{ "cells": [ { "cell_type": "markdown", "id": "6476c8bf", "metadata": {}, "source": [ "# Logistic regression: confidence intervals and bands\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "58c263cb", "metadata": { "execution": { "iopub.execute_input": "2026-09-14T14:45:22.034440Z", "iopub.status.busy": "2026-09-14T14:45:22.034440Z", "iopub.status.idle": "2026-09-14T14:45:25.496161Z", "shell.execute_reply": "2026-09-14T14:45:25.494396Z" } }, "outputs": [], "source": [ "from pathlib import Path\n", "import sys\n", "\n", "PROJECT_ROOT = Path.cwd().resolve()\n", "while not (PROJECT_ROOT / 'data.py').exists():\n", " if PROJECT_ROOT.parent == PROJECT_ROOT:\n", " raise FileNotFoundError('Open this notebook from inside organized_uncertainty_analysis.')\n", " PROJECT_ROOT = PROJECT_ROOT.parent\n", "if str(PROJECT_ROOT.parent) not in sys.path:\n", " sys.path.insert(0, str(PROJECT_ROOT.parent))\n", "\n", "from organized_uncertainty_analysis.logistic.data_fit_gof import prepare_full_trim\n", "from organized_uncertainty_analysis.logistic import ci_estimation as ci\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "5f570784", "metadata": { "execution": { "iopub.execute_input": "2026-09-14T14:45:25.496161Z", "iopub.status.busy": "2026-09-14T14:45:25.496161Z", "iopub.status.idle": "2026-09-14T14:56:58.717361Z", "shell.execute_reply": "2026-09-14T14:56:58.715345Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[trim] removed index=53, x_raw=2.481226, y=0\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ ".\\logistic\\core.py:1263: RuntimeWarning: overflow encountered in exp\n", " return float(np.exp(value)) if trans == \"log\" else float(value)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ ".\\logistic\\core.py:518: RuntimeWarning: overflow encountered in exp\n", " x50_raw = np.exp(x50_model)\n" ] }, { "data": { "text/html": [ "
| \n", " | Panel | \n", "Method | \n", "b0_hat | \n", "b0_LCL | \n", "b0_UCL | \n", "b0_width | \n", "b1_hat | \n", "b1_LCL | \n", "b1_UCL | \n", "b1_width | \n", "... | \n", "SUV50_UCL | \n", "SUV50_width | \n", "s50_hat | \n", "s50_med | \n", "s50_LCL | \n", "s50_UCL | \n", "s50_width | \n", "transform | \n", "l2 | \n", "B_used | \n", "
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "FULL-RAW | \n", "Wald | \n", "-11.683870 | \n", "-18.564162 | \n", "-4.803579 | \n", "13.760583 | \n", "5.686964 | \n", "1.856861 | \n", "9.517068 | \n", "7.660207 | \n", "... | \n", "2.373852 | \n", "0.638704 | \n", "1.421741 | \n", "1.421741 | \n", "0.464215 | \n", "2.379267 | \n", "1.915052 | \n", "raw | \n", "1.000000e-08 | \n", "NaN | \n", "
| 1 | \n", "FULL-RAW | \n", "MC | \n", "-11.683870 | \n", "-18.574470 | \n", "-4.916885 | \n", "13.657585 | \n", "5.686964 | \n", "1.907961 | \n", "9.526966 | \n", "7.619004 | \n", "... | \n", "2.767253 | \n", "0.963235 | \n", "1.421741 | \n", "1.424010 | \n", "0.476990 | \n", "2.381741 | \n", "1.904751 | \n", "raw | \n", "1.000000e-08 | \n", "200000.0 | \n", "
| 2 | \n", "FULL-RAW | \n", "Nonparametric | \n", "-11.683870 | \n", "-286.976315 | \n", "-7.309847 | \n", "279.666467 | \n", "5.686964 | \n", "2.833559 | \n", "177.551499 | \n", "174.717940 | \n", "... | \n", "2.797724 | \n", "1.185923 | \n", "1.421741 | \n", "1.551703 | \n", "0.708390 | \n", "44.387875 | \n", "43.679485 | \n", "raw | \n", "1.000000e-08 | \n", "4970.0 | \n", "
| 4 | \n", "FULL-RAW | \n", "Parametric | \n", "-11.683870 | \n", "-1888.751742 | \n", "-7.285259 | \n", "1881.466483 | \n", "5.686964 | \n", "3.040610 | \n", "899.767373 | \n", "896.726763 | \n", "... | \n", "2.495321 | \n", "0.765042 | \n", "1.421741 | \n", "1.639014 | \n", "0.760152 | \n", "224.941843 | \n", "224.181691 | \n", "raw | \n", "1.000000e-08 | \n", "5000.0 | \n", "
| 5 | \n", "TRIM-RAW | \n", "Wald | \n", "-26.022861 | \n", "-51.187492 | \n", "-0.858229 | \n", "50.329263 | \n", "14.660490 | \n", "-0.505241 | \n", "29.826221 | \n", "30.331461 | \n", "... | \n", "1.978951 | \n", "0.407834 | \n", "3.665123 | \n", "3.665123 | \n", "-0.126310 | \n", "7.456555 | \n", "7.582865 | \n", "raw | \n", "1.000000e-08 | \n", "NaN | \n", "
| 6 | \n", "TRIM-RAW | \n", "MC | \n", "-26.022861 | \n", "-51.289174 | \n", "-5.293575 | \n", "45.995599 | \n", "14.660490 | \n", "2.167869 | \n", "29.880488 | \n", "27.712619 | \n", "... | \n", "2.576262 | \n", "0.963308 | \n", "3.665123 | \n", "3.733415 | \n", "0.541967 | \n", "7.470122 | \n", "6.928155 | \n", "raw | \n", "1.000000e-08 | \n", "200000.0 | \n", "
| 7 | \n", "TRIM-RAW | \n", "Nonparametric | \n", "-26.022861 | \n", "-295.036870 | \n", "-20.363367 | \n", "274.673503 | \n", "14.660490 | \n", "11.108140 | \n", "182.394572 | \n", "171.286432 | \n", "... | \n", "2.007056 | \n", "0.399488 | \n", "3.665123 | \n", "12.366577 | \n", "2.777035 | \n", "45.598643 | \n", "42.821608 | \n", "raw | \n", "1.000000e-08 | \n", "4970.0 | \n", "
| 9 | \n", "TRIM-RAW | \n", "Parametric | \n", "-26.022861 | \n", "-300.442716 | \n", "-15.603787 | \n", "284.838928 | \n", "14.660490 | \n", "8.529826 | \n", "173.638295 | \n", "165.108469 | \n", "... | \n", "1.936547 | \n", "0.319191 | \n", "3.665123 | \n", "18.804932 | \n", "2.132456 | \n", "43.409574 | \n", "41.277117 | \n", "raw | \n", "1.000000e-08 | \n", "5000.0 | \n", "
| 10 | \n", "FULL-LOG | \n", "Wald | \n", "-7.527408 | \n", "-11.931980 | \n", "-3.122835 | \n", "8.809145 | \n", "10.738157 | \n", "3.403081 | \n", "18.073234 | \n", "14.670153 | \n", "... | \n", "2.375287 | \n", "0.664636 | \n", "1.331775 | \n", "1.331775 | \n", "0.283943 | \n", "2.379607 | \n", "2.095664 | \n", "log | \n", "1.000000e-08 | \n", "NaN | \n", "
| 11 | \n", "FULL-LOG | \n", "MC | \n", "-7.527408 | \n", "-11.926281 | \n", "-3.213234 | \n", "8.713047 | \n", "10.738157 | \n", "3.542076 | \n", "18.069587 | \n", "14.527511 | \n", "... | \n", "2.872277 | \n", "1.113003 | \n", "1.331775 | \n", "1.337967 | \n", "0.328864 | \n", "2.388138 | \n", "2.059274 | \n", "log | \n", "1.000000e-08 | \n", "200000.0 | \n", "
| 12 | \n", "FULL-LOG | \n", "Nonparametric | \n", "-7.527408 | \n", "-139.210089 | \n", "-5.228716 | \n", "133.981373 | \n", "10.738157 | \n", "5.787698 | \n", "289.823805 | \n", "284.036107 | \n", "... | \n", "2.772984 | \n", "1.162479 | \n", "1.331775 | \n", "1.479498 | \n", "0.572833 | \n", "44.860686 | \n", "44.287853 | \n", "log | \n", "1.000000e-08 | \n", "4970.0 | \n", "
| 14 | \n", "FULL-LOG | \n", "Parametric | \n", "-7.527408 | \n", "-1350.391938 | \n", "-4.886625 | \n", "1345.505313 | \n", "10.738157 | \n", "5.895253 | \n", "1821.085324 | \n", "1815.190071 | \n", "... | \n", "2.500422 | \n", "0.786229 | \n", "1.331775 | \n", "1.642708 | \n", "0.607452 | \n", "216.883898 | \n", "216.276447 | \n", "log | \n", "1.000000e-08 | \n", "5000.0 | \n", "
| 15 | \n", "TRIM-LOG | \n", "Wald | \n", "-14.173996 | \n", "-27.119165 | \n", "-1.228827 | \n", "25.890339 | \n", "24.851636 | \n", "-0.211973 | \n", "49.915245 | \n", "50.127218 | \n", "... | \n", "1.981094 | \n", "0.401703 | \n", "3.512347 | \n", "3.512347 | \n", "-0.265437 | \n", "7.290132 | \n", "7.555569 | \n", "log | \n", "1.000000e-08 | \n", "NaN | \n", "
| 16 | \n", "TRIM-LOG | \n", "MC | \n", "-14.173996 | \n", "-27.150547 | \n", "-3.303921 | \n", "23.846626 | \n", "24.851636 | \n", "3.835445 | \n", "49.925087 | \n", "46.089642 | \n", "... | \n", "2.651319 | \n", "1.049637 | \n", "3.512347 | \n", "3.568860 | \n", "0.392368 | \n", "7.308244 | \n", "6.915877 | \n", "log | \n", "1.000000e-08 | \n", "200000.0 | \n", "
| 17 | \n", "TRIM-LOG | \n", "Nonparametric | \n", "-14.173996 | \n", "-142.982238 | \n", "-11.125988 | \n", "131.856250 | \n", "24.851636 | \n", "18.794856 | \n", "297.809265 | \n", "279.014409 | \n", "... | \n", "1.995369 | \n", "0.389246 | \n", "3.512347 | \n", "12.350910 | \n", "2.558150 | \n", "46.058014 | \n", "43.499864 | \n", "log | \n", "1.000000e-08 | \n", "4970.0 | \n", "
| 19 | \n", "TRIM-LOG | \n", "Parametric | \n", "-14.173996 | \n", "-164.940747 | \n", "-8.669324 | \n", "156.271423 | \n", "24.851636 | \n", "14.316762 | \n", "301.097648 | \n", "286.780887 | \n", "... | \n", "1.930646 | \n", "0.314281 | \n", "3.512347 | \n", "18.685352 | \n", "1.964429 | \n", "43.525287 | \n", "41.560858 | \n", "log | \n", "1.000000e-08 | \n", "5000.0 | \n", "
16 rows × 28 columns
\n", "| \n", " | Panel | \n", "Method | \n", "transform | \n", "x50_hat | \n", "x50_LCL | \n", "x50_UCL | \n", "x50_width | \n", "SUV50_hat | \n", "SUV50_LCL | \n", "SUV50_UCL | \n", "... | \n", "b0_UCL | \n", "b0_width | \n", "b1_hat | \n", "b1_LCL | \n", "b1_UCL | \n", "b1_width | \n", "x50_med | \n", "SUV50_med | \n", "s50_med | \n", "l2 | \n", "
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "FULL-RAW | \n", "Wald | \n", "raw | \n", "2.054500 | \n", "1.735148 | \n", "2.373852 | \n", "0.638704 | \n", "2.054500 | \n", "1.735148 | \n", "2.373852 | \n", "... | \n", "-4.803579 | \n", "13.760583 | \n", "5.686964 | \n", "1.856861 | \n", "9.517068 | \n", "7.660207 | \n", "2.054500 | \n", "2.054500 | \n", "1.421741 | \n", "1.000000e-08 | \n", "
| 1 | \n", "FULL-RAW | \n", "MC | \n", "raw | \n", "2.054500 | \n", "1.804018 | \n", "2.767253 | \n", "0.963235 | \n", "2.054500 | \n", "1.804018 | \n", "2.767253 | \n", "... | \n", "-4.916885 | \n", "13.657585 | \n", "5.686964 | \n", "1.907961 | \n", "9.526966 | \n", "7.619004 | \n", "2.054326 | \n", "2.054326 | \n", "1.424010 | \n", "1.000000e-08 | \n", "
| 2 | \n", "FULL-RAW | \n", "Nonparametric | \n", "raw | \n", "2.054500 | \n", "1.611801 | \n", "2.797724 | \n", "1.185923 | \n", "2.054500 | \n", "1.611801 | \n", "2.797724 | \n", "... | \n", "-7.309847 | \n", "279.666467 | \n", "5.686964 | \n", "2.833559 | \n", "177.551499 | \n", "174.717940 | \n", "2.029787 | \n", "2.029787 | \n", "1.551703 | \n", "1.000000e-08 | \n", "
| 4 | \n", "FULL-RAW | \n", "Parametric | \n", "raw | \n", "2.054500 | \n", "1.730279 | \n", "2.495321 | \n", "0.765042 | \n", "2.054500 | \n", "1.730279 | \n", "2.495321 | \n", "... | \n", "-7.285259 | \n", "1881.466483 | \n", "5.686964 | \n", "3.040610 | \n", "899.767373 | \n", "896.726763 | \n", "2.062106 | \n", "2.062106 | \n", "1.639014 | \n", "1.000000e-08 | \n", "
| 5 | \n", "TRIM-RAW | \n", "Wald | \n", "raw | \n", "1.775033 | \n", "1.571116 | \n", "1.978951 | \n", "0.407834 | \n", "1.775033 | \n", "1.571116 | \n", "1.978951 | \n", "... | \n", "-0.858229 | \n", "50.329263 | \n", "14.660490 | \n", "-0.505241 | \n", "29.826221 | \n", "30.331461 | \n", "1.775033 | \n", "1.775033 | \n", "3.665123 | \n", "1.000000e-08 | \n", "
| 6 | \n", "TRIM-RAW | \n", "MC | \n", "raw | \n", "1.775033 | \n", "1.612954 | \n", "2.576262 | \n", "0.963308 | \n", "1.775033 | \n", "1.612954 | \n", "2.576262 | \n", "... | \n", "-5.293575 | \n", "45.995599 | \n", "14.660490 | \n", "2.167869 | \n", "29.880488 | \n", "27.712619 | \n", "1.772581 | \n", "1.772581 | \n", "3.733415 | \n", "1.000000e-08 | \n", "
| 7 | \n", "TRIM-RAW | \n", "Nonparametric | \n", "raw | \n", "1.775033 | \n", "1.607569 | \n", "2.007056 | \n", "0.399488 | \n", "1.775033 | \n", "1.607569 | \n", "2.007056 | \n", "... | \n", "-20.363367 | \n", "274.673503 | \n", "14.660490 | \n", "11.108140 | \n", "182.394572 | \n", "171.286432 | \n", "1.780713 | \n", "1.780713 | \n", "12.366577 | \n", "1.000000e-08 | \n", "
| 9 | \n", "TRIM-RAW | \n", "Parametric | \n", "raw | \n", "1.775033 | \n", "1.617356 | \n", "1.936547 | \n", "0.319191 | \n", "1.775033 | \n", "1.617356 | \n", "1.936547 | \n", "... | \n", "-15.603787 | \n", "284.838928 | \n", "14.660490 | \n", "8.529826 | \n", "173.638295 | \n", "165.108469 | \n", "1.730279 | \n", "1.730279 | \n", "18.804932 | \n", "1.000000e-08 | \n", "
| 10 | \n", "FULL-LOG | \n", "Wald | \n", "log | \n", "0.700996 | \n", "0.536874 | \n", "0.865118 | \n", "0.328244 | \n", "2.015760 | \n", "1.710651 | \n", "2.375287 | \n", "... | \n", "-3.122835 | \n", "8.809145 | \n", "10.738157 | \n", "3.403081 | \n", "18.073234 | \n", "14.670153 | \n", "0.700996 | \n", "2.015760 | \n", "1.331775 | \n", "1.000000e-08 | \n", "
| 11 | \n", "FULL-LOG | \n", "MC | \n", "log | \n", "0.700996 | \n", "0.564902 | \n", "1.055105 | \n", "0.490204 | \n", "2.015760 | \n", "1.759275 | \n", "2.872277 | \n", "... | \n", "-3.213234 | \n", "8.713047 | \n", "10.738157 | \n", "3.542076 | \n", "18.069587 | \n", "14.527511 | \n", "0.700560 | \n", "2.014880 | \n", "1.337967 | \n", "1.000000e-08 | \n", "
| 12 | \n", "FULL-LOG | \n", "Nonparametric | \n", "log | \n", "0.700996 | \n", "0.476548 | \n", "1.019924 | \n", "0.543376 | \n", "2.015760 | \n", "1.610505 | \n", "2.772984 | \n", "... | \n", "-5.228716 | \n", "133.981373 | \n", "10.738157 | \n", "5.787698 | \n", "289.823805 | \n", "284.036107 | \n", "0.690820 | \n", "1.995351 | \n", "1.479498 | \n", "1.000000e-08 | \n", "
| 14 | \n", "FULL-LOG | \n", "Parametric | \n", "log | \n", "0.700996 | \n", "0.538942 | \n", "0.916460 | \n", "0.377517 | \n", "2.015760 | \n", "1.714193 | \n", "2.500422 | \n", "... | \n", "-4.886625 | \n", "1345.505313 | \n", "10.738157 | \n", "5.895253 | \n", "1821.085324 | \n", "1815.190071 | \n", "0.700921 | \n", "2.015608 | \n", "1.642708 | \n", "1.000000e-08 | \n", "
| 15 | \n", "TRIM-LOG | \n", "Wald | \n", "log | \n", "0.570345 | \n", "0.457040 | \n", "0.683649 | \n", "0.226610 | \n", "1.768876 | \n", "1.579392 | \n", "1.981094 | \n", "... | \n", "-1.228827 | \n", "25.890339 | \n", "24.851636 | \n", "-0.211973 | \n", "49.915245 | \n", "50.127218 | \n", "0.570345 | \n", "1.768876 | \n", "3.512347 | \n", "1.000000e-08 | \n", "
| 16 | \n", "TRIM-LOG | \n", "MC | \n", "log | \n", "0.570345 | \n", "0.471055 | \n", "0.975351 | \n", "0.504296 | \n", "1.768876 | \n", "1.601682 | \n", "2.651319 | \n", "... | \n", "-3.303921 | \n", "23.846626 | \n", "24.851636 | \n", "3.835445 | \n", "49.925087 | \n", "46.089642 | \n", "0.568913 | \n", "1.766343 | \n", "3.568860 | \n", "1.000000e-08 | \n", "
| 17 | \n", "TRIM-LOG | \n", "Nonparametric | \n", "log | \n", "0.570345 | \n", "0.473823 | \n", "0.690829 | \n", "0.217006 | \n", "1.768876 | \n", "1.606123 | \n", "1.995369 | \n", "... | \n", "-11.125988 | \n", "131.856250 | \n", "24.851636 | \n", "18.794856 | \n", "297.809265 | \n", "279.014409 | \n", "0.574927 | \n", "1.777000 | \n", "12.350910 | \n", "1.000000e-08 | \n", "
| 19 | \n", "TRIM-LOG | \n", "Parametric | \n", "log | \n", "0.570345 | \n", "0.480180 | \n", "0.657855 | \n", "0.177675 | \n", "1.768876 | \n", "1.616365 | \n", "1.930646 | \n", "... | \n", "-8.669324 | \n", "156.271423 | \n", "24.851636 | \n", "14.316762 | \n", "301.097648 | \n", "286.780887 | \n", "0.547798 | \n", "1.729441 | \n", "18.685352 | \n", "1.000000e-08 | \n", "
16 rows × 35 columns
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