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<!DOCTYPE html>
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<title>Auto Ownership</title>
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<h1 class="title">Auto Ownership</h1>
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<h2><a href="#content">Auto Ownership</a></h2>
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<ul>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#model-structure">Model Structure</a></li>
<li><a href="#coefficients">Coefficients</a></li>
<li><a href="#calibration">Calibration</a></li>
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<p class="author"><span class="glyphicon glyphicon-user"></span> Caliper Corporation</p>
<p class="date"><span class="glyphicon glyphicon-calendar"></span> June 19, 2021</p>
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<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Auto ownership is a long-term decision that directly impacts daily mode choice. The choice is influenced by household factors like income and number of workers, but also by where people choose to live. The auto ownership model allows TRMG2 to be sensitive to these factors and respond to changes in the future.</p>
<p>Auto ownership is predicted using a discrete choice model. For more details on general model form, click <a href="https://tfresource.org/topics/Choice_models.html">here</a>.</p>
</div>
<div id="model-structure" class="section level2">
<h2>Model Structure</h2>
<p>The auto ownership model in TRMG2 makes use of variables from the synthetic population and zonal accessibility to make predictions. The model structure is a simple multinomial logistic (MNL) regression model with five alternatives:</p>
<ul>
<li>0 Vehicles</li>
<li>1 Vehicle</li>
<li>2 Vehicles</li>
<li>3 Vehicles</li>
<li>4+ Vehicles</li>
</ul>
</div>
<div id="coefficients" class="section level2">
<h2>Coefficients</h2>
<p>Model estimation was performed using TransCADs built-in logit model engine, and the table below shows the utility terms, coefficients, and goodness of fit.</p>
<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:left;">
Term
</th>
<th style="text-align:left;">
v0
</th>
<th style="text-align:right;">
v1
</th>
<th style="text-align:right;">
v2
</th>
<th style="text-align:left;">
v3
</th>
<th style="text-align:left;">
v4
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
Constant
</td>
<td style="text-align:left;">
0
</td>
<td style="text-align:right;">
4.9
</td>
<td style="text-align:right;">
2.4
</td>
<td style="text-align:left;">
1.7
</td>
<td style="text-align:left;">
0.7
</td>
</tr>
<tr>
<td style="text-align:left;">
Workers
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
0.7
</td>
<td style="text-align:right;">
3.3
</td>
<td style="text-align:left;">
4.3
</td>
<td style="text-align:left;">
5.3
</td>
</tr>
<tr>
<td style="text-align:left;">
Non-working adults
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
0.0
</td>
<td style="text-align:right;">
2.1
</td>
<td style="text-align:left;">
2.8
</td>
<td style="text-align:left;">
3.6
</td>
</tr>
<tr>
<td style="text-align:left;">
Seniors
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
0.1
</td>
<td style="text-align:right;">
0.1
</td>
<td style="text-align:left;">
</td>
<td style="text-align:left;">
</td>
</tr>
<tr>
<td style="text-align:left;">
Walk access
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
-0.4
</td>
<td style="text-align:right;">
-0.6
</td>
<td style="text-align:left;">
-0.6
</td>
<td style="text-align:left;">
-0.7
</td>
</tr>
<tr>
<td style="text-align:left;">
Transit access
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
-0.1
</td>
<td style="text-align:right;">
-0.1
</td>
<td style="text-align:left;">
-0.2
</td>
<td style="text-align:left;">
-0.2
</td>
</tr>
<tr>
<td style="text-align:left;">
Nearby access
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
-0.4
</td>
<td style="text-align:right;">
-0.5
</td>
<td style="text-align:left;">
-0.8
</td>
<td style="text-align:left;">
-1.1
</td>
</tr>
<tr>
<td style="text-align:left;">
Walkability (intrazonal)
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
-0.5
</td>
<td style="text-align:right;">
-0.5
</td>
<td style="text-align:left;">
-0.5
</td>
<td style="text-align:left;">
-0.5
</td>
</tr>
<tr>
<td style="text-align:left;">
Income Category 1 HHs
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
-0.6
</td>
<td style="text-align:right;">
-1.8
</td>
<td style="text-align:left;">
-1.8
</td>
<td style="text-align:left;">
-3.2
</td>
</tr>
<tr>
<td style="text-align:left;">
Income Category 2 HHs
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
1.6
</td>
<td style="text-align:right;">
1.6
</td>
<td style="text-align:left;">
1.6
</td>
<td style="text-align:left;">
1.6
</td>
</tr>
<tr>
<td style="text-align:left;">
Income Category 3 HHs
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
1.8
</td>
<td style="text-align:right;">
2.6
</td>
<td style="text-align:left;">
2.7
</td>
<td style="text-align:left;">
2.7
</td>
</tr>
<tr>
<td style="text-align:left;">
Income Category 4 HHs
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
2.2
</td>
<td style="text-align:right;">
3.7
</td>
<td style="text-align:left;">
4.1
</td>
<td style="text-align:left;">
4.5
</td>
</tr>
<tr>
<td style="text-align:left;">
Calibration constant
</td>
<td style="text-align:left;">
</td>
<td style="text-align:right;">
-0.1
</td>
<td style="text-align:right;">
0.0
</td>
<td style="text-align:left;">
0.1
</td>
<td style="text-align:left;">
0
</td>
</tr>
</tbody>
</table>
<p>Household income categories are defined <a href="population_synthesis.html#household-income">here</a>. Accessibility terms are discussed in detail <a href="accessibility.html">here</a>.</p>
<p>As an example, the 1-vehicle coefficients in the table above translate into a utility formula that starts like this:</p>
<p><span class="math inline">\(U = 4.88 + 0.7 * Workers + 0.1 * Seniors - 0.4 * WalkAccess + ...\)</span></p>
<p>The coefficients all have the right sign and the relative sizes are intuitive. For example, higher-income households are more likely to own more cars. One particularly encouraging result of this model is that households with strong walk and transit accessibility are less likely to own a vehicle and even less likely to own multiple vehicles. This adds another dimension of model sensitivity to transit investments. New transit routes will affect long-term household decisions about auto ownership, which further influence their daily transportation decisions.</p>
<p>Looking in more detail, the trend for coefficients across alternatives is also intuitive. Large numbers of workers in a household have a small positive impact on the utility of owning 1 auto, but a large impact on owning 2 or more. High income households are more likely to own more vehicles. Finally, the model’s Rho^2 of 0.42 shows strong predictive power.</p>
</div>
<div id="calibration" class="section level2">
<h2>Calibration</h2>
<p>The estimated coefficients produce results that closely matched the survey as shown in the table below.</p>
<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:right;">
Autos
</th>
<th style="text-align:right;">
Survey %
</th>
<th style="text-align:right;">
Model %
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;">
0
</td>
<td style="text-align:right;">
5.1
</td>
<td style="text-align:right;">
5.3
</td>
</tr>
<tr>
<td style="text-align:right;">
1
</td>
<td style="text-align:right;">
31.5
</td>
<td style="text-align:right;">
33.5
</td>
</tr>
<tr>
<td style="text-align:right;">
2
</td>
<td style="text-align:right;">
41.7
</td>
<td style="text-align:right;">
37.9
</td>
</tr>
<tr>
<td style="text-align:right;">
3
</td>
<td style="text-align:right;">
15.3
</td>
<td style="text-align:right;">
13.4
</td>
</tr>
<tr>
<td style="text-align:right;">
4
</td>
<td style="text-align:right;">
6.5
</td>
<td style="text-align:right;">
9.9
</td>
</tr>
</tbody>
</table>
<p>Caliper created an auto-calibration tool for the auto ownership model and used it to ensure the model matched the observed shares more closely. Importantly, the calibration constants required to do this were small as shown below.</p>
<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:left;">
Alternative
</th>
<th style="text-align:right;">
Calibration Constant
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
v1
</td>
<td style="text-align:right;">
-0.0852
</td>
</tr>
<tr>
<td style="text-align:left;">
v2
</td>
<td style="text-align:right;">
0.0483
</td>
</tr>
<tr>
<td style="text-align:left;">
v3
</td>
<td style="text-align:right;">
0.1047
</td>
</tr>
<tr>
<td style="text-align:left;">
v4
</td>
<td style="text-align:right;">
0.0197
</td>
</tr>
</tbody>
</table>
</div>
</div>
<br>
<br>
<br>
<hr>
<p><a href="https://www.caliper.com/">TransCAD GIS Software</a>, 2022</p>
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