notebooks/multivariate-statistics/factor_analysis.ipynb

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    "### 1. **Orthogonal Factor Model**\n",
    "\n",
    "$$\n",
    "X = \\mu + \\Lambda F + \\epsilon\n",
    "$$\n",
    "\n",
    "where:\n",
    "- $X \\in \\mathbb{R}^{p}$ is the vector of observed variables.\n",
    "- $\\mu \\in \\mathbb{R}^{p}$ is the mean of the observed variables.\n",
    "- $\\Lambda \\in \\mathbb{R}^{p \\times k}$ is the loading matrix.\n",
    "- $F \\in \\mathbb{R}^{k}$ is the vector of latent factors.\n",
    "- $\\epsilon \\in \\mathbb{R}^{p}$ is the vector of errors.\n",
    "\n",
    "---\n",
    "\n",
    "### 2. **Assumptions on Latent Factors**\n",
    "\n",
    "- **Uncorrelated Factors**:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(F) = I_k\n",
    "$$\n",
    "\n",
    "- **Independence from Errors**:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(F, \\epsilon) = 0\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### 3. **Assumption on Error**\n",
    "\n",
    "- **No Correlation Among Errors**:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(\\epsilon) = \\Psi, \\quad \\Psi \\in \\mathbb{R}^{p \\times p}, \\quad \\text{diagonal}\n",
    "$$\n",
    "\n",
    "- **Independence from Latent Factors**:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(F, \\epsilon) = 0\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### 4. **Covariance Expressed in Terms of Latent Factors and Error**\n",
    "\n",
    "We start with:\n",
    "\n",
    "$$\n",
    "\\Sigma = \\text{Cov}(X) = E[(X - \\mu)(X - \\mu)']\n",
    "$$\n",
    "\n",
    "Substitute $X = \\mu + \\Lambda F + \\epsilon$:\n",
    "\n",
    "$$\n",
    "\\Sigma = E[(\\Lambda F + \\epsilon)(\\Lambda F + \\epsilon)']\n",
    "$$\n",
    "\n",
    "Expanding the product:\n",
    "\n",
    "$$\n",
    "\\Sigma = E[\\Lambda F F' \\Lambda' + \\Lambda F \\epsilon' + \\epsilon F' \\Lambda' + \\epsilon \\epsilon']\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Sigma = \\Lambda \\Lambda' + \\Psi\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### 5. **Why the Loading Matrix Need Not Be Unique**\n",
    "\n",
    "#### Proof:\n",
    "\n",
    "**Original Model**:\n",
    "\n",
    "$$\n",
    "X = \\mu + \\Lambda F + \\epsilon\n",
    "$$\n",
    "\n",
    "**Covariance of $X$**:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(X) = \\Sigma = \\Lambda \\Lambda^T + \\Psi\n",
    "$$\n",
    "\n",
    "**Orthogonal Rotation**: Let $Q \\in \\mathbb{R}^{k \\times k}$ be an orthogonal matrix, $Q^T Q = I_k$. Apply rotation:\n",
    "\n",
    "$$\n",
    "\\Lambda' = \\Lambda Q\n",
    "$$\n",
    "\n",
    "Substituting $\\Lambda' = \\Lambda Q$:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(X) = (\\Lambda Q)(Q^T \\Lambda^T) + \\Psi\n",
    "$$\n",
    "\n",
    "Since $Q^T Q = I_k$:\n",
    "\n",
    "$$\n",
    "\\text{Cov}(X) = \\Lambda \\Lambda^T + \\Psi\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### 6. **Rotation Schemes for Improving Interpretation**\n",
    "\n",
    "#### a) **Varimax Rotation**:\n",
    "Maximizes the variance of squared loadings for each factor:\n",
    "\n",
    "$$\n",
    "\\sum_{j=1}^k \\left( \\sum_{i=1}^p \\lambda_{ij}^2 \\right)^2 \\quad \\text{maximize over } Q\n",
    "$$\n",
    "\n",
    "#### b) **Quartimax Rotation**:\n",
    "Maximizes the variance of squared loadings for each observed variable:\n",
    "\n",
    "$$\n",
    "\\sum_{i=1}^p \\left( \\sum_{j=1}^k \\lambda_{ij}^2 \\right)^2 \\quad \\text{maximize over } Q\n",
    "$$\n",
    "\n",
    "#### c) **Equamax Rotation**:\n",
    "Balance between varimax and quartimax:\n",
    "\n",
    "$$\n",
    "\\sum_{i=1}^p \\left( \\sum_{j=1}^k \\lambda_{ij}^2 \\right)^2 + \\sum_{j=1}^k \\left( \\sum_{i=1}^p \\lambda_{ij}^2 \\right)^2 \\quad \\text{maximize over } Q\n",
    "$$"
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      "text/plain": [
       "<Figure size 1800x1800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_regression\n",
    "from statsmodels.multivariate.factor import Factor\n",
    "\n",
    "plt.style.use('dark_background')\n",
    "\n",
    "X, _ = make_regression(\n",
    "    n_samples=100, n_features=5, \n",
    "    noise=0.1, effective_rank=2, \n",
    "    random_state=47\n",
    ")\n",
    "\n",
    "fa = Factor(X, n_factor=2) \n",
    "fa_results = fa.fit()\n",
    "\n",
    "X_fa = np.dot(X, fa_results.loadings)\n",
    "\n",
    "# Plot the results to visualize\n",
    "plt.figure(figsize=(6, 6), dpi=300)\n",
    "plt.scatter(X_fa[:, 0], X_fa[:, 1], c='blue', edgecolors='k')\n",
    "plt.xlabel('Latent Factor 1')\n",
    "plt.ylabel('Latent Factor 2')\n",
    "plt.title('Factor Analysis - 2 Components')\n",
    "plt.savefig('factor_analysis.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93f8e648-b03c-40a6-88b9-7ffd1cbfa690",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "genai",
   "language": "python",
   "name": "genai"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}