ai/u/bobbrown)\
**Post date:** [January 29, 2022, 6:55pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/6 "2022-01-29T18:55:34Z")

</div>

Dr Mohamed- Could you please enlighten on what might have been the numerical error that caused the original error of Dr Lee? Understanding the root cause might help avoid this error in the future. I am assuming vcov stands for variance-covariance matrix representing the SE of each estimated parameter. Thank you sir!  
Bob

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 29, 2022, 7:11pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/7 "2022-01-29T19:11:44Z")

</div>

It is not uncommon in floating point operations that 2 numbers calculated in 2 different ways won’t be “exactly” equal to each other up to the last decimal place even if theoretically in exact arithmetic they should be equal. In Julia, we have the `Symmetric` wrapper which you can wrap an almost symmetric matrix with to tell Julia to only worry about one side of the matrix because the other side is identical to it for all practical purposes. We should probably make use of this wrapper internally so users don’t have to think about it.

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 29, 2022, 7:13pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/8 "2022-01-29T19:13:55Z")

</div>

> [@bobbrown](#):
>
> I am assuming vcov stands for variance-covariance matrix representing the SE of each estimated parameter.

Yes it’s the variance-covariance matrix estimate. The square root of the diagonal of the vcov matrix gives an estimate of the standard errors of the parameters.

---

<div class="post-metadata">

**Author:** ![bobbrown](https://avatars.discourse-cdn.com/v4/letter/b/c2a13f/32.png) [@bobbrown](https://discourse.pumas.ai/u/bobbrown)\
**Post date:** [January 29, 2022, 7:33pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/9 "2022-01-29T19:33:02Z")

</div>

Dr Mohamed. Thank you. In order for me to understand this clearly, consider a simple one compartment model for an intravenous bolus dosing. This model would have 5 parameters: tvcl, tvvc, bsv\_cl, bsv\_vc, sigma\_add. The vcov would be:  
se\_tvcl 0 0 0 0  
0 se\_tvvc 0 0 0  
0 0 se\_bsv\_cl 0 0  
0 0 0 se\_bsv\_vc 0  
0 0 0 0 se\_sigma\_add  
is this correct? If so, what does ‘other side’ in your reply mean ?  
Bob

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 29, 2022, 7:51pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/10 "2022-01-29T19:51:03Z")

</div>

The off-diagonal terms will not be 0. They will give an estimate of the covariance between the parameter estimates. So the estimate of the covariance between the tvcl and tvvc parameter estimates will be in the (1, 2) element or (2, 1) element of the matrix since covariance is symmetric. If `vcov[1,2]` and `vcov[2,1]` are not 100% equal to each other but only because of numerical roundoff errors in intermediate computations, the `Symmetric` wrapper will tell Julia to only use one of them and consider the other one equal. The same is true for `vcov[1,3]` and `vcov[3,1]` and all such pairs of off-diagonal entries in the `vcov` matrix.

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 29, 2022, 7:53pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/11 "2022-01-29T19:53:22Z")

</div>

Additionally the diagonal will be an estimate of `se_tvcl^2`, `se_tvvc^2`, `se_bsv_cl^2`, `se_bsv_vc^2` and `se_sigma_add^2`. Note the squares since they are variances and the standard error estimate is the square root of the variance estimate.

---

<div class="post-metadata">

**Author:** ![bobbrown](https://avatars.discourse-cdn.com/v4/letter/b/c2a13f/32.png) [@bobbrown](https://discourse.pumas.ai/u/bobbrown)\
**Post date:** [January 29, 2022, 7:55pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/12 "2022-01-29T19:55:27Z")

</div>

Thank you very much. I was reviewing one of your tutorials on your web page, and found this example output.

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/pumas/original/1X/6826e2d20a6291905863b14f34154429551691c8.png)

Did not find the off-diagonal SEs. How do I output the full var-covariance matrix please?  
Bob

---

<div class="post-metadata">

**Author:** ![vijay](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/vijay/32/96_2.png) [@vijay](https://discourse.pumas.ai/u/vijay)\
**Post date:** [January 29, 2022, 8:02pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/13 "2022-01-29T20:02:07Z")

</div>

Let’s say you have this

```auto
pkfit_1cmp = fit(pk_1cmp,
                 pop,
                 pkparams_1cmp,
                 Pumas.FOCE())

```

you can then make an inference of your parameters using

```auto
# make an inference
infer_1cmp = infer(pkfit_1cmp)

```

you can then query the variance-covariance from the inferred result by typing in `infer_1cmp.vcov`

see below for an example

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/pumas/original/1X/8927b56eea1b5b8acdc4a849e0d8deef2861aa91.png)

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 29, 2022, 8:08pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/14 "2022-01-29T20:08:27Z")

</div>

To clarify when I mention a symmetric matrix, I am referring to a matrix `V` where `V[i,j] == V[j,i]` for all `i` and `j`. For example the following matrix is symmetric:

```auto
V1 = [
1.0 -0.1;
-0.1 1.0;
]

```

but this one is not:

```auto
V2 = [
1.0 -0.1;
-0.100001 1.0;
]

```

even if the difference between `V2[1,2]` and `V2[2,1]` is tiny. The matrix `Symmetric(V2)` will be treated as a symmetric matrix ignoring the slight difference between the `V2[1,2]` and `V2[2,1]`.

---

<div class="post-metadata">

**Author:** ![bobbrown](https://avatars.discourse-cdn.com/v4/letter/b/c2a13f/32.png) [@bobbrown](https://discourse.pumas.ai/u/bobbrown)\
**Post date:** [January 29, 2022, 8:18pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/15 "2022-01-29T20:18:24Z")

</div>

Thank you. I will review your tutorials again, I might have missed infer\_mymodel.vcov command.  
Bob

---

<div class="post-metadata">

**Author:** ![bobbrown](https://avatars.discourse-cdn.com/v4/letter/b/c2a13f/32.png) [@bobbrown](https://discourse.pumas.ai/u/bobbrown)\
**Post date:** [January 29, 2022, 8:25pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/16 "2022-01-29T20:25:27Z")

</div>

Dr Mohamed. Yes this is consistent with my understanding regarding a symmetric matrix. Two questions:

1. Does Pumas allow simulations directly reading from infer\_mymodel.vcov() ? Does it take the off-diagonal elements as well? This is what @donaldlee3 was attempting I presume.
2. some of my friends use NONMEM software. I attended a training 25-30 years ago, do not remember a thing. Do you or one of the other experts know if NONMEM does this as well. I ask because, predicting dose in patients by taking the uncertainty is something that scientists have not performed. I am assuming perhaps this is something modern in Pumas?  
Bob

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<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 29, 2022, 10:22pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/17 "2022-01-29T22:22:58Z")

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> [@bobbrown](#):
>
> Does Pumas allow simulations directly reading from infer\_mymodel.vcov() ? Does it take the off-diagonal elements as well?

Yes and yes. And indeed this is what Donald was attempting above.

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**Author:** ![benjaminrich](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/benjaminrich/32/156_2.png) [@benjaminrich](https://discourse.pumas.ai/u/benjaminrich)\
**Post date:** [January 31, 2022, 8:36pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/18 "2022-01-31T20:36:43Z")

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Hi @bobbrown. Certainly, NONMEM outputs this matrix as well, so indeed the same approach can be used with NONMEM.

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**Author:** ![bobbrown](https://avatars.discourse-cdn.com/v4/letter/b/c2a13f/32.png) [@bobbrown](https://discourse.pumas.ai/u/bobbrown)\
**Post date:** [February 2, 2022, 5:09pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/19 "2022-02-02T17:09:38Z")

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@benjaminrich Thank you sir. Can NONMEM perform this type of simulation with uncertainty automatically or seamlessly, compared to Pumas? If I can achieve this with less overhead, I would rather use Pumas.  
Bob

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**Author:** ![vijay](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/vijay/32/96_2.png) [@vijay](https://discourse.pumas.ai/u/vijay)\
**Post date:** [February 2, 2022, 6:22pm UTC](https://discourse.pumas.ai/t/simulating-with-vcov/575/20 "2022-02-02T18:22:17Z")

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> [@bobbrown](#):
>
> @benjaminrich Thank you sir. Can NONMEM perform this type of simulation with uncertainty automatically or seamlessly, compared to Pumas? If I can achieve this with less overhead, I would rather use Pumas.

not as seamless in Pumas, but there are certain routines that can be used. 99% of folks take the variance-covariance matrix to R, and simulate it there after writing the model into mrgsolve.

[Next page](https://discourse.pumas.ai/t/simulating-with-vcov/575.md?page=2)