ISA 401: Business Intelligence & Data Visualization

class: center, middle, inverse, title-slide

.title[
# ISA 401: Business Intelligence & Data Visualization
]
.subtitle[
## 12: Data Correction and Imputation
]
.author[
### <br>Fadel M. Megahed, PhD <br><br>Raymond E. Glos Professor in Business <br> Farmer School of Business<br> Miami University<br><br> <a href="https://twitter.com/FadelMegahed"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" /></svg> <span class="citation">@FadelMegahed</span></a> <br> <a href="https://github.com/fmegahed/"><svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" /></svg> fmegahed</a> <br> <a href="mailto:fmegahed@miamioh.edu"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z" /></svg> fmegahed@miamioh.edu</a><br> <a href="https://calendly.com/fmegahed"><svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z" /></svg> Automated Scheduler for Office Hours</a><br><br>
]
.date[
### Fall 2025
]

---

# Quick Refresher from Last Class

✅ Converting tidy data to technically correct data

✅ Examining the consistency of data

---

# Learning Objectives for Today's Class

- Correct errors (with transformation rules, deductive correction and deterministic imputation)

- Describe different scenarios for missing data

- Apply some basic imputation techniques for missing data (e.g., mean/median/mode, kNN, etc)

---
class: center, inverse, middle

# Error Correction <br>(i.e., Correcting Inconsistencies in the Data)

---

# Correction

> Correction methods aim to fix inconsistent observations by **altering invalid values in a record based on information from valid values**. Depending on the method this is either a **single-step procedure** or a **two-step procedure** where first, an error localization method is used to empty certain fields, followed by an imputation step. --- [De Jonge and Van Der Loo (2013)](https://cran.r-project.org/doc/contrib/de_Jonge+van_der_Loo-Introduction_to_data_cleaning_with_R.pdf)

---

# Simple Transformation Rules

In practice, data cleaning procedures involve a lot of **ad-hoc transformations**. This may lead to long scripts where one selects parts of the data, changes some variables, selects another part, changes some more variables, etc.

- When such scripts are neatly written and commented, they can almost be **treated as a log of the actions** performed by the analyst.

- However, as scripts get longer it is **better to store the transformation rules separately and log which rule is executed on what record**.

One approach to **do** this in R is through the [deducorrect package](https://cran.r-project.org/web/packages/deducorrect/deducorrect.pdf).

<div id="ncoykpuptr" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
  
  <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false" style="-webkit-font-smoothing: antialiased; -moz-osx-font-smoothing: grayscale; font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji'; display: table; border-collapse: collapse; line-height: normal; margin-left: auto; margin-right: auto; color: #333333; font-size: 16px; font-weight: normal; font-style: normal; background-color: #FFFFFF; width: auto; border-top-style: solid; border-top-width: 2px; border-top-color: #A8A8A8; border-right-style: none; border-right-width: 2px; border-right-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #A8A8A8; border-left-style: none; border-left-width: 2px; border-left-color: #D3D3D3;" bgcolor="#FFFFFF">
  <thead style="border-style: none;">
    <tr class="gt_col_headings" style="border-style: none; border-top-style: solid; border-top-width: 2px; border-top-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3;">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="type" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">type</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="package_name" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">package</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="fun()" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">function()</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="description" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">description</code></span></th>
    </tr>
  </thead>
  <tbody class="gt_table_body" style="border-style: none; border-top-style: solid; border-top-width: 2px; border-top-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #D3D3D3;">
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">rules</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deducorrect</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">correctionRules()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Rules for determinstic correction</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">correction</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deducorrect</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">correctWithRules()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Apply simple replacement rules to a data.frame.</span></td></tr>
  </tbody>
  
  
</table>
</div>

---

# Simple Transformation Rules: Example

.pull-left[

``` r
people = tibble::tibble(
  name = c('Tom Cruise', 'Serena Williams', 'Taylor Swift', 'Ariana Grande', 'The Rock'),
  height = c(172, 1.75, 69.3, 154, 6.25),
  unit = c('cm', 'm', 'inch', 'cm', 'ft')
)

u <- deducorrect::correctionRules(
  expression(
    ## 1-------
    if(unit == "cm") height <- height/100,
    ## 2-------
    if(unit == "inch") height <- height/39.37,
    ## 3-------
    if(unit == "ft") height <- height/3.28,
    ## 4-------
    unit <- "m"
  ))
```
Note that the rules **can also be stored in a txt file**.

]

.pull-right[

``` r
*people_corrected = deducorrect::correctWithRules(
* rules = u, dat = people)

people_corrected$corrected
```

```
## # A tibble: 5 × 3
##   name            height unit 
##   <chr>            <dbl> <chr>
## 1 Tom Cruise        1.72 m    
## 2 Serena Williams   1.75 m    
## 3 Taylor Swift      1.76 m    
## 4 Ariana Grande     1.54 m    
## 5 The Rock          1.91 m
```

``` r
people_corrected$corrections
```

```
##   row variable  old      new                                        how
## 1   1   height  172     1.72     if (unit == "cm") height <- height/100
## 2   1     unit   cm        m                                unit <- "m"
## 3   3   height 69.3 1.760224 if (unit == "inch") height <- height/39.37
## 4   3     unit inch        m                                unit <- "m"
## 5   4   height  154     1.54     if (unit == "cm") height <- height/100
## 6   4     unit   cm        m                                unit <- "m"
## 7   5   height 6.25 1.905488    if (unit == "ft") height <- height/3.28
## 8   5     unit   ft        m                                unit <- "m"
```
]

---

# Deductive Correction

When the data you are analyzing is generated by people rather than machines or measurement devices, certain typical human-generated errors are likely to occur. Examples include: (a) **typing errors** in numbers, (b) **rounding errors** in numbers, and (c) **sign errors**.

These errors can be accounted for through the [deducorrect package](https://cran.r-project.org/web/packages/deducorrect/deducorrect.pdf).

<div id="eupjzjidgb" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
  
  <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false" style="-webkit-font-smoothing: antialiased; -moz-osx-font-smoothing: grayscale; font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji'; display: table; border-collapse: collapse; line-height: normal; margin-left: auto; margin-right: auto; color: #333333; font-size: 16px; font-weight: normal; font-style: normal; background-color: #FFFFFF; width: auto; border-top-style: solid; border-top-width: 2px; border-top-color: #A8A8A8; border-right-style: none; border-right-width: 2px; border-right-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #A8A8A8; border-left-style: none; border-left-width: 2px; border-left-color: #D3D3D3;" bgcolor="#FFFFFF">
  <thead style="border-style: none;">
    <tr class="gt_col_headings" style="border-style: none; border-top-style: solid; border-top-width: 2px; border-top-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3;">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="type" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">type</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="package_name" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">package</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="fun()" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">function()</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="description" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">description</code></span></th>
    </tr>
  </thead>
  <tbody class="gt_table_body" style="border-style: none; border-top-style: solid; border-top-width: 2px; border-top-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #D3D3D3;">
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">rule def</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">editrules</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">editmatrix()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">A set of comparison operators representing a linear system of (in)equations. The function editmatrix generates an editmatrix from a character vector, or an expression vector.</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">typos</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deducorrect</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">correctTypos()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Tries to detect and repair records that violate linear equality constraints by correcting simple typos</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">rounding</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deducorrect</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">correctRounding()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Tries to detect and repair records that violate linear (in)equality constraints by correcting possible rounding errors</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">sign</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deducorrect</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">correctSigns()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Correct sign errors and value interchanges in data records.</span></td></tr>
  </tbody>
  
  
</table>
</div>

---

# Deductive Correction: Correct Typos

``` r
e <- editrules::editmatrix("x + y == z") # defining the rules
d <- data.frame(x = 123, y = 132, z = 246) # creating the data frame
*cor <- deducorrect::correctTypos(e, d) # attempting to correct Typos
cor$corrected # new values for the data.frame
```

```
##     x   y   z
## 1 123 123 246
```

``` r
cor$corrections # the log of what has changed
```

```
##   row variable old new
## 1   1        y 132 123
```

---

# Deductive Correction: Correct Rounding Errors

``` r
e <- editrules::editmatrix("x + y == z") # defining the rules
d <- data.frame(x = 101, y = 100, z = 200) # creating the data frame
*cor <- deducorrect::correctRounding(e, d) # attempting to correct Rounding
cor$corrected # new values for the data.frame (may not be unique)
```

```
##     x   y   z
## 1 100 100 200
```

``` r
cor$corrections # the log of what has changed
```

```
##   row variable old new
## 1   1        x 101 100
```

---

# Deductive Correction: Correct Sign Errors

``` r
e <- editrules::editmatrix("x + y == z") # defining the rules
d <- data.frame(x = -100, y = 100, z = 200) # creating the data frame
*cor <- deducorrect::correctSigns(e, d) # attempting to correct the sign
cor$corrected # new values for the data.frame
```

```
##     x   y   z
## 1 100 100 200
```

``` r
cor$corrections # the log of what has changed
```

```
##   row variable  old new
## 1   1        x -100 100
```

---

# Non-Graded Activity

.panelset[

.panel[.panel-name[Activity]

> _Over the next 3 minutes, please examine the following:_

- Which of the aforementioned `correct...()` functions can be used to correct the following situation?  
  1. `correctWithRules()` 
  2. `correctTypos()` 
  3. `correctSigns()`  
  4. `correctRounding()`

``` r
d <- data.frame(x = 173, y = 200, z = 379) # creating the data frame
```

]

.panel[.panel-name[Your Solution]

.can-edit.key-activity1[

Please insert your solution below.

..............................

Why did you pick your answer?

.............................. 
]
]
]

---
class: center, inverse, middle

# Missing Data Handling <br>(Complete Cases, Col. Deletion, & Imputation)

---

# Types of Missing Data: MCAR

Missing data are typically grouped into three categories:

- **Missing completely at random (MCAR):** When data are MCAR, the fact that the data are missing is independent of the observed and unobserved data. For example,  
  * If we were to perform annual health checks for all FSB students, some of you may have missing lab values because a batch of lab samples was processed improperly.  
  * Here, the missing data **reduce the analyzable population of the study and consequently, the statistical power, but do not introduce bias:** when data are MCAR, the **remaining data can be considered a simple random sample of the full data set** of interest. 
  * Hence, the `NA` data can be simply be handled by removing such observations. In R, the `na.omit()` can be used without the need for introducing any packages. We refer to this `NA` handling approach as **complete case analysis**.

.footnote[
<html>
<hr>
</html>

**Source:** Mack C, Su Z, Westreich D. Managing Missing Data in Patient Registries: Addendum to Registries for Evaluating Patient Outcomes: A User’s Guide, Third Edition [Internet]. Rockville (MD): Agency for Healthcare Research and Quality (US); 2018 Feb. Types of Missing Data. Available from: <https://www.ncbi.nlm.nih.gov/books/NBK493614/>
]

---

# Types of Missing Data: MAR

- **Missing at random (MAR):** When data are MAR, the fact that the **data are missing is systematically related to the observed but not the unobserved data**. For example,   
  * A dataset examining depression may encounter data that are MAR if male participants are less likely to complete a survey about depression severity than female participants.   
  * That is, if the probability of survey completion is related to their `sex` (which is fully observed) but **not the severity of their depression**, then the data may be regarded as MAR. 
  * Approaches to Handle `NAs` for MAR Data:    
      + Complete case analyses of MAR data may or may not result in bias.  
      + Impute (i.e., guess) the missing values based on a proper accounting of the known factors (e.g., their sex)

.footnote[
<html>
<hr>
</html>

---

# Types of Missing Data: MNAR

- **Missing not at random (MNAR):** When data are MNAR, the fact that the data are missing is **systematically related to the unobserved data**, that is, the missingness is related to events or factors which are not measured by the researcher. To extend the previous example,   
  * the depression registry may encounter data that are MNAR if participants with severe depression are more likely to refuse to complete the survey about depression severity.  
  * Approaches to Handle `NAs` for MAR Data:    
      + Complete case analyses of MAR data may or may not result in bias.  
      + Imputation approaches **may not be suitable since the missigness pattern is due to the impact of unobserved auxiliary variables**.

.footnote[
<html>
<hr>
</html>

---

# The Bike Sharing Dataset

``` r
bike_tbl = readr::read_csv('../../data/bike_sharing_data.csv') |> 
  # making their column names tidy
  janitor::clean_names() |> 
  # creating date, hours, and day of the week variables
  dplyr::mutate(datetime = lubridate::mdy_hm(datetime), date = lubridate::as_date(datetime), 
         hours = lubridate::hour(datetime), day_of_week =  lubridate::wday(date)) |>
  # moving them to the front
  dplyr::relocate(date, day_of_week, hours) |> 
  select(-c(datetime)) |> 
  # converting int columns to factors
  dplyr::mutate(dplyr::across(.cols = c(hours, season, holiday, workingday, weather),
                       .fn = as.character)) |> 
  dplyr::mutate(dplyr::across(.cols = c(hours, season, holiday, workingday, weather),
                       .fn = as.factor))
```

---

# Bike Sharing Data: Viz Missing [1]

``` r
*visdat::vis_dat(bike_tbl) # function from visdat
```

---

# Bike Sharing Data: Viz Missing [2]

``` r
*visdat::vis_miss(bike_tbl) # function from visdat
```

---

# Bike Sharing Data: Missing Relationships [1]

``` r
bike_tbl_grouped = bike_tbl |> 
  dplyr::group_by(day_of_week) |> # group_by from dplyr #>>
  dplyr::summarise(nmissing = is.na(sources) |> sum()) # summarise from dplyr #>>

bike_tbl_grouped |> DT::datatable(
  fillContainer = FALSE, options = list(pageLength = 4), height = 600)
```

<div id="htmlwidget-17b2722c35f29c374295" style="width:100%;height:600px;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-17b2722c35f29c374295">{"x":{"filter":"none","vertical":false,"fillContainer":false,"data":[["1","2","3","4","5","6","7"],[1,2,3,4,5,6,7],[77,88,75,79,74,82,79]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>day_of_week<\/th>\n      <th>nmissing<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":4,"columnDefs":[{"className":"dt-right","targets":[1,2]},{"orderable":false,"targets":0},{"name":" ","targets":0},{"name":"day_of_week","targets":1},{"name":"nmissing","targets":2}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[4,10,25,50,100]},"selection":{"mode":"multiple","selected":null,"target":"row","selectable":null}},"evals":[],"jsHooks":[]}</script>

---

# Bike Sharing Data: Missing Relationships [2]

``` r
bike_tbl_grouped = bike_tbl |> 
  dplyr::group_by(day_of_week, hours) |> # group_by from dplyr #>>
  dplyr::summarise(nmissing = is.na(sources) |> sum()) # summarise from dplyr #>>

bike_tbl_grouped |> DT::datatable(
  fillContainer = FALSE, options = list(pageLength = 4), height = 600)
```

<div id="htmlwidget-2ce42390bf399c6e531c" style="width:100%;height:600px;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-2ce42390bf399c6e531c">{"x":{"filter":"none","vertical":false,"fillContainer":false,"data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40","41","42","43","44","45","46","47","48","49","50","51","52","53","54","55","56","57","58","59","60","61","62","63","64","65","66","67","68","69","70","71","72","73","74","75","76","77","78","79","80","81","82","83","84","85","86","87","88","89","90","91","92","93","94","95","96","97","98","99","100","101","102","103","104","105","106","107","108","109","110","111","112","113","114","115","116","117","118","119","120","121","122","123","124","125","126","127","128","129","130","131","132","133","134","135","136","137","138","139","140","141","142","143","144","145","146","147","148","149","150","151","152","153","154","155","156","157","158","159","160","161","162","163","164","165","166","167","168"],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7],["0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9","0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9","0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9","0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9","0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9","0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9","0","1","10","11","12","13","14","15","16","17","18","19","2","20","21","22","23","3","4","5","6","7","8","9"],[4,3,3,1,5,1,2,3,4,4,4,8,2,4,1,5,3,1,5,1,2,2,3,6,4,3,4,3,3,5,5,2,1,3,2,5,4,6,5,4,3,5,1,2,4,3,4,7,6,3,4,1,1,3,1,4,2,3,2,5,5,5,0,4,4,2,2,3,5,1,4,5,1,3,2,5,3,3,3,4,4,9,2,4,1,3,2,3,6,1,5,3,1,5,2,4,4,3,3,1,3,5,2,3,2,2,6,3,3,3,5,3,3,3,5,3,3,3,3,0,5,6,3,4,3,1,6,2,1,6,5,3,3,3,2,4,3,4,2,5,3,2,4,2,0,5,3,1,4,2,1,0,1,1,5,1,4,2,7,5,3,6,2,4,7,6,5,4]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>day_of_week<\/th>\n      <th>hours<\/th>\n      <th>nmissing<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":4,"columnDefs":[{"className":"dt-right","targets":[1,3]},{"orderable":false,"targets":0},{"name":" ","targets":0},{"name":"day_of_week","targets":1},{"name":"hours","targets":2},{"name":"nmissing","targets":3}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[4,10,25,50,100]},"selection":{"mode":"multiple","selected":null,"target":"row","selectable":null}},"evals":[],"jsHooks":[]}</script>

---

# Some Useful Imputation Functions

<div id="xssmvsxcvm" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
  
  <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false" style="-webkit-font-smoothing: antialiased; -moz-osx-font-smoothing: grayscale; font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji'; display: table; border-collapse: collapse; line-height: normal; margin-left: auto; margin-right: auto; color: #333333; font-size: 16px; font-weight: normal; font-style: normal; background-color: #FFFFFF; width: auto; border-top-style: solid; border-top-width: 2px; border-top-color: #A8A8A8; border-right-style: none; border-right-width: 2px; border-right-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #A8A8A8; border-left-style: none; border-left-width: 2px; border-left-color: #D3D3D3;" bgcolor="#FFFFFF">
  <thead style="border-style: none;">
    <tr class="gt_col_headings" style="border-style: none; border-top-style: solid; border-top-width: 2px; border-top-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3;">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="type" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">type</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="package_name" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">package</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="fun()" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">function()</code></span></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="description" style="border-style: none; color: #333333; background-color: #FFFFFF; font-size: 100%; font-weight: normal; text-transform: inherit; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: bottom; padding-top: 5px; padding-bottom: 6px; padding-left: 5px; padding-right: 5px; overflow-x: hidden; text-align: left;" bgcolor="#FFFFFF" valign="bottom" align="left"><span class="gt_from_md"><code style="margin-top: 0; margin-bottom: 0;">description</code></span></th>
    </tr>
  </thead>
  <tbody class="gt_table_body" style="border-style: none; border-top-style: solid; border-top-width: 2px; border-top-color: #D3D3D3; border-bottom-style: solid; border-bottom-width: 2px; border-bottom-color: #D3D3D3;">
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">identify NA cells</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">base</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">is.na()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">returns logicals T/F for each NA cell</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">identify NA in each col</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">base & purrr</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">purrr::map_df(.x = df, .f= is.na) |> colSums()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">returns total NA per column</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">rule-based deductions</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deducorrect</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">deduImpute()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Based on observed values and edit rules, impute as many variables deductively as possible.</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">replace NAs</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">tidyr</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">replace_na(list(x = 0, y = ‘unknown’))</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">Replace/Impute NA with pre-configured values <br style="margin-top: 0; margin-bottom: 0;"> (e.g., mean, median, VIM::maxCat(), etc.)</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">across column imputations</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">VIM</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">kNN()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">k-nearest neighbours for imputation</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">across column imputations</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">VIM</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">rangerImpute()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">use of random forests for imputation</span></td></tr>
    <tr style="border-style: none;"><td headers="type" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md"><strong style="margin-top: 0; margin-bottom: 0;">multiple imputation</strong></span></td>
<td headers="package_name" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">mice</span></td>
<td headers="fun()" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">mice()</span></td>
<td headers="description" class="gt_row gt_left" style="border-style: none; padding-top: 8px; padding-bottom: 8px; padding-left: 5px; padding-right: 5px; margin: 10px; border-top-style: solid; border-top-width: 1px; border-top-color: #D3D3D3; border-left-style: none; border-left-width: 1px; border-left-color: #D3D3D3; border-right-style: none; border-right-width: 1px; border-right-color: #D3D3D3; vertical-align: middle; overflow-x: hidden; text-align: left;" valign="middle" align="left"><span class="gt_from_md">multivariate imputation by chained equations</span></td></tr>
  </tbody>
  
  
</table>
</div>

---

# A Simple Demo Using a Modified Iris Dataset

Please refer to our in class demo for more details.

---

class: center, inverse, middle

# Recap

---

# Summary of Main Points

By now, you should be able to do the following:

- Correct errors (with transformation rules, deductive correction and deterministic imputation)

- Describe different scenarios for missing data

- Apply some basic imputation techniques for missing data (e.g., mean/median/mode, kNN, etc)

---

# Supplementary Reading

.center[[<img src="../../figures/intro_data_cleaning_book.png" height="450px">](https://cran.r-project.org/doc/contrib/de_Jonge+van_der_Loo-Introduction_to_data_cleaning_with_R.pdf)]
* [From technically correct to consistent data](https://cran.r-project.org/doc/contrib/de_Jonge+van_der_Loo-Introduction_to_data_cleaning_with_R.pdf)