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and an rstanreg model of y, 
this function returns 4 cross-validated measures of the model's posterior prediction quality: 
Median absolute prediction error (mae) measures the typical difference between the observed y values and their posterior predictive medians (stable = TRUE) or means (stable = FALSE).
Scaled mae (mae_scaled) measures the typical number of absolute deviations (stable = TRUE) or standard deviations (stable = FALSE) that observed y values fall from their predictive medians (stable = TRUE) or means (stable = FALSE).
within_50 and within_90 report the proportion of observed y values that fall within their posterior prediction intervals, the probability levels of which are set by the user.
For hierarchical models of class lmerMod, the folds are comprised by collections of groups, not individual observations."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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    <h1>Cross-Validated Posterior Predictive Summaries</h1>
    <small class="dont-index">Source: <a href="https://github.com/bayes-rules/bayesrules/blob/HEAD/R/prediction_summary_cv.R" class="external-link"><code>R/prediction_summary_cv.R</code></a></small>
    <div class="hidden name"><code>prediction_summary_cv.Rd</code></div>
    </div>

    <div class="ref-description">
    <p>Given a set of observed data including a quantitative response variable y 
and an rstanreg model of y, 
this function returns 4 cross-validated measures of the model's posterior prediction quality: 
Median absolute prediction error (mae) measures the typical difference between the observed y values and their posterior predictive medians (stable = TRUE) or means (stable = FALSE).
Scaled mae (mae_scaled) measures the typical number of absolute deviations (stable = TRUE) or standard deviations (stable = FALSE) that observed y values fall from their predictive medians (stable = TRUE) or means (stable = FALSE).
within_50 and within_90 report the proportion of observed y values that fall within their posterior prediction intervals, the probability levels of which are set by the user.
For hierarchical models of class lmerMod, the folds are comprised by collections of groups, not individual observations.</p>
    </div>

    <div id="ref-usage">
    <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">prediction_summary_cv</span><span class="op">(</span>
  <span class="va">data</span>,
  <span class="va">group</span>,
  <span class="va">model</span>,
  <span class="va">k</span>,
  prob_inner <span class="op">=</span> <span class="fl">0.5</span>,
  prob_outer <span class="op">=</span> <span class="fl">0.95</span>
<span class="op">)</span></code></pre></div>
    </div>

    <div id="arguments">
    <h2>Arguments</h2>
    <dl><dt>data</dt>
<dd><p>data frame including the variables in the model, both response y and predictors x</p></dd>
<dt>group</dt>
<dd><p>a character string representing the name of the factor grouping variable, ie. random effect (only used for hierarchical models)</p></dd>
<dt>model</dt>
<dd><p>an rstanreg model object with quantitative y</p></dd>
<dt>k</dt>
<dd><p>the number of folds to use for cross validation</p></dd>
<dt>prob_inner</dt>
<dd><p>posterior predictive interval probability (a value between 0 and 1)</p></dd>
<dt>prob_outer</dt>
<dd><p>posterior predictive interval probability (a value between 0 and 1)</p></dd>
</dl></div>
    <div id="value">
    <h2>Value</h2>
    <p>list</p>
    </div>

    <div id="ref-examples">
    <h2>Examples</h2>
    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="va">example_data</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>x <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">100</span>, <span class="fl">20</span><span class="op">)</span><span class="op">)</span></span>
<span class="r-in"><span class="va">example_data</span><span class="op">$</span><span class="va">y</span> <span class="op">&lt;-</span> <span class="va">example_data</span><span class="op">$</span><span class="va">x</span><span class="op">*</span><span class="fl">3</span> <span class="op">+</span> <span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">rnorm</a></span><span class="op">(</span><span class="fl">20</span>, <span class="fl">0</span>, <span class="fl">5</span><span class="op">)</span></span>
<span class="r-in"><span class="va">example_model</span> <span class="op">&lt;-</span> <span class="fu">rstanarm</span><span class="fu">::</span><span class="fu"><a href="https://mc-stan.org/rstanarm/reference/stan_glm.html" class="external-link">stan_glm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>,  data <span class="op">=</span> <span class="va">example_data</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Gradient evaluation took 1.6e-05 seconds</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Adjust your expectations accordingly!</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:  Elapsed Time: 0.034403 seconds (Warm-up)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.019515 seconds (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1:                0.053918 seconds (Total)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 1: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Gradient evaluation took 1e-05 seconds</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Adjust your expectations accordingly!</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2:  Elapsed Time: 0.035173 seconds (Warm-up)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2:                0.018238 seconds (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2:                0.053411 seconds (Total)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 2: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Gradient evaluation took 5e-06 seconds</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Adjust your expectations accordingly!</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3:  Elapsed Time: 0.026411 seconds (Warm-up)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3:                0.01767 seconds (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3:                0.044081 seconds (Total)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 3: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Gradient evaluation took 4e-06 seconds</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.04 seconds.</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Adjust your expectations accordingly!</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4:  Elapsed Time: 0.042678 seconds (Warm-up)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4:                0.023425 seconds (Sampling)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4:                0.066103 seconds (Total)</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> Chain 4: </span>
<span class="r-in"><span class="fu">prediction_summary_cv</span><span class="op">(</span>model <span class="op">=</span> <span class="va">example_model</span>, data <span class="op">=</span> <span class="va">example_data</span>, k <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $folds</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   fold      mae mae_scaled within_50 within_95</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 1    1 3.026477  0.6104125       0.5       0.9</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 2    2 2.428045  0.3298622       0.8       1.0</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
<span class="r-out co"><span class="r-pr">#&gt;</span> $cv</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>        mae mae_scaled within_50 within_95</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 1 2.727261  0.4701373      0.65      0.95</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
</code></pre></div>
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