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"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
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| subject_intercept_sigma | \n", "0.766 | \n", "0.084 | \n", "0.604 | \n", "0.917 | \n", "0.002 | \n", "0.001 | \n", "2852.0 | \n", "2579.0 | \n", "1.0 | \n", "
| global_intercept | \n", "0.913 | \n", "0.100 | \n", "0.709 | \n", "1.088 | \n", "0.003 | \n", "0.002 | \n", "1032.0 | \n", "1798.0 | \n", "1.0 | \n", "
| global_sigma | \n", "0.757 | \n", "0.043 | \n", "0.676 | \n", "0.833 | \n", "0.001 | \n", "0.001 | \n", "3442.0 | \n", "2960.0 | \n", "1.0 | \n", "
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"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
|---|---|---|---|---|---|---|---|---|---|
| global_intercept | \n", "0.644 | \n", "0.103 | \n", "0.441 | \n", "0.830 | \n", "0.002 | \n", "0.002 | \n", "2100.0 | \n", "2584.0 | \n", "1.00 | \n", "
| global_sigma | \n", "0.612 | \n", "0.045 | \n", "0.526 | \n", "0.696 | \n", "0.001 | \n", "0.001 | \n", "1293.0 | \n", "2791.0 | \n", "1.00 | \n", "
| global_age_beta | \n", "0.271 | \n", "0.062 | \n", "0.158 | \n", "0.389 | \n", "0.001 | \n", "0.001 | \n", "4585.0 | \n", "3257.0 | \n", "1.00 | \n", "
| subject_intercept_sigma | \n", "0.754 | \n", "0.084 | \n", "0.597 | \n", "0.909 | \n", "0.001 | \n", "0.001 | \n", "3178.0 | \n", "3130.0 | \n", "1.00 | \n", "
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"| \n", " | median | \n", "mad | \n", "eti_3% | \n", "eti_97% | \n", "mcse_median | \n", "ess_median | \n", "ess_tail | \n", "r_hat | \n", "
|---|---|---|---|---|---|---|---|---|
| global_intercept | \n", "0.320 | \n", "0.087 | \n", "0.088 | \n", "0.565 | \n", "0.004 | \n", "2284.281 | \n", "2552.0 | \n", "1.00 | \n", "
| global_sigma | \n", "0.613 | \n", "0.030 | \n", "0.537 | \n", "0.705 | \n", "0.002 | \n", "1577.315 | \n", "2186.0 | \n", "1.01 | \n", "
| global_age_beta | \n", "0.290 | \n", "0.057 | \n", "0.129 | \n", "0.449 | \n", "0.002 | \n", "2820.643 | \n", "2815.0 | \n", "1.00 | \n", "
| global_coa_age_beta | \n", "-0.046 | \n", "0.081 | \n", "-0.268 | \n", "0.182 | \n", "0.003 | \n", "2861.193 | \n", "2935.0 | \n", "1.00 | \n", "
| subject_intercept_sigma | \n", "0.663 | \n", "0.054 | \n", "0.524 | \n", "0.814 | \n", "0.002 | \n", "2662.958 | \n", "2366.0 | \n", "1.00 | \n", "
| subject_age_sigma | \n", "0.351 | \n", "0.045 | \n", "0.215 | \n", "0.469 | \n", "0.002 | \n", "1046.679 | \n", "752.0 | \n", "1.01 | \n", "
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"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
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| global_intercept | \n", "0.395 | \n", "0.112 | \n", "0.177 | \n", "0.601 | \n", "0.002 | \n", "0.002 | \n", "2210.0 | \n", "2599.0 | \n", "1.0 | \n", "
| global_sigma | \n", "0.595 | \n", "0.042 | \n", "0.522 | \n", "0.676 | \n", "0.001 | \n", "0.001 | \n", "1589.0 | \n", "2884.0 | \n", "1.0 | \n", "
| global_age_beta | \n", "0.273 | \n", "0.085 | \n", "0.117 | \n", "0.434 | \n", "0.002 | \n", "0.001 | \n", "2382.0 | \n", "2805.0 | \n", "1.0 | \n", "
| global_coa_age_beta | \n", "-0.007 | \n", "0.128 | \n", "-0.245 | \n", "0.225 | \n", "0.003 | \n", "0.002 | \n", "2364.0 | \n", "2734.0 | \n", "1.0 | \n", "
| global_peer_beta | \n", "0.683 | \n", "0.114 | \n", "0.483 | \n", "0.904 | \n", "0.002 | \n", "0.001 | \n", "3072.0 | \n", "2872.0 | \n", "1.0 | \n", "
| global_peer_age_beta | \n", "-0.146 | \n", "0.090 | \n", "-0.313 | \n", "0.022 | \n", "0.002 | \n", "0.001 | \n", "3080.0 | \n", "2617.0 | \n", "1.0 | \n", "
| subject_intercept_sigma | \n", "0.500 | \n", "0.077 | \n", "0.356 | \n", "0.647 | \n", "0.002 | \n", "0.002 | \n", "1023.0 | \n", "1231.0 | \n", "1.0 | \n", "
| subject_age_sigma | \n", "0.384 | \n", "0.061 | \n", "0.271 | \n", "0.497 | \n", "0.002 | \n", "0.001 | \n", "1080.0 | \n", "1407.0 | \n", "1.0 | \n", "
| \n", " | rank | \n", "elpd_loo | \n", "p_loo | \n", "elpd_diff | \n", "weight | \n", "se | \n", "dse | \n", "warning | \n", "scale | \n", "
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| COA_Peer_Model | \n", "0 | \n", "-280.547108 | \n", "88.317101 | \n", "0.000000 | \n", "0.919592 | \n", "12.286282 | \n", "0.000000 | \n", "True | \n", "log | \n", "
| COA growth Model | \n", "1 | \n", "-289.267096 | \n", "89.708607 | \n", "8.719988 | \n", "0.000000 | \n", "12.723690 | \n", "4.226971 | \n", "True | \n", "log | \n", "
| Unconditional Growth | \n", "2 | \n", "-289.776375 | \n", "91.650347 | \n", "9.229267 | \n", "0.080408 | \n", "12.808780 | \n", "4.784305 | \n", "True | \n", "log | \n", "
| Grand Mean | \n", "3 | \n", "-315.943445 | \n", "58.611975 | \n", "35.396337 | \n", "0.000000 | \n", "12.426100 | \n", "8.431326 | \n", "True | \n", "log | \n", "
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| Intercept | \n", "0.390 | \n", "0.107 | \n", "0.170 | \n", "0.579 | \n", "0.002 | \n", "0.001 | \n", "2855.0 | \n", "3083.0 | \n", "1.0 | \n", "
| age_14 | \n", "0.277 | \n", "0.084 | \n", "0.123 | \n", "0.438 | \n", "0.002 | \n", "0.001 | \n", "2283.0 | \n", "2994.0 | \n", "1.0 | \n", "
| coa | \n", "0.581 | \n", "0.162 | \n", "0.268 | \n", "0.873 | \n", "0.003 | \n", "0.002 | \n", "2784.0 | \n", "3038.0 | \n", "1.0 | \n", "
| cpeer | \n", "0.692 | \n", "0.116 | \n", "0.480 | \n", "0.914 | \n", "0.002 | \n", "0.002 | \n", "2959.0 | \n", "3040.0 | \n", "1.0 | \n", "
| age_14:coa | \n", "-0.013 | \n", "0.123 | \n", "-0.237 | \n", "0.219 | \n", "0.002 | \n", "0.002 | \n", "2441.0 | \n", "2928.0 | \n", "1.0 | \n", "
| age_14:cpeer | \n", "-0.150 | \n", "0.087 | \n", "-0.303 | \n", "0.020 | \n", "0.002 | \n", "0.001 | \n", "2890.0 | \n", "3103.0 | \n", "1.0 | \n", "
| 1|id_sigma | \n", "0.502 | \n", "0.078 | \n", "0.356 | \n", "0.645 | \n", "0.002 | \n", "0.002 | \n", "1315.0 | \n", "2130.0 | \n", "1.0 | \n", "
| age_14|id_sigma | \n", "0.379 | \n", "0.060 | \n", "0.262 | \n", "0.488 | \n", "0.002 | \n", "0.001 | \n", "1244.0 | \n", "1860.0 | \n", "1.0 | \n", "
| sigma | \n", "0.595 | \n", "0.043 | \n", "0.516 | \n", "0.674 | \n", "0.001 | \n", "0.001 | \n", "1124.0 | \n", "2355.0 | \n", "1.0 | \n", "
| \n", " | ID | \n", "EXTERNAL | \n", "FEMALE | \n", "TIME | \n", "GRADE | \n", "
|---|---|---|---|---|---|
| 0 | \n", "1 | \n", "50 | \n", "0 | \n", "0 | \n", "1 | \n", "
| 1 | \n", "1 | \n", "57 | \n", "0 | \n", "1 | \n", "2 | \n", "
| 2 | \n", "1 | \n", "51 | \n", "0 | \n", "2 | \n", "3 | \n", "
| 3 | \n", "1 | \n", "48 | \n", "0 | \n", "3 | \n", "4 | \n", "
| 4 | \n", "1 | \n", "43 | \n", "0 | \n", "4 | \n", "5 | \n", "
\n",
"\n"
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"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 11 seconds.\n",
"Sampling: [outcome]\n"
]
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"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
|---|---|---|---|---|---|---|---|---|---|
| global_intercept | \n", "7.347 | \n", "0.754 | \n", "5.950 | \n", "8.769 | \n", "0.019 | \n", "0.013 | \n", "1612.0 | \n", "2336.0 | \n", "1.0 | \n", "
| global_sigma | \n", "6.810 | \n", "0.380 | \n", "6.118 | \n", "7.546 | \n", "0.006 | \n", "0.004 | \n", "4726.0 | \n", "2892.0 | \n", "1.0 | \n", "
| subject_intercept_sigma | \n", "6.802 | \n", "0.895 | \n", "5.158 | \n", "8.459 | \n", "0.016 | \n", "0.011 | \n", "3045.0 | \n", "2681.0 | \n", "1.0 | \n", "
\n",
"\n"
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"\n"
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"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 33 seconds.\n",
"There were 60 divergences after tuning. Increase `target_accept` or reparameterize.\n",
"The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
"The effective sample size per chain is smaller than 100 for some parameters. A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n",
"Sampling: [outcome]\n"
]
},
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"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
|---|---|---|---|---|---|---|---|---|---|
| global_intercept | \n", "5.246 | \n", "0.746 | \n", "3.952 | \n", "6.829 | \n", "0.078 | \n", "0.061 | \n", "143.0 | \n", "2169.0 | \n", "1.09 | \n", "
| global_sigma | \n", "6.875 | \n", "0.279 | \n", "6.343 | \n", "7.456 | \n", "0.004 | \n", "0.003 | \n", "3986.0 | \n", "1885.0 | \n", "1.39 | \n", "
| global_beta_grade | \n", "-0.262 | \n", "0.242 | \n", "-0.673 | \n", "0.253 | \n", "0.028 | \n", "0.020 | \n", "99.0 | \n", "1903.0 | \n", "1.07 | \n", "
| subject_intercept_sigma | \n", "5.320 | \n", "0.887 | \n", "3.416 | \n", "6.789 | \n", "0.133 | \n", "0.095 | \n", "55.0 | \n", "976.0 | \n", "1.06 | \n", "
| subject_beta_grade_sigma | \n", "0.625 | \n", "0.444 | \n", "0.019 | \n", "1.266 | \n", "0.166 | \n", "0.123 | \n", "8.0 | \n", "5.0 | \n", "1.49 | \n", "
\n",
"\n"
],
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"\n"
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"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 79 seconds.\n",
"There were 849 divergences after tuning. Increase `target_accept` or reparameterize.\n",
"The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
"The effective sample size per chain is smaller than 100 for some parameters. A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n",
"Sampling: [outcome]\n"
]
},
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"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
|---|---|---|---|---|---|---|---|---|---|
| global_intercept | \n", "6.160 | \n", "1.136 | \n", "4.591 | \n", "8.464 | \n", "0.306 | \n", "0.221 | \n", "16.0 | \n", "1359.0 | \n", "1.17 | \n", "
| global_sigma | \n", "6.978 | \n", "0.333 | \n", "6.329 | \n", "7.650 | \n", "0.013 | \n", "0.010 | \n", "809.0 | \n", "1315.0 | \n", "1.53 | \n", "
| global_beta_grade | \n", "-0.117 | \n", "0.591 | \n", "-1.328 | \n", "0.958 | \n", "0.040 | \n", "0.065 | \n", "590.0 | \n", "1156.0 | \n", "1.53 | \n", "
| global_beta_grade2 | \n", "0.071 | \n", "0.093 | \n", "-0.118 | \n", "0.246 | \n", "0.006 | \n", "0.004 | \n", "445.0 | \n", "1403.0 | \n", "1.53 | \n", "
| subject_intercept_sigma | \n", "1.174 | \n", "1.173 | \n", "0.010 | \n", "3.273 | \n", "0.424 | \n", "0.312 | \n", "6.0 | \n", "4.0 | \n", "1.79 | \n", "
| subject_beta_grade_sigma | \n", "1.337 | \n", "0.293 | \n", "0.745 | \n", "1.731 | \n", "0.083 | \n", "0.063 | \n", "13.0 | \n", "393.0 | \n", "1.22 | \n", "
| subject_beta_grade2_sigma | \n", "0.081 | \n", "0.076 | \n", "0.001 | \n", "0.212 | \n", "0.027 | \n", "0.020 | \n", "6.0 | \n", "4.0 | \n", "1.67 | \n", "
\n",
"\n"
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"source": [
"id_indx, unique_ids = pd.factorize(df_external[\"ID\"])\n",
"coords = {\"ids\": unique_ids, \"obs\": range(len(df_external[\"EXTERNAL\"]))}\n",
"with pm.Model(coords=coords) as model:\n",
" grade = pm.MutableData(\"grade_data\", df_external[\"GRADE\"].values)\n",
" grade2 = pm.MutableData(\"grade2_data\", df_external[\"GRADE\"].values ** 2)\n",
" grade3 = pm.MutableData(\"grade3_data\", df_external[\"GRADE\"].values ** 3)\n",
" external = pm.MutableData(\"external_data\", df_external[\"EXTERNAL\"].values + 1e-25)\n",
" female = pm.MutableData(\"female_data\", df_external[\"FEMALE\"].values)\n",
"\n",
" global_intercept = pm.Normal(\"global_intercept\", 6, 2)\n",
" global_sigma = pm.Normal(\"global_sigma\", 7, 1)\n",
" global_beta_grade = pm.Normal(\"global_beta_grade\", 0, 1)\n",
" global_beta_grade2 = pm.Normal(\"global_beta_grade2\", 0, 1)\n",
" global_beta_grade3 = pm.Normal(\"global_beta_grade3\", 0, 1)\n",
" global_beta_female = pm.Normal(\"global_beta_female\", 0, 1)\n",
" global_beta_female_grade = pm.Normal(\"global_beta_female_grade\", 0, 1)\n",
" global_beta_female_grade2 = pm.Normal(\"global_beta_female_grade2\", 0, 1)\n",
" global_beta_female_grade3 = pm.Normal(\"global_beta_female_grade3\", 0, 1)\n",
"\n",
" subject_intercept_sigma = pm.Exponential(\"subject_intercept_sigma\", 1)\n",
" subject_intercept = pm.Normal(\"subject_intercept\", 3, subject_intercept_sigma, dims=\"ids\")\n",
"\n",
" subject_beta_grade_sigma = pm.Exponential(\"subject_beta_grade_sigma\", 1)\n",
" subject_beta_grade = pm.Normal(\"subject_beta_grade\", 0, subject_beta_grade_sigma, dims=\"ids\")\n",
"\n",
" subject_beta_grade2_sigma = pm.Exponential(\"subject_beta_grade2_sigma\", 1)\n",
" subject_beta_grade2 = pm.Normal(\"subject_beta_grade2\", 0, subject_beta_grade2_sigma, dims=\"ids\")\n",
"\n",
" subject_beta_grade3_sigma = pm.Exponential(\"subject_beta_grade3_sigma\", 1)\n",
" subject_beta_grade3 = pm.Normal(\"subject_beta_grade3\", 0, subject_beta_grade3_sigma, dims=\"ids\")\n",
"\n",
" mu = pm.Deterministic(\n",
" \"growth_model\",\n",
" global_intercept\n",
" + subject_intercept[id_indx]\n",
" + global_beta_female * female\n",
" + global_beta_female_grade * (female * grade)\n",
" + global_beta_female_grade2 * (female * grade2)\n",
" + global_beta_female_grade3 * (female * grade3)\n",
" + (global_beta_grade + subject_beta_grade[id_indx]) * grade\n",
" + (global_beta_grade2 + subject_beta_grade2[id_indx]) * grade2\n",
" + (global_beta_grade3 + subject_beta_grade3[id_indx]) * grade3,\n",
" )\n",
"\n",
" outcome_latent = pm.Gumbel.dist(mu, global_sigma)\n",
" outcome = pm.Censored(\n",
" \"outcome\", outcome_latent, lower=0, upper=68, observed=external, dims=\"obs\"\n",
" )\n",
"\n",
" idata_m7 = pm.sample_prior_predictive()\n",
" idata_m7.extend(\n",
" pm.sample(\n",
" draws=5000,\n",
" random_seed=100,\n",
" target_accept=0.99,\n",
" nuts_sampler=\"numpyro\",\n",
" idata_kwargs={\"log_likelihood\": True},\n",
" )\n",
" )\n",
" idata_m7.extend(pm.sample_posterior_predictive(idata_m7))"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
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"\n",
"\n",
"\n",
"\n",
"\n"
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"text/plain": [
"| \n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
|---|---|---|---|---|---|---|---|---|---|
| global_intercept | \n", "6.557 | \n", "1.297 | \n", "4.027 | \n", "8.916 | \n", "0.016 | \n", "0.011 | \n", "6847.0 | \n", "10276.0 | \n", "1.00 | \n", "
| global_sigma | \n", "6.633 | \n", "0.408 | \n", "5.871 | \n", "7.393 | \n", "0.010 | \n", "0.007 | \n", "1777.0 | \n", "8061.0 | \n", "1.00 | \n", "
| global_beta_grade | \n", "0.009 | \n", "0.878 | \n", "-1.577 | \n", "1.735 | \n", "0.011 | \n", "0.008 | \n", "6155.0 | \n", "9098.0 | \n", "1.00 | \n", "
| global_beta_grade2 | \n", "-0.139 | \n", "0.390 | \n", "-0.840 | \n", "0.621 | \n", "0.006 | \n", "0.004 | \n", "4503.0 | \n", "7911.0 | \n", "1.00 | \n", "
| subject_intercept_sigma | \n", "5.786 | \n", "1.239 | \n", "3.392 | \n", "8.144 | \n", "0.054 | \n", "0.038 | \n", "573.0 | \n", "550.0 | \n", "1.01 | \n", "
| subject_beta_grade_sigma | \n", "0.552 | \n", "0.379 | \n", "0.003 | \n", "1.218 | \n", "0.047 | \n", "0.033 | \n", "50.0 | \n", "166.0 | \n", "1.07 | \n", "
| subject_beta_grade2_sigma | \n", "0.098 | \n", "0.072 | \n", "0.001 | \n", "0.220 | \n", "0.009 | \n", "0.006 | \n", "60.0 | \n", "171.0 | \n", "1.07 | \n", "
| subject_beta_grade3_sigma | \n", "0.019 | \n", "0.013 | \n", "0.000 | \n", "0.042 | \n", "0.001 | \n", "0.001 | \n", "131.0 | \n", "111.0 | \n", "1.05 | \n", "
| global_beta_female | \n", "-0.212 | \n", "0.940 | \n", "-1.968 | \n", "1.573 | \n", "0.009 | \n", "0.007 | \n", "9904.0 | \n", "10717.0 | \n", "1.00 | \n", "
| global_beta_female_grade | \n", "-0.132 | \n", "0.898 | \n", "-1.804 | \n", "1.565 | \n", "0.010 | \n", "0.007 | \n", "7308.0 | \n", "10362.0 | \n", "1.00 | \n", "
| global_beta_female_grade2 | \n", "0.020 | \n", "0.495 | \n", "-0.903 | \n", "0.958 | \n", "0.007 | \n", "0.005 | \n", "4831.0 | \n", "7979.0 | \n", "1.00 | \n", "
| global_beta_female_grade3 | \n", "-0.008 | \n", "0.071 | \n", "-0.141 | \n", "0.124 | \n", "0.001 | \n", "0.001 | \n", "4882.0 | \n", "8440.0 | \n", "1.00 | \n", "
| \n", " | rank | \n", "elpd_loo | \n", "p_loo | \n", "elpd_diff | \n", "weight | \n", "se | \n", "dse | \n", "warning | \n", "scale | \n", "
|---|---|---|---|---|---|---|---|---|---|
| Linear Model | \n", "0 | \n", "-913.492285 | \n", "32.270139 | \n", "0.000000 | \n", "8.146420e-01 | \n", "13.556027 | \n", "0.000000 | \n", "True | \n", "log | \n", "
| Polynomial + Gender | \n", "1 | \n", "-915.895242 | \n", "49.043791 | \n", "2.402957 | \n", "8.394507e-16 | \n", "13.449388 | \n", "2.597256 | \n", "True | \n", "log | \n", "
| Minimal Model | \n", "2 | \n", "-917.384833 | \n", "33.632784 | \n", "3.892548 | \n", "7.475052e-16 | \n", "13.823280 | \n", "2.375968 | \n", "True | \n", "log | \n", "
| Polynomial Model | \n", "3 | \n", "-921.859743 | \n", "27.035846 | \n", "8.367458 | \n", "1.853580e-01 | \n", "14.762473 | \n", "5.305436 | \n", "True | \n", "log | \n", "