unwanted-effects.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am curious about how to ignoring/removing unwanted effects by using Anova.\n",
    "I am going to make up the tech variable as unwanted effect which I would like to remove from the response variable. For example, tech1 is measured by technician 1 and tech2 is measure by technician 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>weight</th><th scope=col>group</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>4.17</td><td>ctrl</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>5.58</td><td>ctrl</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>5.18</td><td>ctrl</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>6.11</td><td>ctrl</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>4.50</td><td>ctrl</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>4.61</td><td>ctrl</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & weight & group\\\\\n",
       "  & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 4.17 & ctrl\\\\\n",
       "\t2 & 5.58 & ctrl\\\\\n",
       "\t3 & 5.18 & ctrl\\\\\n",
       "\t4 & 6.11 & ctrl\\\\\n",
       "\t5 & 4.50 & ctrl\\\\\n",
       "\t6 & 4.61 & ctrl\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | weight &lt;dbl&gt; | group &lt;fct&gt; |\n",
       "|---|---|---|\n",
       "| 1 | 4.17 | ctrl |\n",
       "| 2 | 5.58 | ctrl |\n",
       "| 3 | 5.18 | ctrl |\n",
       "| 4 | 6.11 | ctrl |\n",
       "| 5 | 4.50 | ctrl |\n",
       "| 6 | 4.61 | ctrl |\n",
       "\n"
      ],
      "text/plain": [
       "  weight group\n",
       "1 4.17   ctrl \n",
       "2 5.58   ctrl \n",
       "3 5.18   ctrl \n",
       "4 6.11   ctrl \n",
       "5 4.50   ctrl \n",
       "6 4.61   ctrl "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(PlantGrowth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>weight</th><th scope=col>group</th><th scope=col>tech</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>4.17</td><td>ctrl</td><td>tech1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>5.58</td><td>ctrl</td><td>tech2</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>5.18</td><td>ctrl</td><td>tech1</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>6.11</td><td>ctrl</td><td>tech2</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>4.50</td><td>ctrl</td><td>tech1</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>4.61</td><td>ctrl</td><td>tech2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & weight & group & tech\\\\\n",
       "  & <dbl> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 4.17 & ctrl & tech1\\\\\n",
       "\t2 & 5.58 & ctrl & tech2\\\\\n",
       "\t3 & 5.18 & ctrl & tech1\\\\\n",
       "\t4 & 6.11 & ctrl & tech2\\\\\n",
       "\t5 & 4.50 & ctrl & tech1\\\\\n",
       "\t6 & 4.61 & ctrl & tech2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 3\n",
       "\n",
       "| <!--/--> | weight &lt;dbl&gt; | group &lt;fct&gt; | tech &lt;fct&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 | 4.17 | ctrl | tech1 |\n",
       "| 2 | 5.58 | ctrl | tech2 |\n",
       "| 3 | 5.18 | ctrl | tech1 |\n",
       "| 4 | 6.11 | ctrl | tech2 |\n",
       "| 5 | 4.50 | ctrl | tech1 |\n",
       "| 6 | 4.61 | ctrl | tech2 |\n",
       "\n"
      ],
      "text/plain": [
       "  weight group tech \n",
       "1 4.17   ctrl  tech1\n",
       "2 5.58   ctrl  tech2\n",
       "3 5.18   ctrl  tech1\n",
       "4 6.11   ctrl  tech2\n",
       "5 4.50   ctrl  tech1\n",
       "6 4.61   ctrl  tech2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tech <- rep(c('tech1', 'tech2'),nrow(PlantGrowth)/2)\n",
    "PlantGrowth$tech <- as.factor(tech)\n",
    "head(PlantGrowth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t30 obs. of  3 variables:\n",
      " $ weight: num  4.17 5.58 5.18 6.11 4.5 4.61 5.17 4.53 5.33 5.14 ...\n",
      " $ group : Factor w/ 3 levels \"ctrl\",\"trt1\",..: 1 1 1 1 1 1 1 1 1 1 ...\n",
      " $ tech  : Factor w/ 2 levels \"tech1\",\"tech2\": 1 2 1 2 1 2 1 2 1 2 ...\n"
     ]
    }
   ],
   "source": [
    "str(PlantGrowth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = weight ~ group + tech, data = PlantGrowth)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.9710 -0.3765 -0.0330  0.2100  1.2600 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   5.1410     0.2280  22.550   <2e-16 ***\n",
       "grouptrt1    -0.3710     0.2792  -1.329   0.1955    \n",
       "grouptrt2     0.4940     0.2792   1.769   0.0886 .  \n",
       "techtech2    -0.2180     0.2280  -0.956   0.3478    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.6244 on 26 degrees of freedom\n",
       "Multiple R-squared:  0.2891,\tAdjusted R-squared:  0.2071 \n",
       "F-statistic: 3.525 on 3 and 26 DF,  p-value: 0.02881\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit <- lm(weight ~ group + tech, data=PlantGrowth)\n",
    "summary(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>5.141</dd><dt>grouptrt1</dt><dd>-0.371</dd><dt>grouptrt2</dt><dd>0.494</dd><dt>techtech2</dt><dd>-0.218</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 5.141\n",
       "\\item[grouptrt1] -0.371\n",
       "\\item[grouptrt2] 0.494\n",
       "\\item[techtech2] -0.218\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   5.141grouptrt1\n",
       ":   -0.371grouptrt2\n",
       ":   0.494techtech2\n",
       ":   -0.218\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)   grouptrt1   grouptrt2   techtech2 \n",
       "      5.141      -0.371       0.494      -0.218 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coefficients(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " group emmean    SE df lower.CL upper.CL\n",
       " ctrl    5.03 0.197 26     4.63     5.44\n",
       " trt1    4.66 0.197 26     4.26     5.07\n",
       " trt2    5.53 0.197 26     5.12     5.93\n",
       "\n",
       "Results are averaged over the levels of: tech \n",
       "Confidence level used: 0.95 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "emmeans(fit, \"group\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My question is, if I knew the coefficient of tech1, then I would have an equation like y = groupctrl * x + grouptrt1 * x + grouptrt2 * x + tech1 * x + tech2 * x. And then ingnoring the coefficient of tech variables makes it look like removing/ignoring the effect of tech variable to me.\n",
    "\n",
    "Is there a nice way of removing/ignoring the unwanted effect?  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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