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6 changes: 3 additions & 3 deletions doc/source/notebooks/tour_of_pygam.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@
"Generalized Additive Models (GAMs) are smooth semi-parametric models of the form:\n",
"\n",
"$$\n",
" g(\\mathbb{E}[y|X]) = \\beta_0 + f_1(X_1) + f_2(X_2, X3) + \\ldots + f_M(X_N)\n",
" g(\\mathbb{E}[y|X]) = \\beta_0 + f_1(X_1) + f_2(X_2, X_3) + \\ldots + f_M(X_N)\n",
"$$\n",
"\n",
"where `X.T = [X_1, X_2, ..., X_N]` are independent variables, `y` is the dependent variable, and `g()` is the link function that relates our predictor variables to the expected value of the dependent variable.\n",
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"\n",
"where \n",
"$$\n",
"g(\\mu|X) = \\beta_0 + f_1(X_1) + f_2(X_2, X3) + \\ldots + f_M(X_N)\n",
"g(\\mu|X) = \\beta_0 + f_1(X_1) + f_2(X_2, X_3) + \\ldots + f_M(X_N)\n",
"$$\n",
"\n",
"So we can see that a GAM has 3 components:\n",
"\n",
"- ``distribution`` from the exponential family\n",
"- ``link function`` $g(\\cdot)$\n",
"- ``functional form`` with an additive structure $\\beta_0 + f_1(X_1) + f_2(X_2, X3) + \\ldots + f_M(X_N)$\n",
"- ``functional form`` with an additive structure $\\beta_0 + f_1(X_1) + f_2(X_2, X_3) + \\ldots + f_M(X_N)$\n",
"\n",
"### Distribution: \n",
"Specified via: ``GAM(distribution='...')``\n",
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