big_between_study_reml.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax\n",
    "jax.config.update('jax_enable_x64',True)\n",
    "jax.config.update(\"jax_default_device\", jax.devices()[6])\n",
    "import jax.numpy as jnp\n",
    "import pandas as pd\n",
    "from jax.random import PRNGKey as pkey\n",
    "from jax.scipy.special import expit\n",
    "from jaxopt import LBFGS\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm.auto import tqdm\n",
    "plt.style.use('ggplot')\n",
    "from functools import partial\n",
    "from scipy.optimize import root_scalar,minimize_scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_study(\n",
    "    key,\n",
    "    beta_true,\n",
    "    gamma_true,\n",
    "    confounding_constant = 0.2,\n",
    "    intercept_val = -2.,\n",
    "    num_subjects_per_group = 200,\n",
    "    num_groups = 4,\n",
    "    num_covs = 1,\n",
    "    ):\n",
    "    total_subjects = num_subjects_per_group*num_groups\n",
    "    num_exposures = num_groups -1\n",
    "    \n",
    "    keys = jax.random.split(key,10)\n",
    "\n",
    "    assignment = jnp.vstack([jnp.arange(num_groups)]*num_subjects_per_group).T.flatten().reshape(-1,1)\n",
    "    covs = jnp.hstack([jax.random.normal(keys[0],(total_subjects,num_covs))]) + confounding_constant*assignment\n",
    "    beta_covs = jax.random.normal(keys[2],(num_covs,))\n",
    "\n",
    "    beta_perturb = jnp.sqrt(gamma_true)*jax.random.normal(keys[8])\n",
    "\n",
    "    beta_study = beta_true+beta_perturb\n",
    "    full_beta = jnp.hstack([beta_study,intercept_val,beta_covs])\n",
    "\n",
    "    #This is just for simulating\n",
    "    X_sim = jnp.hstack([assignment,jnp.ones((total_subjects,1)),covs])\n",
    "    Y_obs = jax.random.binomial(keys[5],1,expit(X_sim@full_beta))\n",
    "\n",
    "    dummies = pd.get_dummies(pd.Series(assignment[:,0]),prefix='treat',drop_first=True).astype('float64')\n",
    "    X_reg = jnp.hstack([jnp.ones((total_subjects,1)),covs,dummies.values])\n",
    "\n",
    "    df_reg = pd.DataFrame(X_reg,columns = ['intercept']+['covariate']+list(dummies.columns))\n",
    "\n",
    "    dummies = pd.get_dummies(pd.Series(assignment[:,0]),prefix='treat',drop_first=True).astype('float64')\n",
    "    X_reg = jnp.hstack([jnp.ones((total_subjects,1)),covs,dummies.values])\n",
    "\n",
    "    df_reg = pd.DataFrame(X_reg,columns = ['intercept']+['covariate']+list(dummies.columns))\n",
    "\n",
    "    model = sm.Logit(Y_obs, df_reg)\n",
    "    results = model.fit(disp = 0)\n",
    "    results.summary()\n",
    "\n",
    "    summary_df = pd.DataFrame({\n",
    "        'assign':assignment[:,0],\n",
    "        'is_case':Y_obs\n",
    "    })\n",
    "    total_non_cases = len(summary_df[summary_df['is_case']==0])\n",
    "    reference_non_cases = len(summary_df[(summary_df['assign']==0)&(summary_df['is_case']==0)])\n",
    "    p = reference_non_cases/total_non_cases\n",
    "    total_cases = summary_df['is_case'].sum()\n",
    "    z = total_non_cases/total_cases\n",
    "\n",
    "    L = results.params[-num_exposures:].values\n",
    "    V = jnp.diag(results.cov_params().values[-num_exposures:,-num_exposures:])\n",
    "    Z = jnp.arange(1.,1+num_exposures).reshape(-1,1)\n",
    "    X = jnp.arange(1.,1+num_exposures).reshape(-1,1)\n",
    "    \n",
    "    return L,results.cov_params().values[-num_exposures:,-num_exposures:],X,Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "logdet = jax.jit(lambda x:jnp.linalg.slogdet(x)[1])\n",
    "num_exposures = 3\n",
    "Z = jnp.arange(1.,1+num_exposures).reshape(-1,1)\n",
    "X = jnp.arange(1.,1+num_exposures).reshape(-1,1)\n",
    "ZZT = Z@Z.T\n",
    "\n",
    "@jax.jit\n",
    "def margin_like(gamma,covariance_matrices,Y,X,Z):\n",
    "    ZZT = Z@Z.T\n",
    "    vmats = jnp.array([ZZT*gamma + C for C in covariance_matrices])\n",
    "    inv_vmats = jnp.array([jnp.linalg.inv(V) for V in vmats])\n",
    "    LNV = jnp.sum(jnp.array([logdet(V) for V in vmats]))\n",
    "    beta = (\n",
    "        jnp.linalg.inv(jnp.sum(jnp.array([X.T@inv_V@X for inv_V in inv_vmats]),axis=0))@ \n",
    "        (jnp.sum(jnp.array([X.T@inv_V@y for inv_V,y in zip(inv_vmats,Y)]),axis=0))\n",
    "    )\n",
    "    res_term = jnp.sum(\n",
    "        jnp.array([\n",
    "            (X@beta - y).T@inv_v@(X@beta-y) \n",
    "            for inv_v,y in zip(inv_vmats,Y)])\n",
    "        )\n",
    "    return LNV+res_term\n",
    "\n",
    "@jax.jit\n",
    "def margin_like_reml(gamma,covariance_matrices,Y,X,Z):\n",
    "    ZZT = Z@Z.T\n",
    "    vmats = jnp.array([ZZT*gamma + C for C in covariance_matrices])\n",
    "    inv_vmats = jnp.array([jnp.linalg.inv(V) for V in vmats])\n",
    "    LNV = jnp.sum(jnp.array([logdet(V) for V in vmats]))\n",
    "    REML_term = jnp.log(jnp.sum(jnp.array([X.T@invV@X for invV in inv_vmats])))\n",
    "    beta = (\n",
    "        jnp.linalg.inv(jnp.sum(jnp.array([X.T@inv_V@X for inv_V in inv_vmats]),axis=0))@ \n",
    "        (jnp.sum(jnp.array([X.T@inv_V@y for inv_V,y in zip(inv_vmats,Y)]),axis=0))\n",
    "    )\n",
    "    res_term = jnp.sum(\n",
    "        jnp.array([\n",
    "            (X@beta - y).T@inv_v@(X@beta-y) \n",
    "            for inv_v,y in zip(inv_vmats,Y)])\n",
    "        )\n",
    "    return LNV + res_term + REML_term\n",
    "vec_reml_like = (\n",
    "    jax.vmap(margin_like_reml,in_axes=[0,None,None,None,None])\n",
    ")\n",
    "diff_reml_like = jax.jit(\n",
    "    jax.grad(margin_like_reml,argnums=0)\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "diff_margin_like = jax.jit(\n",
    "    jax.grad(margin_like,argnums=0)\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "vec_margin_like = (\n",
    "    jax.vmap(margin_like,in_axes=[0,None,None,None,None])\n",
    ")\n",
    "\n",
    "#Old grid search code:\n",
    "# gamma_grid = jnp.logspace(-2,1.,300)\n",
    "# nll_corr = vec_margin_like(gamma_grid,cov_mats,L_vals,X,Z)\n",
    "# gamma_corr = gamma_grid[jnp.argmin(nll_corr)]\n",
    "# nll_diag = vec_margin_like(gamma_grid,diag_cov_mats,L_vals,X,Z)\n",
    "# gamma_diag = gamma_grid[jnp.argmin(nll_diag)]\n",
    "\n",
    "\n",
    "def estimate_gamma(L_vals,cov_mats,X,Z):\n",
    "    gamma_grid = jnp.logspace(-4,2.,20)\n",
    "    try:\n",
    "        gamma = root_scalar(lambda x:diff_margin_like(x,cov_mats,L_vals,X,Z),bracket = (1e-3,10.)).root\n",
    "    except:\n",
    "        nll = vec_margin_like(gamma_grid,cov_mats,L_vals,X,Z)\n",
    "        gamma = gamma_grid[jnp.argmin(nll)]\n",
    "    ZZT = Z@Z.T\n",
    "    vmats = jnp.array([ZZT*gamma + C for C in cov_mats])\n",
    "    inv_vmats = jnp.array([jnp.linalg.inv(V) for V in vmats])\n",
    "    beta = (\n",
    "        jnp.linalg.inv(jnp.sum(jnp.array([X.T@inv_V@X for inv_V in inv_vmats]),axis=0))@ \n",
    "        (jnp.sum(jnp.array([X.T@inv_V@y for inv_V,y in zip(inv_vmats,L_vals)]),axis=0))\n",
    "    )\n",
    "    return jnp.array(gamma),beta[0]\n",
    "\n",
    "def estimate_gamma_reml(L_vals,cov_mats,X,Z):\n",
    "    gamma_grid = jnp.logspace(-4,2.,20)\n",
    "    try:\n",
    "        gamma = root_scalar(lambda x:diff_reml_like(x,cov_mats,L_vals,X,Z),bracket = (1e-3,10.)).root\n",
    "    except:\n",
    "        nll = vec_reml_like(gamma_grid,cov_mats,L_vals,X,Z)\n",
    "        gamma = gamma_grid[jnp.argmin(nll)]\n",
    "    ZZT = Z@Z.T\n",
    "    vmats = jnp.array([ZZT*gamma + C for C in cov_mats])\n",
    "    inv_vmats = jnp.array([jnp.linalg.inv(V) for V in vmats])\n",
    "    beta = (\n",
    "        jnp.linalg.inv(jnp.sum(jnp.array([X.T@inv_V@X for inv_V in inv_vmats]),axis=0))@ \n",
    "        (jnp.sum(jnp.array([X.T@inv_V@y for inv_V,y in zip(inv_vmats,L_vals)]),axis=0))\n",
    "    )\n",
    "    return gamma,beta[0]\n",
    "\n",
    "# def estimate_gamma(L_vals,cov_mats,X,Z):\n",
    "#     diag_cov_mats = [jnp.diag(jnp.diag(C)) for C in cov_mats]\n",
    "\n",
    "#     gamma_grid = jnp.logspace(-4,2.,20)\n",
    "#     try:\n",
    "#         gamma_corr = root_scalar(lambda x:diff_margin_like(x,cov_mats,L_vals,X,Z),bracket = (1e-3,10.)).root\n",
    "#     except:\n",
    "#         nll_corr = vec_margin_like(gamma_grid,cov_mats,L_vals,X,Z)\n",
    "#         gamma_corr = gamma_grid[jnp.argmin(nll_corr)]\n",
    "#     try:\n",
    "#         gamma_diag = root_scalar(lambda x:diff_margin_like(x,diag_cov_mats,L_vals,X,Z),bracket = (1e-3,10.)).root\n",
    "#     except:\n",
    "#         nll_diag = vec_margin_like(gamma_grid,diag_cov_mats,L_vals,X,Z)\n",
    "#         gamma_diag = gamma_grid[jnp.argmin(nll_diag)]\n",
    "#     return gamma_corr,gamma_diag\n",
    "\n",
    "\n",
    "def drop_ith(ar,i):\n",
    "    return jnp.concat([ar[:i],ar[i+1:]])\n",
    "\n",
    "def jackknife_correct_gamma_est(L_vals,cov_mats,X,Z):\n",
    "    n = len(cov_mats)\n",
    "    jack_ests = jnp.array([\n",
    "        estimate_gamma(\n",
    "            drop_ith(L_vals,i),\n",
    "            drop_ith(cov_mats,i),\n",
    "            X,Z)\n",
    "            for i in range(n)\n",
    "        ]\n",
    "    )\n",
    "    main_est = estimate_gamma(L_vals,cov_mats,X,Z)\n",
    "    return n*jnp.array(main_est) - (n-1)*jnp.mean(jack_ests,axis=0)\n",
    "\n",
    "def simulate_meta_analysis(\n",
    "    key,\n",
    "    num_studies,\n",
    "    beta_true,\n",
    "    gamma_true,\n",
    "    confounding_constant = 0.2,\n",
    "    num_subjects_per_group = 200,\n",
    "    num_groups = 4,\n",
    "    num_covs = 1,\n",
    "    intercept_val = -2.,\n",
    "):\n",
    "    study_keys = jax.random.split(key,num_studies)\n",
    "    simulation_results = [\n",
    "        simulate_study(\n",
    "            study_key,\n",
    "            beta_true=beta_true,\n",
    "            gamma_true=gamma_true,\n",
    "            confounding_constant = confounding_constant,\n",
    "            num_subjects_per_group = num_subjects_per_group,\n",
    "            num_groups = num_groups,\n",
    "            num_covs = num_covs,\n",
    "            intercept_val=intercept_val\n",
    "            ) for study_key in study_keys\n",
    "    ]\n",
    "    L_vals,Covs,Xs,Zs = map(lambda x:jnp.array(x),zip(*simulation_results))\n",
    "    #Assume exposures are shared\n",
    "    return L_vals,Covs,Xs[0],Zs[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "Lvals,covmats,X,Z = simulate_meta_analysis(\n",
    "    pkey(3),\n",
    "    num_studies=5,\n",
    "    beta_true = 0.5,\n",
    "    gamma_true=0.2,\n",
    "    num_subjects_per_group=200,\n",
    "    num_groups = 4,\n",
    "    num_covs = 1,\n",
    "    intercept_val=-1,\n",
    "    )\n",
    "\n",
    "res = estimate_gamma(Lvals,covmats,X,Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 29,
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.53901326, 0.70411939], dtype=float64)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jackknife_correct_gamma_est(Lvals,covmats,X,Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5878016072274909\n"
     ]
    },
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     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@jax.jit\n",
    "def margin_like_reml(gamma,covariance_matrices,Y,X,Z):\n",
    "    ZZT = Z@Z.T\n",
    "    vmats = jnp.array([ZZT*gamma + C for C in covariance_matrices])\n",
    "    inv_vmats = jnp.array([jnp.linalg.inv(V) for V in vmats])\n",
    "    LNV = jnp.sum(jnp.array([logdet(V) for V in vmats]))\n",
    "    REML_term = jnp.log(jnp.sum(jnp.array([X.T@invV@X for invV in inv_vmats])))\n",
    "    beta = (\n",
    "        jnp.linalg.inv(jnp.sum(jnp.array([X.T@inv_V@X for inv_V in inv_vmats]),axis=0))@ \n",
    "        (jnp.sum(jnp.array([X.T@inv_V@y for inv_V,y in zip(inv_vmats,Y)]),axis=0))\n",
    "    )\n",
    "    res_term = jnp.sum(\n",
    "        jnp.array([\n",
    "            (X@beta - y).T@inv_v@(X@beta-y) \n",
    "            for inv_v,y in zip(inv_vmats,Y)])\n",
    "        )\n",
    "    # return LNV + res_term + REML_term\n",
    "    return LNV + res_term + REML_term\n",
    "vec_reml_like = (\n",
    "    jax.vmap(margin_like_reml,in_axes=[0,None,None,None,None])\n",
    ")\n",
    "diff_reml_like = jax.jit(\n",
    "    jax.grad(margin_like_reml,argnums=0)\n",
    ")\n",
    "\n",
    "\n",
    "gamma_grid = jnp.logspace(-3,3.,40)\n",
    "plt.plot(gamma_grid,vec_reml_like(gamma_grid,covmats,Lvals,X,Z))\n",
    "plt.xscale('log')\n",
    "print(gamma_grid[jnp.argmin(vec_reml_like(gamma_grid,covmats,Lvals,X,Z))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = covmats[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(-4.02739049, dtype=float64)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = 10\n",
    "C = covmats[0]\n",
    "logdet(Z.T@jnp.linalg.inv(C + g * Z@Z.T)@Z) + logdet((C + g * Z@Z.T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Mixed Linear Model Regression Results\n",
      "=====================================================\n",
      "Model:            MixedLM Dependent Variable: L      \n",
      "No. Observations: 15      Method:             REML   \n",
      "No. Groups:       5       Scale:              0.0289 \n",
      "Min. group size:  3       Log-Likelihood:     -8.2360\n",
      "Max. group size:  3       Converged:          Yes    \n",
      "Mean group size:  3.0                                \n",
      "------------------------------------------------------\n",
      "         Coef.  Std.Err.    z    P>|z|  [0.025  0.975]\n",
      "------------------------------------------------------\n",
      "X        0.728     0.322  2.265  0.024   0.098   1.358\n",
      "X Var    0.515     2.542                              \n",
      "=====================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "groups = jnp.arange(0,5).reshape(-1,1)@jnp.ones((1,3))\n",
    "\n",
    "df = pd.DataFrame({\n",
    "    'L':Lvals.flatten(),\n",
    "    \"group\":groups.flatten(),\n",
    "    'X':jnp.vstack([X]*5).flatten()\n",
    "})\n",
    "\n",
    "md = smf.mixedlm(\"L ~ 0 + X\", df, groups=df['group'],re_formula = '~ 0 + X')\n",
    "\n",
    "mdf = md.fit()\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5148296729430427"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "id_covmats = [0.0289*jnp.eye(3)]*5\n",
    "estimate_gamma_reml(Lvals,id_covmats,X,Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimate_gamma_reml(Lvals,covmats,X,Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[0;31mSignature:\u001b[0m\n",
      "\u001b[0mmd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mstart_params\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mreml\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mniter_sa\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mdo_cg\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mfe_pen\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mcov_pen\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mfree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mfull_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m    \u001b[0;34m**\u001b[0m\u001b[0mfit_kwargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
      "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mDocstring:\u001b[0m\n",
      "Fit a linear mixed model to the data.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "start_params : array_like or MixedLMParams\n",
      "    Starting values for the profile log-likelihood.  If not a\n",
      "    `MixedLMParams` instance, this should be an array\n",
      "    containing the packed parameters for the profile\n",
      "    log-likelihood, including the fixed effects\n",
      "    parameters.\n",
      "reml : bool\n",
      "    If true, fit according to the REML likelihood, else\n",
      "    fit the standard likelihood using ML.\n",
      "niter_sa : int\n",
      "    Currently this argument is ignored and has no effect\n",
      "    on the results.\n",
      "cov_pen : CovariancePenalty object\n",
      "    A penalty for the random effects covariance matrix\n",
      "do_cg : bool, defaults to True\n",
      "    If False, the optimization is skipped and a results\n",
      "    object at the given (or default) starting values is\n",
      "    returned.\n",
      "fe_pen : Penalty object\n",
      "    A penalty on the fixed effects\n",
      "free : MixedLMParams object\n",
      "    If not `None`, this is a mask that allows parameters to be\n",
      "    held fixed at specified values.  A 1 indicates that the\n",
      "    corresponding parameter is estimated, a 0 indicates that\n",
      "    it is fixed at its starting value.  Setting the `cov_re`\n",
      "    component to the identity matrix fits a model with\n",
      "    independent random effects.  Note that some optimization\n",
      "    methods do not respect this constraint (bfgs and lbfgs both\n",
      "    work).\n",
      "full_output : bool\n",
      "    If true, attach iteration history to results\n",
      "method : str\n",
      "    Optimization method.  Can be a scipy.optimize method name,\n",
      "    or a list of such names to be tried in sequence.\n",
      "**fit_kwargs\n",
      "    Additional keyword arguments passed to fit.\n",
      "\n",
      "Returns\n",
      "-------\n",
      "A MixedLMResults instance.\n",
      "\u001b[0;31mFile:\u001b[0m      ~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/statsmodels/regression/mixed_linear_model.py\n",
      "\u001b[0;31mType:\u001b[0m      method"
     ]
    }
   ],
   "source": [
    "md.fit?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "g = 0.2\n",
    "\n",
    "def f1(g):\n",
    "    return jnp.sum(jnp.array([logdet(C+ g * Z@Z.T) for C in covmats]))\n",
    "def f2(g):\n",
    "    return jnp.sum(jnp.array([logdet(X.T@jnp.linalg.inv(C+ g * Z@Z.T)@X) for C in covmats]))\n",
    "\n",
    "def f1(g):\n",
    "    return logdet(jnp.eye(3)+g*Z@Z.T)\n",
    "def f2(g):\n",
    "    return logdet(Z.T@jnp.linalg.inv(jnp.eye(3)+g*Z@Z.T)@Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(1.75, dtype=float64, weak_type=True)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.grad(f1)(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(-0.93333333, dtype=float64, weak_type=True)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.grad(f2)(1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(2.07944154, dtype=float64)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logdet(jnp.eye(3) + 0.5 * Z@Z.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(2.07944154, dtype=float64)"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jnp.log(1+(jnp.linalg.norm(Z)**2)*0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9e7d46b010>]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = jnp.linspace(0.1,0.5,10)\n",
    "plt.plot(jax.vmap(f1)(grid)+jax.vmap(f2)(grid))\n",
    "#plt.plot(jax.vmap(f2)(grid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([-0.13756539, -4.73308824, -7.07188194, -8.23142831, -8.79886027,\n",
       "       -9.07476244, -9.20849597, -9.2732203 , -9.30452262, -9.31965583,\n",
       "       -9.32697078, -9.33050632, -9.33221508, -9.33304093, -9.33344006,\n",
       "       -9.33363296, -9.33372619, -9.33377124, -9.33379302, -9.33380354],      dtype=float64)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_reml_like(gamma_grid,covmats,Lvals,X,Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (706950802.py, line 10)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Cell \u001b[0;32mIn[10], line 10\u001b[0;36m\u001b[0m\n\u001b[0;31m    \"REML\":estimate_gamma_reml\u001b[0m\n\u001b[0m    ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "num_repeats = 3\n",
    "study_counts = [\n",
    "    3,5,7,10,20]#,30,40\n",
    "    #],50,60,70,80,90,100]\n",
    "\n",
    "\n",
    "estimators = {\n",
    "    \"MLE\":estimate_gamma,\n",
    "    \"JackMLE\":jackknife_correct_gamma_est,\n",
    "    \"REML\":estimate_gamma_reml\n",
    "}\n",
    "\n",
    "results_gamma = {\n",
    "    name+\"_diag\":{k:[] for k in study_counts} for name in estimators.keys()\n",
    "}|{\n",
    "    name+\"_corr\":{k:[] for k in study_counts} for name in estimators.keys()\n",
    "}\n",
    "\n",
    "results_beta = {\n",
    "    name+\"_diag\":{k:[] for k in study_counts} for name in estimators.keys()\n",
    "}|{\n",
    "    name+\"_corr\":{k:[] for k in study_counts} for name in estimators.keys()\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d7c068fb055140a792c1e2a9b05ba567",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5fbce046782e473ea0bcdded838c4513",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4410486f0fa140c2a099061c71386fca",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8d6533ffb2ea4ceca40e118933543d4c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "43f494888b1a4f10b680d62c0eec2d9a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "ValueError",
     "evalue": "setting an array element with a sequence.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;31mTypeError\u001b[0m: float() argument must be a string or a real number, not 'tuple'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[41], line 61\u001b[0m\n\u001b[1;32m     57\u001b[0m     sim_results_reml[num_studies] \u001b[38;5;241m=\u001b[39m reml_results\n\u001b[1;32m     58\u001b[0m     sim_results_reml_diag[num_studies] \u001b[38;5;241m=\u001b[39m sim_results_reml_diag\n\u001b[0;32m---> 61\u001b[0m sim_results_corr \u001b[38;5;241m=\u001b[39m \u001b[43mpd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mDataFrame\u001b[49m\u001b[43m(\u001b[49m\u001b[43msim_results_corr\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mastype\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mfloat\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     62\u001b[0m sim_results_diag \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mDataFrame(sim_results_diag)\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mfloat\u001b[39m)\n\u001b[1;32m     63\u001b[0m sim_results_jack_corr \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mDataFrame(sim_results_jack_corr)\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mfloat\u001b[39m)\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/generic.py:6643\u001b[0m, in \u001b[0;36mNDFrame.astype\u001b[0;34m(self, dtype, copy, errors)\u001b[0m\n\u001b[1;32m   6637\u001b[0m     results \u001b[38;5;241m=\u001b[39m [\n\u001b[1;32m   6638\u001b[0m         ser\u001b[38;5;241m.\u001b[39mastype(dtype, copy\u001b[38;5;241m=\u001b[39mcopy, errors\u001b[38;5;241m=\u001b[39merrors) \u001b[38;5;28;01mfor\u001b[39;00m _, ser \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mitems()\n\u001b[1;32m   6639\u001b[0m     ]\n\u001b[1;32m   6641\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m   6642\u001b[0m     \u001b[38;5;66;03m# else, only a single dtype is given\u001b[39;00m\n\u001b[0;32m-> 6643\u001b[0m     new_data \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_mgr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mastype\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43merrors\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43merrors\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   6644\u001b[0m     res \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_constructor_from_mgr(new_data, axes\u001b[38;5;241m=\u001b[39mnew_data\u001b[38;5;241m.\u001b[39maxes)\n\u001b[1;32m   6645\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m res\u001b[38;5;241m.\u001b[39m__finalize__(\u001b[38;5;28mself\u001b[39m, method\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mastype\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/internals/managers.py:430\u001b[0m, in \u001b[0;36mBaseBlockManager.astype\u001b[0;34m(self, dtype, copy, errors)\u001b[0m\n\u001b[1;32m    427\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m using_copy_on_write():\n\u001b[1;32m    428\u001b[0m     copy \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[0;32m--> 430\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mapply\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    431\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mastype\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m    432\u001b[0m \u001b[43m    \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    433\u001b[0m \u001b[43m    \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    434\u001b[0m \u001b[43m    \u001b[49m\u001b[43merrors\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43merrors\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    435\u001b[0m \u001b[43m    \u001b[49m\u001b[43musing_cow\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43musing_copy_on_write\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    436\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/internals/managers.py:363\u001b[0m, in \u001b[0;36mBaseBlockManager.apply\u001b[0;34m(self, f, align_keys, **kwargs)\u001b[0m\n\u001b[1;32m    361\u001b[0m         applied \u001b[38;5;241m=\u001b[39m b\u001b[38;5;241m.\u001b[39mapply(f, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    362\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 363\u001b[0m         applied \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mgetattr\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    364\u001b[0m     result_blocks \u001b[38;5;241m=\u001b[39m extend_blocks(applied, result_blocks)\n\u001b[1;32m    366\u001b[0m out \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtype\u001b[39m(\u001b[38;5;28mself\u001b[39m)\u001b[38;5;241m.\u001b[39mfrom_blocks(result_blocks, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxes)\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/internals/blocks.py:758\u001b[0m, in \u001b[0;36mBlock.astype\u001b[0;34m(self, dtype, copy, errors, using_cow, squeeze)\u001b[0m\n\u001b[1;32m    755\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCan not squeeze with more than one column.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    756\u001b[0m     values \u001b[38;5;241m=\u001b[39m values[\u001b[38;5;241m0\u001b[39m, :]  \u001b[38;5;66;03m# type: ignore[call-overload]\u001b[39;00m\n\u001b[0;32m--> 758\u001b[0m new_values \u001b[38;5;241m=\u001b[39m \u001b[43mastype_array_safe\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43merrors\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43merrors\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    760\u001b[0m new_values \u001b[38;5;241m=\u001b[39m maybe_coerce_values(new_values)\n\u001b[1;32m    762\u001b[0m refs \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/dtypes/astype.py:237\u001b[0m, in \u001b[0;36mastype_array_safe\u001b[0;34m(values, dtype, copy, errors)\u001b[0m\n\u001b[1;32m    234\u001b[0m     dtype \u001b[38;5;241m=\u001b[39m dtype\u001b[38;5;241m.\u001b[39mnumpy_dtype\n\u001b[1;32m    236\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 237\u001b[0m     new_values \u001b[38;5;241m=\u001b[39m \u001b[43mastype_array\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    238\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m (\u001b[38;5;167;01mValueError\u001b[39;00m, \u001b[38;5;167;01mTypeError\u001b[39;00m):\n\u001b[1;32m    239\u001b[0m     \u001b[38;5;66;03m# e.g. _astype_nansafe can fail on object-dtype of strings\u001b[39;00m\n\u001b[1;32m    240\u001b[0m     \u001b[38;5;66;03m#  trying to convert to float\u001b[39;00m\n\u001b[1;32m    241\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m errors \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mignore\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/dtypes/astype.py:182\u001b[0m, in \u001b[0;36mastype_array\u001b[0;34m(values, dtype, copy)\u001b[0m\n\u001b[1;32m    179\u001b[0m     values \u001b[38;5;241m=\u001b[39m values\u001b[38;5;241m.\u001b[39mastype(dtype, copy\u001b[38;5;241m=\u001b[39mcopy)\n\u001b[1;32m    181\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 182\u001b[0m     values \u001b[38;5;241m=\u001b[39m \u001b[43m_astype_nansafe\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    184\u001b[0m \u001b[38;5;66;03m# in pandas we don't store numpy str dtypes, so convert to object\u001b[39;00m\n\u001b[1;32m    185\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(dtype, np\u001b[38;5;241m.\u001b[39mdtype) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28missubclass\u001b[39m(values\u001b[38;5;241m.\u001b[39mdtype\u001b[38;5;241m.\u001b[39mtype, \u001b[38;5;28mstr\u001b[39m):\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/dtypes/astype.py:133\u001b[0m, in \u001b[0;36m_astype_nansafe\u001b[0;34m(arr, dtype, copy, skipna)\u001b[0m\n\u001b[1;32m    129\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(msg)\n\u001b[1;32m    131\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m copy \u001b[38;5;129;01mor\u001b[39;00m arr\u001b[38;5;241m.\u001b[39mdtype \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mobject\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m dtype \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mobject\u001b[39m:\n\u001b[1;32m    132\u001b[0m     \u001b[38;5;66;03m# Explicit copy, or required since NumPy can't view from / to object.\u001b[39;00m\n\u001b[0;32m--> 133\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43marr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mastype\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m    135\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m arr\u001b[38;5;241m.\u001b[39mastype(dtype, copy\u001b[38;5;241m=\u001b[39mcopy)\n",
      "\u001b[0;31mValueError\u001b[0m: setting an array element with a sequence."
     ]
    }
   ],
   "source": [
    "num_repeats = 3\n",
    "study_counts = [\n",
    "    3,5,7,10,20]#,30,40\n",
    "\n",
    "beta_true = 0.25\n",
    "gamma_true = 0.1\n",
    "\n",
    "study_keys = jax.random.split(pkey(10384),len(study_counts))\n",
    "sim_results_corr = dict()\n",
    "sim_results_diag = dict()\n",
    "sim_results_jack_corr = dict()\n",
    "sim_results_jack_diag = dict()\n",
    "sim_results_reml = dict()\n",
    "sim_results_reml_diag = dict()\n",
    "\n",
    "for num_studies,key in zip(study_counts,study_keys):\n",
    "    print(num_studies)\n",
    "    corr_results = []\n",
    "    diag_results = []\n",
    "    reml_results = []\n",
    "    jack_corr_results = []\n",
    "    jack_diag_results = []\n",
    "    reml_results_diag = []\n",
    "    keys = jax.random.split(key,num_repeats)\n",
    "    for i in tqdm(range(num_repeats)):\n",
    "        Lvals,covmats,X,Z = simulate_meta_analysis(\n",
    "            keys[i],\n",
    "            num_studies=num_studies,\n",
    "            beta_true = beta_true,\n",
    "            gamma_true=gamma_true,\n",
    "            num_subjects_per_group=200,\n",
    "            num_groups = 4,\n",
    "            num_covs = 1,\n",
    "            intercept_val=-1,\n",
    "            )\n",
    "        diag_cov_mats = jnp.array([jnp.diag(jnp.diag(C)) for C in covmats])\n",
    "\n",
    "        gamma_corr = estimate_gamma(Lvals,covmats,X,Z)\n",
    "        gamma_reml = estimate_gamma_reml(Lvals,covmats,X,Z)\n",
    "        gamma_reml_diag = estimate_gamma_reml(Lvals,diag_cov_mats,X,Z)\n",
    "        gamma_diag = estimate_gamma(Lvals,diag_cov_mats,X,Z)\n",
    "\n",
    "        jack_gamma_corr = jackknife_correct_gamma_est(Lvals,covmats,X,Z)\n",
    "        jack_gamma_diag = jackknife_correct_gamma_est(Lvals,diag_cov_mats,X,Z)\n",
    "\n",
    "        corr_results.append(gamma_corr)\n",
    "        diag_results.append(gamma_diag)\n",
    "        jack_corr_results.append(jack_gamma_corr)\n",
    "        jack_diag_results.append(jack_gamma_diag)\n",
    "        reml_results.append(gamma_reml)\n",
    "        reml_results_diag.append(gamma_reml_diag)\n",
    "\n",
    "    sim_results_corr[num_studies] = corr_results\n",
    "    sim_results_diag[num_studies] = diag_results\n",
    "    sim_results_jack_corr[num_studies] = jack_corr_results\n",
    "    sim_results_jack_diag[num_studies] = jack_diag_results\n",
    "    sim_results_reml[num_studies] = reml_results\n",
    "    sim_results_reml_diag[num_studies] = sim_results_reml_diag\n",
    "\n",
    "\n",
    "sim_results_corr = pd.DataFrame(sim_results_corr).astype(float)\n",
    "sim_results_diag = pd.DataFrame(sim_results_diag).astype(float)\n",
    "sim_results_jack_corr = pd.DataFrame(sim_results_jack_corr).astype(float)\n",
    "sim_results_jack_diag = pd.DataFrame(sim_results_jack_diag).astype(float)\n",
    "# sim_results_reml_diag = pd.DataFrame(sim_results_reml_diag).astype(float)\n",
    "# sim_results_reml = pd.DataFrame(sim_results_reml).astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_results_corr = pd.DataFrame(sim_results_corr)\n",
    "sim_results_diag = pd.DataFrame(sim_results_diag)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(0.030782361151644955, 0.4213830541611346)</td>\n",
       "      <td>(0.0525278356908579, 0.18294101229829815)</td>\n",
       "      <td>(0.09055299453428298, 0.14720267371571052)</td>\n",
       "      <td>(0.02997836229445469, 0.2664268578138167)</td>\n",
       "      <td>(0.10313497280129696, 0.15876444776235774)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(9.999999999999999e-05, 0.004938338920295289)</td>\n",
       "      <td>(0.028116702913816547, 0.6226152057315072)</td>\n",
       "      <td>(0.16801990934281927, 0.28382244432770787)</td>\n",
       "      <td>(0.033079369868172004, 0.32522736355553294)</td>\n",
       "      <td>(0.09885562316216824, 0.18918810722208237)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(0.0008858667904100831, 0.2853630842885546)</td>\n",
       "      <td>(0.020594674856393727, 0.2911083214945525)</td>\n",
       "      <td>(0.12002121051268085, 0.3300382893739422)</td>\n",
       "      <td>(0.059852873253871314, 0.42095004636937616)</td>\n",
       "      <td>(0.04385999887171212, 0.4090175757603159)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                              3   \\\n",
       "0     (0.030782361151644955, 0.4213830541611346)   \n",
       "1  (9.999999999999999e-05, 0.004938338920295289)   \n",
       "2    (0.0008858667904100831, 0.2853630842885546)   \n",
       "\n",
       "                                           5   \\\n",
       "0   (0.0525278356908579, 0.18294101229829815)   \n",
       "1  (0.028116702913816547, 0.6226152057315072)   \n",
       "2  (0.020594674856393727, 0.2911083214945525)   \n",
       "\n",
       "                                           7   \\\n",
       "0  (0.09055299453428298, 0.14720267371571052)   \n",
       "1  (0.16801990934281927, 0.28382244432770787)   \n",
       "2   (0.12002121051268085, 0.3300382893739422)   \n",
       "\n",
       "                                            10  \\\n",
       "0    (0.02997836229445469, 0.2664268578138167)   \n",
       "1  (0.033079369868172004, 0.32522736355553294)   \n",
       "2  (0.059852873253871314, 0.42095004636937616)   \n",
       "\n",
       "                                           20  \n",
       "0  (0.10313497280129696, 0.15876444776235774)  \n",
       "1  (0.09885562316216824, 0.18918810722208237)  \n",
       "2   (0.04385999887171212, 0.4090175757603159)  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_results_diag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f55b474c82d249c29f2af5a35f7833bf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7cc52e28102d4342822d60676d32b507",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "80a18efc2671422e9271d7ac51245689",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d19d300ae6974de483be40e9707682e2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "53bcf3928e074d04b3e4c0912d44c5d0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "TypeError",
     "evalue": "float() argument must be a string or a real number, not 'dict'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[10], line 66\u001b[0m\n\u001b[1;32m     64\u001b[0m sim_results_jack_corr \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mDataFrame(sim_results_jack_corr)\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mfloat\u001b[39m)\n\u001b[1;32m     65\u001b[0m sim_results_jack_diag \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mDataFrame(sim_results_jack_diag)\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mfloat\u001b[39m)\n\u001b[0;32m---> 66\u001b[0m sim_results_reml_diag \u001b[38;5;241m=\u001b[39m \u001b[43mpd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mDataFrame\u001b[49m\u001b[43m(\u001b[49m\u001b[43msim_results_reml_diag\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mastype\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mfloat\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     67\u001b[0m sim_results_reml \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mDataFrame(sim_results_reml)\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mfloat\u001b[39m)\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/generic.py:6643\u001b[0m, in \u001b[0;36mNDFrame.astype\u001b[0;34m(self, dtype, copy, errors)\u001b[0m\n\u001b[1;32m   6637\u001b[0m     results \u001b[38;5;241m=\u001b[39m [\n\u001b[1;32m   6638\u001b[0m         ser\u001b[38;5;241m.\u001b[39mastype(dtype, copy\u001b[38;5;241m=\u001b[39mcopy, errors\u001b[38;5;241m=\u001b[39merrors) \u001b[38;5;28;01mfor\u001b[39;00m _, ser \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mitems()\n\u001b[1;32m   6639\u001b[0m     ]\n\u001b[1;32m   6641\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m   6642\u001b[0m     \u001b[38;5;66;03m# else, only a single dtype is given\u001b[39;00m\n\u001b[0;32m-> 6643\u001b[0m     new_data \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_mgr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mastype\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43merrors\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43merrors\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   6644\u001b[0m     res \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_constructor_from_mgr(new_data, axes\u001b[38;5;241m=\u001b[39mnew_data\u001b[38;5;241m.\u001b[39maxes)\n\u001b[1;32m   6645\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m res\u001b[38;5;241m.\u001b[39m__finalize__(\u001b[38;5;28mself\u001b[39m, method\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mastype\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/internals/managers.py:430\u001b[0m, in \u001b[0;36mBaseBlockManager.astype\u001b[0;34m(self, dtype, copy, errors)\u001b[0m\n\u001b[1;32m    427\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m using_copy_on_write():\n\u001b[1;32m    428\u001b[0m     copy \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[0;32m--> 430\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mapply\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    431\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mastype\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m    432\u001b[0m \u001b[43m    \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    433\u001b[0m \u001b[43m    \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    434\u001b[0m \u001b[43m    \u001b[49m\u001b[43merrors\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43merrors\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    435\u001b[0m \u001b[43m    \u001b[49m\u001b[43musing_cow\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43musing_copy_on_write\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    436\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/internals/managers.py:363\u001b[0m, in \u001b[0;36mBaseBlockManager.apply\u001b[0;34m(self, f, align_keys, **kwargs)\u001b[0m\n\u001b[1;32m    361\u001b[0m         applied \u001b[38;5;241m=\u001b[39m b\u001b[38;5;241m.\u001b[39mapply(f, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    362\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 363\u001b[0m         applied \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mgetattr\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    364\u001b[0m     result_blocks \u001b[38;5;241m=\u001b[39m extend_blocks(applied, result_blocks)\n\u001b[1;32m    366\u001b[0m out \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtype\u001b[39m(\u001b[38;5;28mself\u001b[39m)\u001b[38;5;241m.\u001b[39mfrom_blocks(result_blocks, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxes)\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/internals/blocks.py:758\u001b[0m, in \u001b[0;36mBlock.astype\u001b[0;34m(self, dtype, copy, errors, using_cow, squeeze)\u001b[0m\n\u001b[1;32m    755\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCan not squeeze with more than one column.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    756\u001b[0m     values \u001b[38;5;241m=\u001b[39m values[\u001b[38;5;241m0\u001b[39m, :]  \u001b[38;5;66;03m# type: ignore[call-overload]\u001b[39;00m\n\u001b[0;32m--> 758\u001b[0m new_values \u001b[38;5;241m=\u001b[39m \u001b[43mastype_array_safe\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43merrors\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43merrors\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    760\u001b[0m new_values \u001b[38;5;241m=\u001b[39m maybe_coerce_values(new_values)\n\u001b[1;32m    762\u001b[0m refs \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/dtypes/astype.py:237\u001b[0m, in \u001b[0;36mastype_array_safe\u001b[0;34m(values, dtype, copy, errors)\u001b[0m\n\u001b[1;32m    234\u001b[0m     dtype \u001b[38;5;241m=\u001b[39m dtype\u001b[38;5;241m.\u001b[39mnumpy_dtype\n\u001b[1;32m    236\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 237\u001b[0m     new_values \u001b[38;5;241m=\u001b[39m \u001b[43mastype_array\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    238\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m (\u001b[38;5;167;01mValueError\u001b[39;00m, \u001b[38;5;167;01mTypeError\u001b[39;00m):\n\u001b[1;32m    239\u001b[0m     \u001b[38;5;66;03m# e.g. _astype_nansafe can fail on object-dtype of strings\u001b[39;00m\n\u001b[1;32m    240\u001b[0m     \u001b[38;5;66;03m#  trying to convert to float\u001b[39;00m\n\u001b[1;32m    241\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m errors \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mignore\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/dtypes/astype.py:182\u001b[0m, in \u001b[0;36mastype_array\u001b[0;34m(values, dtype, copy)\u001b[0m\n\u001b[1;32m    179\u001b[0m     values \u001b[38;5;241m=\u001b[39m values\u001b[38;5;241m.\u001b[39mastype(dtype, copy\u001b[38;5;241m=\u001b[39mcopy)\n\u001b[1;32m    181\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 182\u001b[0m     values \u001b[38;5;241m=\u001b[39m \u001b[43m_astype_nansafe\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    184\u001b[0m \u001b[38;5;66;03m# in pandas we don't store numpy str dtypes, so convert to object\u001b[39;00m\n\u001b[1;32m    185\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(dtype, np\u001b[38;5;241m.\u001b[39mdtype) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28missubclass\u001b[39m(values\u001b[38;5;241m.\u001b[39mdtype\u001b[38;5;241m.\u001b[39mtype, \u001b[38;5;28mstr\u001b[39m):\n",
      "File \u001b[0;32m~/miniconda3/envs/onemod_gpu/lib/python3.11/site-packages/pandas/core/dtypes/astype.py:133\u001b[0m, in \u001b[0;36m_astype_nansafe\u001b[0;34m(arr, dtype, copy, skipna)\u001b[0m\n\u001b[1;32m    129\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(msg)\n\u001b[1;32m    131\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m copy \u001b[38;5;129;01mor\u001b[39;00m arr\u001b[38;5;241m.\u001b[39mdtype \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mobject\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m dtype \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mobject\u001b[39m:\n\u001b[1;32m    132\u001b[0m     \u001b[38;5;66;03m# Explicit copy, or required since NumPy can't view from / to object.\u001b[39;00m\n\u001b[0;32m--> 133\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43marr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mastype\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcopy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m    135\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m arr\u001b[38;5;241m.\u001b[39mastype(dtype, copy\u001b[38;5;241m=\u001b[39mcopy)\n",
      "\u001b[0;31mTypeError\u001b[0m: float() argument must be a string or a real number, not 'dict'"
     ]
    }
   ],
   "source": [
    "num_repeats = 50\n",
    "study_counts = [\n",
    "    3,5,7,10,20]#,30,40\n",
    "    #],50,60,70,80,90,100]\n",
    "\n",
    "beta_true = 0.25\n",
    "gamma_true = 0.1\n",
    "\n",
    "study_keys = jax.random.split(pkey(10384),len(study_counts))\n",
    "sim_results_corr = dict()\n",
    "sim_results_diag = dict()\n",
    "sim_results_jack_corr = dict()\n",
    "sim_results_jack_diag = dict()\n",
    "# sim_results_reml = dict()\n",
    "# sim_results_reml_diag = dict()\n",
    "\n",
    "for num_studies,key in zip(study_counts,study_keys):\n",
    "    print(num_studies)\n",
    "    corr_results = []\n",
    "    diag_results = []\n",
    "    reml_results = []\n",
    "    jack_corr_results = []\n",
    "    jack_diag_results = []\n",
    "    # reml_results_diag = []\n",
    "    keys = jax.random.split(key,num_repeats)\n",
    "    for i in tqdm(range(num_repeats)):\n",
    "        Lvals,covmats,X,Z = simulate_meta_analysis(\n",
    "            keys[i],\n",
    "            num_studies=num_studies,\n",
    "            beta_true = beta_true,\n",
    "            gamma_true=gamma_true,\n",
    "            num_subjects_per_group=200,\n",
    "            num_groups = 4,\n",
    "            num_covs = 1,\n",
    "            intercept_val=-1,\n",
    "            )\n",
    "        diag_cov_mats = jnp.array([jnp.diag(jnp.diag(C)) for C in covmats])\n",
    "\n",
    "        gamma_corr = estimate_gamma(Lvals,covmats,X,Z)\n",
    "        gamma_reml = estimate_gamma_reml(Lvals,covmats,X,Z)\n",
    "        gamma_reml_diag = estimate_gamma_reml(Lvals,diag_cov_mats,X,Z)\n",
    "        gamma_diag = estimate_gamma(Lvals,diag_cov_mats,X,Z)\n",
    "\n",
    "        jack_gamma_corr = jackknife_correct_gamma_est(Lvals,covmats,X,Z)\n",
    "        jack_gamma_diag = jackknife_correct_gamma_est(Lvals,diag_cov_mats,X,Z)\n",
    "\n",
    "        corr_results.append(gamma_corr)\n",
    "        diag_results.append(gamma_diag)\n",
    "        jack_corr_results.append(jack_gamma_corr)\n",
    "        jack_diag_results.append(jack_gamma_diag)\n",
    "        #reml_results.append(gamma_reml)\n",
    "        #reml_results_diag.append(gamma_reml_diag)\n",
    "\n",
    "    sim_results_corr[num_studies] = corr_results\n",
    "    sim_results_diag[num_studies] = diag_results\n",
    "    sim_results_jack_corr[num_studies] = jack_corr_results\n",
    "    sim_results_jack_diag[num_studies] = jack_diag_results\n",
    "    # sim_results_reml[num_studies] = reml_results\n",
    "    # sim_results_reml_diag[num_studies] = reml_results_diag\n",
    "\n",
    "\n",
    "sim_results_corr = pd.DataFrame(sim_results_corr).astype(float)\n",
    "sim_results_diag = pd.DataFrame(sim_results_diag).astype(float)\n",
    "sim_results_jack_corr = pd.DataFrame(sim_results_jack_corr).astype(float)\n",
    "sim_results_jack_diag = pd.DataFrame(sim_results_jack_diag).astype(float)\n",
    "# sim_results_reml_diag = pd.DataFrame(sim_results_reml_diag).astype(float)\n",
    "# sim_results_reml = pd.DataFrame(sim_results_reml).astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_results_corr.to_csv(\"sim_results_corr.csv\")\n",
    "sim_results_diag.to_csv(\"sim_results_diag.csv\")\n",
    "sim_results_jack_corr.to_csv(\"sim_results_jack_corr.csv\")\n",
    "sim_results_jack_diag.to_csv(\"sim_results_jack_diag.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Gamma Estimate')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,6))\n",
    "plt.plot(sim_results_corr.mean(),label = 'corr',c='blue')\n",
    "plt.plot(sim_results_diag.mean(),label = 'diag',c='red')\n",
    "\n",
    "plt.plot(sim_results_jack_corr.mean(),label = 'jack_corr',c='blue',ls = '--')\n",
    "plt.plot(sim_results_jack_diag.mean(),label = 'jack_diag',c='red',ls = '--')\n",
    "\n",
    "\n",
    "plt.fill_between(\n",
    "    study_counts,\n",
    "    sim_results_corr.mean()+sim_results_corr.sem(),\n",
    "    sim_results_corr.mean()-sim_results_corr.sem(),\n",
    "    color = 'blue',alpha=0.2,\n",
    "    label = '$\\\\pm$ 1 standard error'\n",
    "    )\n",
    "\n",
    "plt.legend()\n",
    "plt.plot([study_counts[0],study_counts[-1]],[gamma_true,gamma_true],c='black',lw = 3,label = 'Truth')\n",
    "plt.title(\"Mean over 500 simulations of gamma estimate \\n Standard error represents uncertainty from finite simulation runs\")\n",
    "plt.xlabel(\"Num Studies\")\n",
    "plt.ylabel(\"Gamma Estimate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Gamma Estimate')"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,6))\n",
    "plt.plot(sim_results_corr.mean(),label = 'corr',c='blue')\n",
    "plt.plot(sim_results_diag.mean(),label = 'diag',c='red')\n",
    "\n",
    "plt.plot(sim_results_jack_corr.mean(),label = 'jack_corr',c='blue',ls = '--')\n",
    "plt.plot(sim_results_jack_diag.mean(),label = 'jack_diag',c='red',ls = '--')\n",
    "\n",
    "\n",
    "plt.fill_between(\n",
    "    study_counts,\n",
    "    sim_results_jack_corr.mean()+sim_results_jack_corr.sem(),\n",
    "    sim_results_jack_corr.mean()-sim_results_jack_corr.sem(),\n",
    "    color = 'blue',alpha=0.2,\n",
    "    label = '$\\\\pm$ 1 standard error'\n",
    "    )\n",
    "\n",
    "plt.legend()\n",
    "plt.plot([study_counts[0],study_counts[-1]],[gamma_true,gamma_true],c='black',lw = 3,label = 'Truth')\n",
    "plt.title(\"Mean over 500 simulations of gamma estimate \\n Standard error represents uncertainty from finite simulation runs\")\n",
    "plt.xlabel(\"Num Studies\")\n",
    "plt.ylabel(\"Gamma Estimate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimates of bias')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(0.1 - sim_results_corr.mean(),label = \"Bias estimate\")\n",
    "plt.plot(jnp.linspace(3,40),0.13 * 1/jnp.linspace(3,40),label = '0.12 * 1/n')\n",
    "plt.legend()\n",
    "plt.xlabel(\"Num studies\")\n",
    "plt.title(\"Estimates of bias\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Bias')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(1/jnp.array(study_counts),0.1 - sim_results_corr.mean(),label = \"Bias estimate\")\n",
    "plt.xlabel(\"1/n\")\n",
    "plt.ylabel(\"Bias\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "sindy",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}