# Model\_comparison **URL:** \ **Category:** ML/Bayesian estimation\ **Created:** [5 October 2020 21:55 UTC](https://forum.dynare.org/t/model-comparison/16724 "2020-10-05T21:55:52Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![harumihas](https://forum.dynare.org/letter_avatar_proxy/v4/letter/h/3ab097/32.png) [@harumihas](https://forum.dynare.org/u/harumihas)\ **Post date:** [5 October 2020 21:55 UTC](https://forum.dynare.org/t/model-comparison/16724/1 "2020-10-05T21:55:52Z")
Dear all, I compared four models by the dynare command: model\_comparison (marginal\_density=laplace). The four models are equaly weighted. My question is, why the Log Marginal Density reported by the command slighty differs from the one reported in the estimation results in the command window in Matlab. Thank you very much ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [7 October 2020 11:25 UTC](https://forum.dynare.org/t/model-comparison/16724/2 "2020-10-07T11:25:56Z")
How big is the difference? Is it more than rounding? ---
**Author:** ![harumihas](https://forum.dynare.org/letter_avatar_proxy/v4/letter/h/3ab097/32.png) [@harumihas](https://forum.dynare.org/u/harumihas)\ **Post date:** [7 October 2020 14:16 UTC](https://forum.dynare.org/t/model-comparison/16724/3 "2020-10-07T14:16:36Z")
Hello Johannes: Yes, it is. In fact, in some cases, the ranking of the models I am comparing changes. For example: These are the log densitys of the four models I am comparing that one can see in the command window in Matlab, when all posteriors all displayed too. The “best” model would be M3 (model with higher log density). M1: 418.4 M2: 410.5 M3: 421.2 M4: 408.1 And using the model\_comparison command, I get this: M1: 419.9 M2: 411.7 M3: 419.5 M4: 408.9 And the “best” model according to this is he M1 ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [8 October 2020 07:15 UTC](https://forum.dynare.org/t/model-comparison/16724/4 "2020-10-08T07:15:49Z")
Are you comparing the right objects? The marginal data density is reported using the Laplace approach and the modified harmonic mean. ---
**Author:** ![harumihas](https://forum.dynare.org/letter_avatar_proxy/v4/letter/h/3ab097/32.png) [@harumihas](https://forum.dynare.org/u/harumihas)\ **Post date:** [8 October 2020 15:09 UTC](https://forum.dynare.org/t/model-comparison/16724/5 "2020-10-08T15:09:26Z")
Well, I am using this: ESTIMATION RESULTS **Log data density is 418.410999.** parameters prior mean post. mean 90% HPD interval prior pstdev rho\_rrf 0.650 0.6672 0.5117 0.8383 invg 0.1000 rho\_mup 0.300 0.2603 0.1718 0.3585 invg 0.1000 rho\_rr 0.300 0.2999 0.2811 0.3161 invg 0.0100 phix 0.800 0.5805 0.4501 0.7241 invg 0.2000 phi 1.500 1.5225 1.2588 1.7569 invg 0.1500 And the command I am using is: model\_comparison(marginal\_density = laplace) mod\_2018\_4\_10\_17(0.25), mod\_2018\_1\_10\_17(0.25), mod\_2018\_2\_10\_17(0.25), mod\_2018\_3\_10\_17(0.25); Would that comparison be ok? Thank you very much ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [9 October 2020 13:45 UTC](https://forum.dynare.org/t/model-comparison/16724/6 "2020-10-09T13:45:00Z")
Please provide the full log-file of that model. ---
**Author:** ![harumihas](https://forum.dynare.org/letter_avatar_proxy/v4/letter/h/3ab097/32.png) [@harumihas](https://forum.dynare.org/u/harumihas)\ **Post date:** [11 October 2020 19:03 UTC](https://forum.dynare.org/t/model-comparison/16724/7 "2020-10-11T19:03:43Z")
Now I see what you mean. Thank you very much. But, what is exactly the difference between the log data density lkaplace approximation and the other log data density? **Log data density [Laplace approximation] is 419.450586.** Estimation::mcmc: Multiple chains mode. Estimation::mcmc: Old mh-files successfully erased! Estimation::mcmc: Old metropolis.log file successfully erased! Estimation::mcmc: Creation of a new metropolis.log file. Estimation::mcmc: Searching for initial values… Estimation::mcmc: Initial values found! Estimation::mcmc: Write details about the MCMC… Ok! Estimation::mcmc: Details about the MCMC are available in mod\_2018\_3\_10\_17/metropolis\mod\_2018\_3\_10\_17\_mh\_history\_0.mat Estimation::mcmc: Number of mh files: 1 per block. Estimation::mcmc: Total number of generated files: 2. Estimation::mcmc: Total number of iterations: 10000. Estimation::mcmc: Current acceptance ratio per chain: Chain 1: 4.13% Chain 2: 22.47% Estimation::mcmc: Total number of MH draws per chain: 10000. Estimation::mcmc: Total number of generated MH files: 1. Estimation::mcmc: I’ll use mh-files 1 to 1. Estimation::mcmc: In MH-file number 1 I’ll start at line 2501. Estimation::mcmc: Finally I keep 7500 draws per chain. MCMC Inefficiency factors per block Parameter Block 1 Block 2 SE\_eps\_RR 633.425 227.863 SE\_eps\_TOT 503.365 189.160 SE\_eps\_AA\_x 621.390 144.295 SE\_eps\_YY 309.409 85.365 SE\_eps\_AA 375.983 103.200 SE\_eps\_INV 317.652 200.704 SE\_eps\_CC 479.942 221.775 SE\_eps\_YYx\_OBS 538.629 98.647 rho\_rrf 627.784 140.894 rho\_mup 126.576 333.789 rho\_rr 543.699 124.894 phix 449.613 61.778 phi 584.109 106.923 pssi 558.992 131.561 beta 439.276 104.352 alpha\_x 549.047 90.655 theta 558.874 77.896 omega 591.967 143.880 sigma 539.671 124.633 epx 576.526 94.695 phi\_gdp 297.325 128.103 gama 598.781 96.679 lamda\_q 460.611 100.704 lamda\_s 434.732 390.720 lamda\_gg 414.808 123.975 lamda\_xi 582.371 119.177 rho\_tot 460.594 109.986 rho\_aa\_x 557.228 122.367 rho\_aa 587.918 141.905 phi\_p 524.589 78.587 Estimation::mcmc::diagnostics: Univariate convergence diagnostic, Brooks and Gelman (1998): Parameter 1… Done! Parameter 2… Done! Parameter 3… Done! Parameter 4… Done! Parameter 5… Done! Parameter 6… Done! Parameter 7… Done! Parameter 8… Done! Parameter 9… Done! Parameter 10… Done! Parameter 11… Done! Parameter 12… Done! Parameter 13… Done! Parameter 14… Done! Parameter 15… Done! Parameter 16… Done! Parameter 17… Done! Parameter 18… Done! Parameter 19… Done! Parameter 20… Done! Parameter 21… Done! Parameter 22… Done! Parameter 23… Done! Parameter 24… Done! Parameter 25… Done! Parameter 26… Done! Parameter 27… Done! Parameter 28… Done! Parameter 29… Done! Parameter 30… Done! Estimation::marginal density: I’m computing the posterior mean and covariance… Done! Estimation::marginal density: I’m computing the posterior log marginal density (modified harmonic mean)… Done! ESTIMATION RESULTS **Log data density is 421.220810.** parameters prior mean post. mean 90% HPD interval prior pstdev rho\_rrf 0.650 0.7009 0.5229 0.8790 invg 0.1000 rho\_mup 0.300 0.6615 0.2230 0.9999 invg 0.1000 rho\_rr 0.300 0.2973 0.2849 0.3093 invg 0.0100 phix 0.800 0.5256 0.4114 0.6508 invg 0.2000 phi 1.500 1.6852 1.3563 1.9670 invg 0.1500 pssi 0.300 0.2272 0.0950 0.3611 beta 0.1000 beta 1.000 0.7395 0.6373 0.8327 invg 0.2000 alpha\_x 0.500 0.5349 0.3587 0.6731 beta 0.1000 theta 1.500 1.4838 1.3247 1.6218 invg 0.1000 omega 2.300 2.2199 1.9436 2.5803 invg 0.2000 sigma 8.500 8.4488 7.7769 9.0810 invg 0.5000 epx 0.500 0.4991 0.4824 0.5129 invg 0.0100 phi\_gdp 1.300 1.3157 1.1755 1.4751 invg 0.1000 gama 0.100 0.0805 0.0225 0.1352 beta 0.0500 lamda\_q 0.360 0.1935 0.1241 0.2762 beta 0.1000 lamda\_s 0.600 0.9643 0.9353 0.9974 beta 0.2000 lamda\_gg 0.700 0.6701 0.5231 0.8389 beta 0.1000 lamda\_xi 0.300 0.2424 0.1446 0.3706 beta 0.1000 rho\_tot 0.950 0.9509 0.9351 0.9648 beta 0.0100 rho\_aa\_x 0.830 0.8297 0.8153 0.8462 beta 0.0100 rho\_aa 0.800 0.8547 0.8028 0.9132 beta 0.1000 phi\_p 2.200 2.1964 2.1800 2.2132 invg 0.0100 standard deviation of shocks prior mean post. mean 90% HPD interval prior pstdev eps\_RR 0.010 0.0305 0.0168 0.0430 invg 2.0000 eps\_TOT 0.300 0.0425 0.0357 0.0509 invg 2.0000 eps\_AA\_x 0.010 0.0052 0.0026 0.0080 invg 2.0000 eps\_YY 0.010 0.0128 0.0101 0.0148 invg 2.0000 eps\_AA 0.100 0.0309 0.0216 0.0415 invg 2.0000 eps\_INV 0.010 0.0285 0.0053 0.0555 invg 2.0000 eps\_CC 0.010 0.0169 0.0126 0.0217 invg 2.0000 eps\_YYx\_OBS 0.010 0.0613 0.0514 0.0743 invg 2.0000 Estimation::mcmc: Posterior (dsge) IRFs… Estimation::mcmc: Posterior IRFs, done! Estimation::compute\_moments\_varendo: I’m computing endogenous moments (this may take a while)… ---
**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\ **Post date:** [12 October 2020 09:22 UTC](https://forum.dynare.org/t/model-comparison/16724/8 "2020-10-12T09:22:37Z")
See > [@The log marginal data density in mode\_computer=6](https://forum.dynare.org/t/the-log-marginal-data-density-in-mode-computer-6/4898/2): > > Both the Laplace approximation and the modified harmonic mean estimator are ways to compute the marginal data density. As computing the marginal data density involves solving a complicated integral, these two methods for tackling the issue have been proposed. In theory, they should yield identical results as they measure the same thing. In practice, both involve approximations and may yield differing results. It is hard to tell which one to prefer. Footnote 11 of Smets/Wouters (2007) states: