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<li><a class="reference internal" href="#">Failure of Machine Learning to infer causal effects</a><ul>
<li><a class="reference internal" href="#the-dataset-simulated-hourly-wages">The dataset: simulated hourly wages</a></li>
<li><a class="reference internal" href="#description-of-the-simulated-data">Description of the simulated data</a></li>
<li><a class="reference internal" href="#income-prediction-with-fully-observed-variables">Income prediction with fully observed variables</a></li>
<li><a class="reference internal" href="#income-prediction-with-partial-observations">Income prediction with partial observations</a></li>
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<section class="sphx-glr-example-title" id="failure-of-machine-learning-to-infer-causal-effects">
<span id="sphx-glr-auto-examples-inspection-plot-causal-interpretation-py"></span><h1>Failure of Machine Learning to infer causal effects<a class="headerlink" href="#failure-of-machine-learning-to-infer-causal-effects" title="Permalink to this heading">¶</a></h1>
<p>Machine Learning models are great for measuring statistical associations.
Unfortunately, unless we’re willing to make strong assumptions about the data,
those models are unable to infer causal effects.</p>
<p>To illustrate this, we will simulate a situation in which we try to answer one
of the most important questions in economics of education: <strong>what is the causal
effect of earning a college degree on hourly wages?</strong> Although the answer to
this question is crucial to policy makers, <a class="reference external" href="https://en.wikipedia.org/wiki/Omitted-variable_bias">Omitted-Variable Biases</a> (OVB) prevent us from
identifying that causal effect.</p>
<section id="the-dataset-simulated-hourly-wages">
<h2>The dataset: simulated hourly wages<a class="headerlink" href="#the-dataset-simulated-hourly-wages" title="Permalink to this heading">¶</a></h2>
<p>The data generating process is laid out in the code below. Work experience in
years and a measure of ability are drawn from Normal distributions; the
hourly wage of one of the parents is drawn from Beta distribution. We then
create an indicator of college degree which is positively impacted by ability
and parental hourly wage. Finally, we model hourly wages as a linear function
of all the previous variables and a random component. Note that all variables
have a positive effect on hourly wages.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">10_000</span>
<span class="n">rng</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">32</span><span class="p">)</span>
<span class="n">experiences</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">n_samples</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
<span class="n">experiences</span><span class="p">[</span><span class="n">experiences</span> <span class="o"><</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">abilities</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.15</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">n_samples</span><span class="p">)</span>
<span class="n">parent_hourly_wages</span> <span class="o">=</span> <span class="mi">50</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">n_samples</span><span class="p">)</span>
<span class="n">parent_hourly_wages</span><span class="p">[</span><span class="n">parent_hourly_wages</span> <span class="o"><</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">college_degrees</span> <span class="o">=</span> <span class="p">(</span>
<span class="mi">9</span> <span class="o">*</span> <span class="n">abilities</span> <span class="o">+</span> <span class="mf">0.02</span> <span class="o">*</span> <span class="n">parent_hourly_wages</span> <span class="o">+</span> <span class="n">rng</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">)</span> <span class="o">></span> <span class="mf">0.7</span>
<span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
<span class="n">true_coef</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.html#pandas.Series" title="pandas.Series" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">Series</span></a><span class="p">(</span>
<span class="p">{</span>
<span class="s2">"college degree"</span><span class="p">:</span> <span class="mf">2.0</span><span class="p">,</span>
<span class="s2">"ability"</span><span class="p">:</span> <span class="mf">5.0</span><span class="p">,</span>
<span class="s2">"experience"</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">,</span>
<span class="s2">"parent hourly wage"</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span>
<span class="p">}</span>
<span class="p">)</span>
<span class="n">hourly_wages</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">true_coef</span><span class="p">[</span><span class="s2">"experience"</span><span class="p">]</span> <span class="o">*</span> <span class="n">experiences</span>
<span class="o">+</span> <span class="n">true_coef</span><span class="p">[</span><span class="s2">"parent hourly wage"</span><span class="p">]</span> <span class="o">*</span> <span class="n">parent_hourly_wages</span>
<span class="o">+</span> <span class="n">true_coef</span><span class="p">[</span><span class="s2">"college degree"</span><span class="p">]</span> <span class="o">*</span> <span class="n">college_degrees</span>
<span class="o">+</span> <span class="n">true_coef</span><span class="p">[</span><span class="s2">"ability"</span><span class="p">]</span> <span class="o">*</span> <span class="n">abilities</span>
<span class="o">+</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">n_samples</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">hourly_wages</span><span class="p">[</span><span class="n">hourly_wages</span> <span class="o"><</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
</pre></div>
</div>
</section>
<section id="description-of-the-simulated-data">
<h2>Description of the simulated data<a class="headerlink" href="#description-of-the-simulated-data" title="Permalink to this heading">¶</a></h2>
<p>The following plot shows the distribution of each variable, and pairwise
scatter plots. Key to our OVB story is the positive relationship between
ability and college degree.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
<span class="n">df</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span>
<span class="p">{</span>
<span class="s2">"college degree"</span><span class="p">:</span> <span class="n">college_degrees</span><span class="p">,</span>
<span class="s2">"ability"</span><span class="p">:</span> <span class="n">abilities</span><span class="p">,</span>
<span class="s2">"hourly wage"</span><span class="p">:</span> <span class="n">hourly_wages</span><span class="p">,</span>
<span class="s2">"experience"</span><span class="p">:</span> <span class="n">experiences</span><span class="p">,</span>
<span class="s2">"parent hourly wage"</span><span class="p">:</span> <span class="n">parent_hourly_wages</span><span class="p">,</span>
<span class="p">}</span>
<span class="p">)</span>
<span class="n">grid</span> <span class="o">=</span> <a href="https://seaborn.pydata.org/generated/seaborn.pairplot.html#seaborn.pairplot" title="seaborn.pairplot" class="sphx-glr-backref-module-seaborn sphx-glr-backref-type-py-function"><span class="n">sns</span><span class="o">.</span><span class="n">pairplot</span></a><span class="p">(</span><span class="n">df</span><span class="p">,</span> <span class="n">diag_kind</span><span class="o">=</span><span class="s2">"kde"</span><span class="p">,</span> <span class="n">corner</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_causal_interpretation_001.png" srcset="../../_images/sphx_glr_plot_causal_interpretation_001.png" alt="plot causal interpretation" class = "sphx-glr-single-img"/><p>In the next section, we train predictive models and we therefore split the
target column from over features and we split the data into a training and a
testing set.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a>
<span class="n">target_name</span> <span class="o">=</span> <span class="s2">"hourly wage"</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span><span class="n">columns</span><span class="o">=</span><span class="n">target_name</span><span class="p">),</span> <span class="n">df</span><span class="p">[</span><span class="n">target_name</span><span class="p">]</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="income-prediction-with-fully-observed-variables">
<h2>Income prediction with fully observed variables<a class="headerlink" href="#income-prediction-with-fully-observed-variables" title="Permalink to this heading">¶</a></h2>
<p>First, we train a predictive model, a
<a class="reference internal" href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="sklearn.linear_model.LinearRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearRegression</span></code></a> model. In this experiment,
we assume that all variables used by the true generative model are available.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="sklearn.linear_model.LinearRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearRegression</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">r2_score</span></a>
<span class="n">features_names</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"experience"</span><span class="p">,</span> <span class="s2">"parent hourly wage"</span><span class="p">,</span> <span class="s2">"college degree"</span><span class="p">,</span> <span class="s2">"ability"</span><span class="p">]</span>
<span class="n">regressor_with_ability</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="sklearn.linear_model.LinearRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearRegression</span></a><span class="p">()</span>
<span class="n">regressor_with_ability</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">[</span><span class="n">features_names</span><span class="p">],</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_pred_with_ability</span> <span class="o">=</span> <span class="n">regressor_with_ability</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">[</span><span class="n">features_names</span><span class="p">])</span>
<span class="n">R2_with_ability</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">r2_score</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_with_ability</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"R2 score with ability: </span><span class="si">{</span><span class="n">R2_with_ability</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>R2 score with ability: 0.975
</pre></div>
</div>
<p>This model predicts well the hourly wages as shown by the high R2 score. We
plot the model coefficients to show that we exactly recover the values of
the true generative model.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">model_coef</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.html#pandas.Series" title="pandas.Series" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">Series</span></a><span class="p">(</span><span class="n">regressor_with_ability</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="n">features_names</span><span class="p">)</span>
<span class="n">coef</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.concat.html#pandas.concat" title="pandas.concat" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-function"><span class="n">pd</span><span class="o">.</span><span class="n">concat</span></a><span class="p">(</span>
<span class="p">[</span><span class="n">true_coef</span><span class="p">[</span><span class="n">features_names</span><span class="p">],</span> <span class="n">model_coef</span><span class="p">],</span>
<span class="n">keys</span><span class="o">=</span><span class="p">[</span><span class="s2">"Coefficients of true generative model"</span><span class="p">,</span> <span class="s2">"Model coefficients"</span><span class="p">],</span>
<span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">coef</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">barh</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Coefficient values"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Coefficients of the linear regression including the ability features"</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_causal_interpretation_002.png" srcset="../../_images/sphx_glr_plot_causal_interpretation_002.png" alt="Coefficients of the linear regression including the ability features" class = "sphx-glr-single-img"/></section>
<section id="income-prediction-with-partial-observations">
<h2>Income prediction with partial observations<a class="headerlink" href="#income-prediction-with-partial-observations" title="Permalink to this heading">¶</a></h2>
<p>In practice, intellectual abilities are not observed or are only estimated
from proxies that inadvertently measure education as well (e.g. by IQ tests).
But omitting the “ability” feature from a linear model inflates the estimate
via a positive OVB.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">features_names</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"experience"</span><span class="p">,</span> <span class="s2">"parent hourly wage"</span><span class="p">,</span> <span class="s2">"college degree"</span><span class="p">]</span>
<span class="n">regressor_without_ability</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="sklearn.linear_model.LinearRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearRegression</span></a><span class="p">()</span>
<span class="n">regressor_without_ability</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">[</span><span class="n">features_names</span><span class="p">],</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_pred_without_ability</span> <span class="o">=</span> <span class="n">regressor_without_ability</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">[</span><span class="n">features_names</span><span class="p">])</span>
<span class="n">R2_without_ability</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">r2_score</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred_without_ability</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"R2 score without ability: </span><span class="si">{</span><span class="n">R2_without_ability</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>R2 score without ability: 0.968
</pre></div>
</div>
<p>The predictive power of our model is similar when we omit the ability feature
in terms of R2 score. We now check if the coefficient of the model are
different from the true generative model.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">model_coef</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.Series.html#pandas.Series" title="pandas.Series" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">Series</span></a><span class="p">(</span><span class="n">regressor_without_ability</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="n">features_names</span><span class="p">)</span>
<span class="n">coef</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.concat.html#pandas.concat" title="pandas.concat" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-function"><span class="n">pd</span><span class="o">.</span><span class="n">concat</span></a><span class="p">(</span>
<span class="p">[</span><span class="n">true_coef</span><span class="p">[</span><span class="n">features_names</span><span class="p">],</span> <span class="n">model_coef</span><span class="p">],</span>
<span class="n">keys</span><span class="o">=</span><span class="p">[</span><span class="s2">"Coefficients of true generative model"</span><span class="p">,</span> <span class="s2">"Model coefficients"</span><span class="p">],</span>
<span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">coef</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">barh</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Coefficient values"</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Coefficients of the linear regression excluding the ability feature"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_causal_interpretation_003.png" srcset="../../_images/sphx_glr_plot_causal_interpretation_003.png" alt="Coefficients of the linear regression excluding the ability feature" class = "sphx-glr-single-img"/><p>To compensate for the omitted variable, the model inflates the coefficient of
the college degree feature. Therefore, interpreting this coefficient value
as a causal effect of the true generative model is incorrect.</p>
</section>
<section id="lessons-learned">
<h2>Lessons learned<a class="headerlink" href="#lessons-learned" title="Permalink to this heading">¶</a></h2>
<p>Machine learning models are not designed for the estimation of causal
effects. While we showed this with a linear model, OVB can affect any type of
model.</p>
<p>Whenever interpreting a coefficient or a change in predictions brought about
by a change in one of the features, it is important to keep in mind
potentially unobserved variables that could be correlated with both the
feature in question and the target variable. Such variables are called
<a class="reference external" href="https://en.wikipedia.org/wiki/Confounding">Confounding Variables</a>. In
order to still estimate causal effect in the presence of confounding,
researchers usually conduct experiments in which the treatment variable (e.g.
college degree) is randomized. When an experiment is prohibitively expensive
or unethical, researchers can sometimes use other causal inference techniques
such as <a class="reference external" href="https://en.wikipedia.org/wiki/Instrumental_variables_estimation">Instrumental Variables</a> (IV)
estimations.</p>
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