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<title>Linear regression of life expectancy on year</title>
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<div id="header">
<h1 class="title">Linear regression of life expectancy on year</h1>
</div>
<div id="TOC">
<ul>
<li><a href="#overview">Overview</a></li>
<li><a href="#load-the-gapminder-data">Load the Gapminder data</a></li>
<li><a href="#get-data-to-practice-with">Get data to practice with</a></li>
<li><a href="#get-some-code-that-works">Get some code that works</a></li>
<li><a href="#turn-working-code-into-a-function">Turn working code into a function</a></li>
<li><a href="#test-on-other-data-and-in-a-clean-workspace">Test on other data and in a clean workspace</a></li>
<li><a href="#are-we-there-yet">Are we there yet?</a></li>
</ul>
</div>
<div id="overview" class="section level3">
<h3>Overview</h3>
<p>We recently learned how to write our own R functions (<a href="block011_write-your-own-function-01.html">Part 1</a>, <a href="block011_write-your-own-function-02.html">Part 2</a>, <a href="block011_write-your-own-function-03.html">Part 3</a>).</p>
<p>Now we use that knowledge to write another useful function, within the context of the Gapminder data:</p>
<ul>
<li>Input: a data.frame that contains (at least) a life expectancy variable <code>lifeExp</code> and a variable for year <code>year</code></li>
<li>Output: a vector of estimated intercept and slope, from a linear regression of <code>lifeExp</code> on <code>year</code></li>
</ul>
<p>The ultimate goal is to apply this function to the Gapminder data for a specific country. We will eventually scale up to <em>all</em> countries using external machinery, e.g., the <code>dplyr::group_by()</code> + <code>dplyr::do()</code>.</p>
</div>
<div id="load-the-gapminder-data" class="section level3">
<h3>Load the Gapminder data</h3>
<p>As usual, load the Gapminder excerpt. Load <code>ggplot2</code> because we’ll make some plots and <code>dplyr</code> too.</p>
<pre class="r"><code>library(gapminder)
library(ggplot2)
suppressPackageStartupMessages(library(dplyr))</code></pre>
</div>
<div id="get-data-to-practice-with" class="section level3">
<h3>Get data to practice with</h3>
<p>I extract the data for one country in order to develop some working code interactively.</p>
<pre class="r"><code>j_country <- "France" # pick, but do not hard wire, an example
(j_dat <- gapminder %>%
filter(country == j_country))
## country continent year lifeExp pop gdpPercap
## 1 France Europe 1952 67.410 42459667 7029.809
## 2 France Europe 1957 68.930 44310863 8662.835
## 3 France Europe 1962 70.510 47124000 10560.486
## 4 France Europe 1967 71.550 49569000 12999.918
## 5 France Europe 1972 72.380 51732000 16107.192
## 6 France Europe 1977 73.830 53165019 18292.635
## 7 France Europe 1982 74.890 54433565 20293.897
## 8 France Europe 1987 76.340 55630100 22066.442
## 9 France Europe 1992 77.460 57374179 24703.796
## 10 France Europe 1997 78.640 58623428 25889.785
## 11 France Europe 2002 79.590 59925035 28926.032
## 12 France Europe 2007 80.657 61083916 30470.017</code></pre>
<p>Always always always plot the data. Yes, even now.</p>
<pre class="r"><code>p <- ggplot(j_dat, aes(x = year, y = lifeExp))
p + geom_point() + geom_smooth(method = "lm", se = FALSE)</code></pre>
<p><img src="block012_function-regress-lifeexp-on-year_files/figure-html/first-example-scatterplot-1.png" alt="" /></p>
</div>
<div id="get-some-code-that-works" class="section level3">
<h3>Get some code that works</h3>
<p>Fit the regression</p>
<pre class="r"><code>j_fit <- lm(lifeExp ~ year, j_dat)
coef(j_fit)
## (Intercept) year
## -397.7646019 0.2385014</code></pre>
<p>Whoa, check out that crazy intercept! Apparently the life expectancy in France around year 0 A.D. was minus 400 years! Never forget to sanity check a model. In this case, a reparametrization is in order. I think it makes more sense for the intercept to correspond to life expectancy in 1952, the earliest date in our dataset. Estimate the intercept eye-ball-o-metrically from the plot and confirm that we’ve got something sane and interpretable now.</p>
<pre class="r"><code>j_fit <- lm(lifeExp ~ I(year - 1952), j_dat)
coef(j_fit)
## (Intercept) I(year - 1952)
## 67.7901282 0.2385014</code></pre>
<div id="sidebar-regression-stuff" class="section level4">
<h4>Sidebar: regression stuff</h4>
<p>There are two things above that might prompt questions.</p>
<p>First, how did I know to get the estimated coefficients from a fitted model via <code>coef()</code>? Years of experience. But how might a novice learn such things? Read <a href="http://www.rdocumentation.org/packages/stats/functions/lm">the documentation for <code>lm()</code></a>, in this case. The “See also” section advises us about many functions that can operate on fitted linear model objects, including, but by no means limited to, <code>coef()</code>. Read <a href="http://www.rdocumentation.org/packages/stats/functions/coef">the documentation on <code>coef()</code></a> too.</p>
<p>Second, what am I doing here: <code>lm(lifeExp ~ I(year - 1952))</code>? I want the intercept to correspond to 1952 and an easy way to accomplish that is to create a new predictor on the fly: year minus 1952. The way I achieve that in the model formula, <code>I(year - 1952)</code>, uses the <code>I()</code> function which “inhibits interpretation/conversion of objects”. By protecting the expression <code>year - 1952</code>, I ensure it is interpreted in the obvious arithmetical way.</p>
</div>
</div>
<div id="turn-working-code-into-a-function" class="section level3">
<h3>Turn working code into a function</h3>
<p>Create the basic definition of a function and drop your working code inside. Add arguments and edit the inner code to match. Apply it to the practice data. Do you get the same result as before?</p>
<pre class="r"><code>le_lin_fit <- function(dat, offset = 1952) {
the_fit <- lm(lifeExp ~ I(year - offset), dat)
coef(the_fit)
}
le_lin_fit(j_dat)
## (Intercept) I(year - offset)
## 67.7901282 0.2385014</code></pre>
<p>I had to decide how to handle the offset. Given that I will scale this up to many countries, which, in theory, might have data for different dates, I chose to set a default of 1952. Strategies that compute the offset from data, either the main Gapminder dataset or the excerpt passed to this function, are also reasonable to consider.</p>
<p>I loathe the names on this return value. This is not my first rodeo and I know that, downstream, these will contaminate variable names and factor levels and show up in public places like plots and tables. Fix names early!</p>
<pre class="r"><code>le_lin_fit <- function(dat, offset = 1952) {
the_fit <- lm(lifeExp ~ I(year - offset), dat)
setNames(coef(the_fit), c("intercept", "slope"))
}
le_lin_fit(j_dat)
## intercept slope
## 67.7901282 0.2385014</code></pre>
<p>Much better!</p>
</div>
<div id="test-on-other-data-and-in-a-clean-workspace" class="section level3">
<h3>Test on other data and in a clean workspace</h3>
<p>It’s always good to rotate through examples during development. The most common error this will help you catch is when you accidentally hard-wire your example into your function. If you’re paying attention to your informal tests, you will find it creepy that your function returns <strong>exactly the same results</strong> regardless which input data you give it. This actually happened to me while I was writing this document, I kid you not! I had left <code>j_fit</code> inside the call to <code>coef()</code>, instead of switching it to <code>the_fit</code>. How did I catch that error? I saw the fitted line below, which clearly did not have an intercept in the late 60s and a positive slope, as my first example did. Figures are a mighty weapon in the fight against nonsense. I don’t trust analyses that have few/no figures.</p>
<pre class="r"><code>j_country <- "Zimbabwe"
(j_dat <- gapminder %>% filter(country == j_country))
## country continent year lifeExp pop gdpPercap
## 1 Zimbabwe Africa 1952 48.451 3080907 406.8841
## 2 Zimbabwe Africa 1957 50.469 3646340 518.7643
## 3 Zimbabwe Africa 1962 52.358 4277736 527.2722
## 4 Zimbabwe Africa 1967 53.995 4995432 569.7951
## 5 Zimbabwe Africa 1972 55.635 5861135 799.3622
## 6 Zimbabwe Africa 1977 57.674 6642107 685.5877
## 7 Zimbabwe Africa 1982 60.363 7636524 788.8550
## 8 Zimbabwe Africa 1987 62.351 9216418 706.1573
## 9 Zimbabwe Africa 1992 60.377 10704340 693.4208
## 10 Zimbabwe Africa 1997 46.809 11404948 792.4500
## 11 Zimbabwe Africa 2002 39.989 11926563 672.0386
## 12 Zimbabwe Africa 2007 43.487 12311143 469.7093
p <- ggplot(j_dat, aes(x = year, y = lifeExp))
p + geom_point() + geom_smooth(method = "lm", se = FALSE)</code></pre>
<p><img src="block012_function-regress-lifeexp-on-year_files/figure-html/second-example-scatterplot-1.png" alt="" /></p>
<pre class="r"><code>le_lin_fit(j_dat)
## intercept slope
## 55.22124359 -0.09302098</code></pre>
<p>The linear fit is comically bad, but yes I believe the visual line and the regression results match up.</p>
<p>It’s also a good idea to clean out the workspace, rerun the minimum amount of code, and retest your function. This will help you catch another common mistake: accidentally relying on objects that were lying around in the workspace during development but that are not actually defined in your function nor passed as formal arguments.</p>
<pre class="r"><code>rm(list = ls())
le_lin_fit <- function(dat, offset = 1952) {
the_fit <- lm(lifeExp ~ I(year - offset), dat)
setNames(coef(the_fit), c("intercept", "slope"))
}
le_lin_fit(gapminder %>% filter(country == "Zimbabwe"))
## intercept slope
## 55.22124359 -0.09302098</code></pre>
</div>
<div id="are-we-there-yet" class="section level3">
<h3>Are we there yet?</h3>
<p>Yes.</p>
<p>Given how I plan to use this function, I don’t feel the need to put it under formal unit tests or put in argument validity checks. Let’s move on to <a href="http://stat545-ubc.github.io/block023_dplyr-do.html">the exciting part</a>, which is scaling this up to <strong>all</strong> countries.</p>
</div>
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