waic comparisons

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   "source": [
    "The example below shows why WAIC could be useful when studies are underpowered. Here we simulate data with a weak polynomial relationship between x an y, with only a small sample. Although the effect of the polynomial term does not reach conventional standards for statistical significance, comparing WAIC (an estimate of how effective each model will be at predicting new, out-of-sample data) indicates we should assign a higher probability that `m2` is 'correct', when compared with `m1` (more than twice as likely)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "set.seed(123)\n",
    "multix <- data_frame(\n",
    "  x=rnorm(50),\n",
    "  y = rnorm(50) + x + .15*x^2\n",
    ")\n",
    "\n",
    "ggplot(multix, aes(y=y,x=x))+geom_point()+geom_smooth()\n",
    "\n",
    "mx.1 <- lm(y~x, data=multix)\n",
    "mx.2 <- lm(y~x+I(x^2), data=multix)\n",
    "\n",
    "anova(mx.2)\n",
    "compare(mx.1, mx.2)\n",
    "\n",
    "plot(compare(mx.1, mx.2))"
   ]
  }
 ],
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