Factorial Design-without duplicate runs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "040856e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from itertools import product,combinations\n",
    "import matplotlib.pyplot as plt\n",
    "from math import log\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "160554a9",
   "metadata": {},
   "source": [
    "### major functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7046422",
   "metadata": {},
   "outputs": [],
   "source": [
    "def design_matrix(n):\n",
    "    D=[]\n",
    "    for i in product([-1,+1],repeat=n):\n",
    "        D.append(list(i))\n",
    "    return D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fc56033f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def effect_matrix(d):\n",
    "    dm=np.flip(d,1)\n",
    "    (r,c)=np.shape(dm)\n",
    "    x=''\n",
    "    for i in range(c):\n",
    "        x+=str(i)\n",
    "    labels=[]\n",
    "    for i in range(c-1):\n",
    "        for j in combinations(x,i+2):\n",
    "            labels.append(list(map(int,j)))\n",
    "    for i in range(len(labels)):\n",
    "        I=np.full(r,1)\n",
    "        for j in labels[i]:\n",
    "            I=I*dm[:,j]\n",
    "        dm=np.insert(dm,np.shape(dm)[1],I,1)\n",
    "    return (dm,labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c629b440",
   "metadata": {},
   "outputs": [],
   "source": [
    "def effects(e,R):\n",
    "    avg=np.mean(R,axis=0)\n",
    "    e=e.astype('float64')\n",
    "    for i in range(len(e)):\n",
    "        for j in range(len(e[i])):\n",
    "            e[i][j]=e[i][j]*avg[i]\n",
    "    return e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0fa06414",
   "metadata": {},
   "outputs": [],
   "source": [
    "def eff_det(E,labels,R):\n",
    "    AVG=np.mean(R)\n",
    "    e=[(\"AVG\",AVG)]\n",
    "    labels2=[]\n",
    "    for i in labels[-1]:\n",
    "        labels2.append([i])\n",
    "    labels2.extend(labels)\n",
    "    (r,c)=np.shape(E)\n",
    "    for i in range(c):\n",
    "        e.append((l2str(labels2[i]),np.sum(E[:,i])/(2**(len(labels[-1])-1))))\n",
    "    if len(R)==2:\n",
    "        N=2*len(R[0])\n",
    "        s2=np.sum((R[0]-R[1])**2)/(2*len(R[0]))\n",
    "        V_eff=(4/N)*s2\n",
    "        sd_eff=np.sqrt(V_eff)\n",
    "        V_ave=(s2/N)\n",
    "        sd_ave=np.sqrt(V_ave)\n",
    "        return (e,sd_eff,sd_ave)\n",
    "    else:\n",
    "        return(e)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "62ab3d08",
   "metadata": {},
   "outputs": [],
   "source": [
    "def significants(eff_ints,sd_ave,sd_eff,DOF,a):\n",
    "    t_crit=scipy.stats.t.ppf(q=1-a,df=DOF)\n",
    "    sig=[]\n",
    "    if eff_ints[0][1]/sd_ave>=t_crit:\n",
    "        sig.append(eff_ints[0])\n",
    "    for i in range(1,len(eff_ints)):\n",
    "        if eff_ints[i][1]/sd_eff>=t_crit:\n",
    "            sig.append(eff_ints[i])\n",
    "    return sig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cb84680e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def seq_eval(sig,seq=''): #,extremes):\n",
    "    if seq:\n",
    "        val=sig[0][1]\n",
    "        for i in range(len(seq)):\n",
    "            if seq[i]==\"+\":\n",
    "                val+=(sig[i+1][1]/2)*1 #extremes[i][1]\n",
    "            elif seq[i]==\"-\":\n",
    "                val+=(sig[i+1][1]/2)*(-1) #extremes[i][0]\n",
    "    return val            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0f0d253b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_eval(sig,seq_list): #,extremes):\n",
    "    L=[]\n",
    "    for seq in seq_list:\n",
    "        L.append((seq,seq_eval(sig,seq)))\n",
    "    return L  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1ab8bec4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#all main effects considered\n",
    "def model(dm,eff_ints,order=1): #,extremes):\n",
    "    n=log(len(dm),2)\n",
    "    est=[]\n",
    "    for i in range(len(dm)):\n",
    "        val=eff_ints[0][1]\n",
    "        for j in range(len(dm[i])):\n",
    "            val+=((eff_ints[j+1][1])/2)*dm[i][j] #extremes[j][1/0]\n",
    "        est.append(val)\n",
    "    return (est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a72f1b31",
   "metadata": {},
   "outputs": [],
   "source": [
    "def resi(A,R):\n",
    "    avg=np.mean(R,axis=0)\n",
    "    res=[]\n",
    "    for i in range(len(avg)):\n",
    "        res.append(avg[i]-A[i])\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "44b26dc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob_plot(A,label,title=''):\n",
    "    m=len(A)\n",
    "    Pi=[(100/m)*(i-0.5) for i in range(1,m+1)]\n",
    "    A.sort()\n",
    "    plt.scatter(A,Pi)\n",
    "    plt.axvline(x=0, c=\"black\")\n",
    "    plt.axhline(y=0, c=\"black\")\n",
    "    plt.ylabel(\"Probability\")\n",
    "    plt.xlabel(label)\n",
    "    plt.title(label+\" Vs \"+ \"Probability\"+title)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dba6faf",
   "metadata": {},
   "source": [
    "### minor functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "16850c50",
   "metadata": {},
   "outputs": [],
   "source": [
    "def l2str(A):\n",
    "    x=''\n",
    "    for i in A:\n",
    "        x+=str(i)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6eae0711",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dm2strL(dm):\n",
    "    L=[]\n",
    "    for i in range(len(dm)):\n",
    "        x=''\n",
    "        for j in range(len(dm[i])):\n",
    "            if dm[i][j]==1:\n",
    "                x+='+'\n",
    "            elif dm[i][j]==-1:\n",
    "                x+='-'\n",
    "        L.append(x)\n",
    "    return (L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3c86653",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f6e9a968",
   "metadata": {},
   "source": [
    "### Model formation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fe00adb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('AVG', 0.4975),\n",
       " ('0', 0.21749999999999997),\n",
       " ('1', 0.0975),\n",
       " ('2', -0.1725),\n",
       " ('3', 0.002500000000000009),\n",
       " ('01', -0.0049999999999999906),\n",
       " ('02', 0.010000000000000023),\n",
       " ('03', -0.010000000000000016),\n",
       " ('12', -0.07500000000000004),\n",
       " ('13', -0.009999999999999988),\n",
       " ('23', 0.004999999999999984),\n",
       " ('012', 0.002500000000000016),\n",
       " ('013', 0.0024999999999999814),\n",
       " ('023', -0.007499999999999986),\n",
       " ('123', 0.01750000000000001),\n",
       " ('0123', 0.010000000000000016)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R=np.array([[0.38,0.59,0.58,0.79,\n",
    "    0.27,0.53,0.30,0.53,\n",
    "    0.40,0.62,0.56,0.75,\n",
    "    0.30,0.50,0.32,0.54]])\n",
    "extremes=[(5,7),(40,45),(10,20),(150,180)]\n",
    "n=4\n",
    "A=design_matrix(n)\n",
    "A=np.array(A)\n",
    "E=effect_matrix(A)\n",
    "E1=effects(E[0],R)\n",
    "eff_ints=eff_det(E1,E[1],R)\n",
    "eff_ints"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d823570",
   "metadata": {},
   "source": [
    "### ignoring higher order terms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b94ba3ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s:  0.01949358868961794\n",
      "sd_avg:  0.004873397172404485\n"
     ]
    }
   ],
   "source": [
    "k=11  #order>3 terms insignificant\n",
    "sum=0\n",
    "for i in range(len(eff_ints[k:])):\n",
    "    sum+=(eff_ints[k:][i][1])**2\n",
    "s2effect=sum/len(eff_ints[k:])\n",
    "s2=((len(R[0]))/4)*s2effect\n",
    "s=np.sqrt(s2)\n",
    "sd_avg=np.sqrt(s2/len(R[0]))\n",
    "print(\"s: \",s)\n",
    "print(\"sd_avg: \",sd_avg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "50a1fe90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('AVG', 0.4975), ('0', 0.21749999999999997), ('1', 0.0975)]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=0.05\n",
    "DOF=len(eff_ints[k:])\n",
    "sig=significants(eff_ints,sd_avg,s,DOF,a)\n",
    "sig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5691527",
   "metadata": {},
   "source": [
    "### probability plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "82ea6cbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_plot([eff_ints[i][1] for i in range(1,len(eff_ints))],label=\"Effects\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1af9754a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24aedda1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "bd9cdbe7",
   "metadata": {},
   "source": [
    "### Residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3d142ed1",
   "metadata": {},
   "outputs": [],
   "source": [
    "B=design_matrix(len(sig)-1)\n",
    "seq_list=dm2strL(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "cf13cc9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('--', 0.34),\n",
       " ('-+', 0.43750000000000006),\n",
       " ('+-', 0.5575),\n",
       " ('++', 0.6549999999999999)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L=model_eval(sig,seq_list)\n",
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0c96dcb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nresiduals=resi(A,R) #fill manually\\nresiduals\\n\\n'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "residuals=resi(A,R) #fill manually\n",
    "residuals\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "073740e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\nprob_plot(residuals,'Residuals')\\n\\n\""
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "prob_plot(residuals,'Residuals')\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4d678f06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.044999999999999984,\n",
       " 0.16249999999999992,\n",
       " 0.32749999999999996,\n",
       " 0.5349999999999999,\n",
       " -0.25250000000000006,\n",
       " 0.0050000000000000044,\n",
       " -0.050000000000000044,\n",
       " 0.17749999999999994,\n",
       " -0.24250000000000005,\n",
       " -0.025000000000000022,\n",
       " 0.09000000000000008,\n",
       " 0.27749999999999997,\n",
       " -0.44,\n",
       " -0.24249999999999994,\n",
       " -0.2474999999999999,\n",
       " -0.029999999999999805]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#all main effects considered\n",
    "M=model(A,eff_ints) #,extremes)\n",
    "residuals=resi(M,R)\n",
    "residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "284427a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_plot(residuals,'Residuals',title=\"(all main effects)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "085a657c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        [ 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1]]),\n",
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       "  [0, 2, 3],\n",
       "  [1, 2, 3],\n",
       "  [0, 1, 2, 3]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d1023395",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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