## Less wordy R

The Swarm Lab presents a nice comparison of R and Python code for a simple (read ‘one could do it in Excel’) problem. The example works, but I was surprised by how wordy the R code was and decided to check if one could easily produce a shorter version.

The beginning is pretty much the same, although I’ll use ggplot2 rather than lattice, because it will be a lot easier (and shorter) to get the desired appearance for the plots:

The whole example relies on only three variables and—as I am not great at typing—I tend to work with shorter variable names. I directly changed the names for variables 1 to 3:

It is a lot easier to compare the regression lines if we change the shape of the data set from wide to long, where there is one variable for year, one for tax type, and one for the actual tax rate. It would be possible to use one of Hadley’s packages to get a simpler syntax for this, but I decided to stick to the minimum set of requirements:

And now we are ready to produce the plots. The first one can be a rough cut to see if we get the right elements:

Yes, this one has the points, lines, linear regression and 95% confidence intervals for the mean predicted responses, but we still need to get rid of the grey background and get black labels (theme_bw()), set the right axis labels and ticks (scale_x... scale_y...) and set the right color palette for points and lines (scale_colour_manual) and filling the confidence intervals (scale_colour_fill) like so:

One can still change font sizes to match the original plots, reposition the legend, change the aspect ratio while saving the png graphs (all simple statements) but you get the idea. If now we move to fitting the regression lines:

This gives the regression coefficients for Corporate (3.45 – 1.564e-04 year) and Individual ([3.45 + 4.41] + [-1.564e-04 + 1.822e-04] year or 7.84 + 2.58e-05 year). As a bonus you get the comparison between regression lines.

In R as a second language I pointed out that ‘brevity reduces the time between thinking and implementation, so we can move on and keep on trying new ideas’. Some times it seriously does.

## R as a second language

Imagine that you are studying English as a second language; you learn the basic rules, some vocabulary and start writing sentences. After a little while, it is very likely that you’ll write grammatically correct sentences that no native speaker would use. You’d be following the formalisms but ignoring culture, idioms, slang and patterns of effective use.

R is a language and any newcomers, particularly if they already know another programming language, will struggle at the beginning to get what is beyond the formal grammar and vocabulary. I use R for inquisition: testing ideas, data exploration, visualization; under this setting, the easiest is to perform a task the more likely is one going to do it. It is possible to use several other languages for this but—and I think this is an important but—R’s brevity reduces the time between thinking and implementation, so we can move on and keep on trying new ideas.

A typical example is when we want to repeat something or iterate over a collection of elements. In most languages if one wants to do something many times the obvious way is using a loop (coded like, for() or while()). It is possible to use a for() loop in R but many times is the wrong tool for the job, as it increases the lag between thought and code, moving us away from ‘the flow’.

One of the distinctive features of R is that there is already a lot of functionality available for jobs that occur frequently in data analysis. The easiest is to perform a task the more likely is one going to do it, which is perfect if one is exploring/thinking about data.

Thomas Lumley reminded me of the ACM citation for John Chambers—father of S of which R is an implementation—which stated that Chambers’s work:

…will forever alter the way people analyze, visualize, and manipulate data . . . S is an elegant, widely accepted, and enduring software system, with conceptual integrity, thanks to the insight, taste, and effort of John Chambers.

If I could summarize the relevance of R in a Tweetable phrase (with hash tags and everything) it would be:

Most data analysis languages underestimate the importance of interactivity/low barrier to exploration. That’s where #Rstats shines.

One could run statistical analyses with many languages (including generic ones), but to provide the right level of interactivity for analysis, visualization and data manipulation one ends up creating functions that, almost invariably, look a bit like R; pandas in Python, for example.

There are some complications with some of the design decisions in R, especially when we get down to consistency which begets memorability. A glaring example is the apply family of functions and here is where master opportunist (in the positive sense of expert at finding good opportunities) Hadley Wickham made sense out of confusion in his package plyr.

There is also a tension in languages under considerable use because speakers/writers/analysts/coders start adapting them to new situations, adding words and turns of phrase. Look at English for an example! This is also happening to R and some people wish the language looked different in some non-trivial ways. A couple of examples: Coffeescript for R and Rasmus Bååth’s suggestions. Not all of them can be implemented, but suggestions like this speak of the success of R.

If you are struggling to start working with R, as with other languages, first let go. The key to learning and working with a new language is immersing yourself in it; even better if you do it with people who already speak it.

Just to be clear, there are several good statistical languages. However, none is as supportive of rapid inquisition as R (IMO). It is not unusual to develop models in one language (e.g. R) and implement it in another for operational purposes (e.g. SAS, Python, whatever).

The first thing I admire about Hadley is his ‘good eye’ for finding points of friction. The second one is doing something about the frictions, often with very good taste.

P.S. It should come clear from this post that English is indeed my second language.

## Teaching linear models

I teach several courses every year and the most difficult to pull off is FORE224/STAT202: regression modeling.

The academic promotion application form in my university includes a section on one’s ‘teaching philosophy’. I struggle with that part because I suspect I lack anything as grandiose as a philosophy when teaching: as most university lecturers I never studied teaching, although I try to do my best. If anything, I can say that I enjoy teaching and helping students to ‘get it’ and that I want to instill a sense of ‘statistics is fun’ in them. I spend quite a bit of time looking for memorable examples, linking to stats in the news (statschat and listening the news while walking my dog are very helpful here) and collecting data. But a philosophy? Don’t think so.

One of the hardest parts of the course is the diversity of student backgrounds. Hitting the right level, the right tone is very hard. Make it too easy and the 1/5 to 1/4 of students with a good mathematical background will hate it; they may even decide to abandon any intention of continuing doing stats if ‘that’s all there is about the topic’. Make it too complicated and half the class will fail and/or hate the content.

Part of the problem is based around what we mean by teaching ‘statistics’. In some cases it seems limited to what specific software does; for example, teaching with Excel means restriction to whatever models are covered in Excel’s Data Analysis Toolpak (DAT). The next choice when teaching is using menu-driven software (e.g. SPSS), which provides much more statistical functionality than Excel + DAT, at the expense of being further removed from common usability conventions. At the other extreme of simplicity is software that requires coding to control the analyses (e.g. R or SAS). In general, the more control we want, the more we have to learn to achieve it.

A while ago I made a distinction between the different levels of learning (user cases) when teaching statistics. In summary, we had i- very few students getting in to statistics and heavy duty coding, ii- a slightly larger group that will use stats while in a while and iii- the majority that will mostly consume statistics. I feel a duty towards the three groups, while admitting that I have predilection for the first one. Nevertheless, the third group provides most of the challenges and need for thinking about how to teach the subject.

When teaching linear models (general form $$y = X eta + epsilon$$) we tend to compartmentalize content: we have an ANOVA course if the design matrix $$X$$ represents categorical predictors (contains only 1s and 0s), a regression course if $$X$$ is full of continuous predictors and we talk about ANCOVA or regression on dummy variables if $$X$$ is a combination of both. The use of different functions for different contents of $$X$$ (for example aov() versus lm() in R or proc reg versus proc glm in SAS) further consolidates the distinction. Even when using menus, software tends to guide students through different submenus depending on the type of $$X$$.

At the beginning of the course we restrict ourselves to $$X$$ full of continuous predictors, but we introduce the notion of matrices with small examples. This permits showing the connection between all the linear model courses (because a rose by any other name…) and it also allows deriving a general expression of the formulas for the regression coefficients (essential for the most advanced students). Slower students may struggle with some of this material; however, working with small examples they can replicate the results from R (or Excel or SAS or whatever one uses to teach). Some times they even think it is cool.

Here is where the model.matrix() R function becomes handy; rather than building incidence matrices by hand—which is easy for tiny examples—we can get the matrices used by the lm() function to then calculate regression parameters (and any other output) for more complex models.

Once students get the idea that on matrix terms our teaching compartments are pretty much the same, we can reinforce the idea by using a single function (or proc) to show that we can obtain all the bits and pieces that make up what we call ‘fitting the model’. This highlights the idea that ANOVA, ANCOVA & regression are subsets of linear models, which are subsets of linear mixed models, which are subsets of generalized linear mixed models. A statistical Russian doll.

We want students to understand, some times so badly that we lower the bar to a point where there is no much to understand. Here is the tricky part, finding the right level of detail so all types of students learn to enjoy the topic, although at different levels of understanding.

There is software that generates code from menus too, like Stata or Genstat.

P.S. This is part of my thinking aloud with hesitation about teaching, as in Statistics unplugged, Excel, fanaticism and R, Split-plot 1: How does a linear mixed model look like?, R, academia and the democratization of statistics, Mid-January flotsam: teaching edition & Teaching with R: the switch. I am always looking for better ways of transferring knowledge.

## Statistics unplugged

How much does statistical software help and how much it interferes when teaching statistical concepts? Software used in the practice of statistics (say R, SAS, Stata, etc) brings to the party a mental model that it’s often alien to students, while being highly optimized for practitioners. It is possible to introduce a minimum of distraction while focusing on teaching concepts, although it requires careful choice of a subset of functionality. Almost invariably some students get stuck with the software and everything goes downhill from there; the student moved from struggling with a concept to struggling with syntax (Do I use a parenthesis here?).

I am a big fan of Tim Bell’s Computer Science Unplugged, a program for teaching Computer Science’s ideas at primary and secondary school without using computers (see example videos).

Here is an example video for public key encryption:

This type of instruction makes me question both how we teach statistics and at what level we can start teaching statistics. The good news is that the New Zealand school curriculum includes statistics in secondary school, for which there is increasing number of resources. However, I think we could be targeting students even earlier.

This year my wife was helping primary school students participating in a science fair and I ended up volunteering to introduce them to some basic concepts so they could design their own experiments. Students got the idea of the need for replication, randomization, etc based on a simple question: Did one of them have special powers to guess the result of flipping a coin? (Of course this is Fisher’s tea-drinking-lady-experiment, but no 10 year old cares about tea, while at least some of them care about super powers). After the discussion one of them ran a very cool experiment on the effect of liquefaction on the growth of native grasses (very pertinent in post-earthquake Christchurch), with 20 replicates (pots) for each treatment. He got the concepts behind the experiment; software just entered the scene when we needed to confirm our understanding of the results in a visual way:

People tell me that teaching stats without a computer is like teaching chemistry without a lab or doing astronomy without a telescope, or… you get the idea. At the same time, there are some books that describe some class activities that do not need a computer; e.g. Gelman’s Teaching Statistics: A Bag of Tricks. (Incidentally, why is that book so friggin’ expensive?)

## Back to uni

Back from primary school kiddies to a regression course at university. Let’s say that we have two variables, x & y, and that we want to regress y (response) on x (predictor) and get diagnostic plots. In R we could simulate some data and plot the relationship using something like this:

We can the fit the linear regression and get some diagnostic plots using:

If we ask students to explain the 4th plot—which displays discrepancy (how far a point is from the general trend) on leverage (how far is a point from the center of mass, pivot of the regression)—many of them will struggle to say what is going on in that plot. At that moment one could go and calculate the Hat matrix of the regression ($$X (X’X)^{-1} X’$$) and get leverage from the diagonal, etc and students will get a foggy idea. Another, probably better, option is to present the issue as a physical system on which students already have experience. A good candidate for physical system is using a seesaw, because many (perhaps most) students experienced playing in one as children.

Take your students to a playground (luckily there is one next to uni), get them playing with a seesaw. The influence of a point is related to the product of leverage (how far from the pivot we are applying force) and discrepancy (how big is the force applied). The influence of a point on the estimated regression coefficients will be very large when we apply a strong force far from the pivot (as in our point y[100]), just as it happens in a seesaw. We can apply lots of force (discrepancy) near the pivot (as in our point [y[50]) and little will happen. Students like mucking around with the seesaw and, more importantly, they remember.

Analogy can go only so far. Some times a physical analogy like a quincunx (to demonstrate the central limit theorem) ends up being more confusing than using an example with variables that are more meaningful for students.

I don’t know what is the maximum proportion of course content that could be replaced by using props, experiments, animations, software specifically designed to make a point (rather than to run analysis), etc. I do know that we still need to introduce ‘proper’ statistical software—at some point students have to face praxis. Nevertheless, developing an intuitive understanding is vital to move from performing monkeys; that is, people clicking on menus or going over the motion of copy/pasting code without understanding what’s going on in the analyses.

I’d like to hear if you have any favorite demos/props/etc when explaining statistical concepts.

P.S. In this post I don’t care if you love stats software, but I specifically care about helping learners who struggle understanding concepts.

## Using Processing and R together (in OS X)

I wanted to develop a small experiment with a front end using the Processing language and the backend calculations in R; the reason why will be another post. This post explained the steps assuming that one already has R and Processing installed:

1. Install the Rserve package. This has to be done from source (e.g. using R CMD INSTALL packagename).
2. Download Rserve jar files and include them in the Processing sketch.

For example, this generates 100 normal distributed random numbers in R and then sorts them (code copy and pasted from second link):

The problem is that this didn’t work, because my OS X (I use macs) R installation didn’t have shared libraries. My not-so-quick solution was to compile R from source, which involved:

1. Downloading R source. I went for the latest stable version, but I could have gone for the development one.
2. Setting up the latest version of C and Fortran compilers. I did have an outdated version of Xcode in my macbook air, but decided to delete it because i- uses many GB of room in a small drive and ii- it’s a monster download. Instead I went for Apple’s Command Line Tools, which is a small fraction of size and do the job.
3. In the case of gfortran, there are many sites pointing to this page that hosts a fairly outdated version, which was giving me all sorts of problems (e.g. “checking for Fortran 77 name-mangling scheme”) because the versions between the C and Fortran compilers were out of whack. Instead, I downloaded the latest version from the GNU site.
4. Changing the config.site file in a few places, ensuring that I had:

Then compiled using (didn’t want X11 and enabling shared library):

And finally installed using:

This used a prefix because I didn’t want to replace my fully functioning R installation, but just having another one with shared libraries. If one types R in terminal then it is still calling the old version; the new one is called via /luis/compiled/R.framework/Versions/Current/Resources/bin/R. I then installed Rserve in the new version and was able to call R from processing so I could obtain.

Now I can move to what I really wanted to do. File under stuff-that-I-may-need-to-remember-one-day.

## Excel, fanaticism and R

This week I’ve been feeling tired of excessive fanaticism (or zealotry) of open source software (OSS) and R in general. I do use a fair amount of OSS and pushed for the adoption of R in our courses; in fact, I do think OSS is a Good ThingTM. I do not like, however, constant yabbering on why using exclusively OSS in science is a good idea and the reduction of science to repeatability and computability (both of which I covered in my previous post). I also dislike the snobbery of ‘you shall use R and not Excel at all, because the latter is evil’ (going back ages).

We often have several experiments running during the year and most of the time we do not bother setting up a data base to keep data. Doing that would essentially mean that I would have to do it, and I have a few things more important to do. Therefore, many data sets end up in… (drum roll here) Microsoft Excel.

How should a researcher setup data in Excel? Rather than reinventing the wheel, I’ll use a(n) (im)perfect diagram that I found years ago in a Genstat manual.

I like it because:

• It makes clear how to setup the experimental and/or sampling structure; one can handle any design with enough columns.
• It also manages any number of traits assessed in the experimental units.
• It contains metadata in the first few rows, which can be easily skipped when reading the file. I normally convert Excel files to text and then I skip the first few lines (using skip in R or firstobs in SAS).

People doing data analysis often start convulsing at the mention of Excel; personally, I deeply dislike it for analyses but it makes data entry very easy, and even a monkey can understand how to use it (I’ve seen them typing, I swear). The secret for sane use is to use Excel only for data entry; any data manipulation (subsetting, merging, derived variables, etc.) or analysis is done in statistical software (I use either R or SAS for general statistics, ASReml for quantitative genetics).

It is far from a perfect solution but it fits in the realm of the possible and, considering all my work responsibilities, it’s a reasonable use of my time. Would it be possible that someone makes a weird change in the spreadsheet? Yes. Could you fart while moving the mouse and create a non-obvious side effect? Yes, I guess so. Will it make your life easier, and make possible to complete your research projects? Yes sir!

P.S. One could even save data using a text-based format (e.g. csv, tab-delimited) and use Excel only as a front-end for data entry. Other spreadsheets are of course equally useful.

P.S.2. Some of my data are machine-generated (e.g. by acoustic scanners and NIR spectroscopy) and get dumped by the machine in a separate—usually very wide; for example 2000 columns—text file for each sample. I never put them in Excel, but read them directly (a directory-full of them) in to R for manipulation and analysis.

As an interesting aside, the post A summary of the evidence that most published research is false provides a good summary for the need to freak out about repeatability.

## Flotsam 13: early July links

Man flu kept me at home today, so I decided to do something ‘useful’ and go for a linkathon:

Sometimes people are truthful and cruel. Here Gappy on a mission goes for the jugular:

Over and out.

## My take on the USA versus Western Europe comparison of GM corn

A few days ago I came across Jack Heinemann and collaborators’ article (Sustainability and innovation in staple crop production in the US Midwest, Open Access) comparing the agricultural sectors of USA and Western Europe. While the article is titled around the word sustainability, the main comparison stems from the use of Genetically Modified crops in USA versus the absence of them in Western Europe.

I was curious about part of the results and discussion which, in a nutshell, suggest that “GM cropping systems have not contributed to yield gains, are not necessary for yield gains, and appear to be eroding yields compared to the equally modern agroecosystem of Western Europe”. The authors relied on several crops for the comparison (Maize/corn, rapeseed/canolasee P.S.6, soybean and cotton); however, I am going to focus on a single one (corn) for two reasons: 1. I can’t afford a lot of time for blog posts when I should be preparing lectures and 2. I like eating corn.

When the authors of the paper tackled corn the comparison was between the USA and Western Europe, using the United Nations definition of Western Europe (i.e. Austria, Belgium, France, Germany, Liechtenstein, Luxembourg, Monaco, Netherlands, Switzerland). Some large European corn producers like Italy are not there because of the narrow definition of Western.

I struggled with the comparison used by the authors because, in my opinion, there are potentially so many confounded effects (different industry structures, weather, varieties, etc.) that it can’t provide the proper counterfactual for GM versus non-GM crops. Anyway, I decided to have a look at the same data to see if I would reach the same conclusions. The article provides a good description of where the data came from, as well as how the analyses were performed. Small details to match exactly the results were fairly easy to figure out. I downloaded the FAO corn data (3.7 MB csv file) for all countries (so I can reuse the code and data later for lectures and assignments). I then repeated the plots using the following code:

I could obtain pretty much the same regression model equations as in the article by expressing the years as deviation from 1960 as in:

Heinemann and collaborators then point out the following:

…the slope in yield increase by year is steeper in W. Europe (y?=?1344.2x?+?31512, R²?=?0.92084) than the United States (y?=?1173.8x?+?38677, R²?=?0.89093) from 1961 to 2010 (Figure 1). This shows that in recent years W. Europe has had similar and even slightly higher yields than the United States despite the latter’s use of GM varieties.

However, that interpretation using all data assumes that both ‘countries’ are using GMO all the time. An interesting thing is that USA and Western Europe were in different trends already before the introduction of GM corn. We can state that because we have some idea of when GM crops were introduced in the USA. This information is collected by the US Department of Agriculture in their June survey to growers and made publicly available at the State level (GMcornPenetration.csv):

This graph tells us that by the year 2000 the percentage of planted corn was way below 50% in most corn producing states (in fact, it was 25% at the country level). From that time on we have a steady increase reaching over 80% for most states by 2008. Given this, it probably makes sense to assume that, at the USA level, yield reflects non-GM corn until 1999 and progressively reflects the effect of GM genotypes from 2000 onwards. This division is somewhat arbitrary, but easy to implement.

We can repeat the previous analyzes limiting the data from 1961 until, say, 1999:

These analyses indicate that Western Europe started with a lower yield than the USA (29,802.17 vs 39,895.57 hectograms/ha) and managed to increase yield much more quickly (1,454.48 vs 1,094.82 hectograms/ha per year) before any use of GM corn by the USA. Figure 1 shows a messy picture because there are numerous factors affecting yield each year (e.g. weather has a large influence). We can take averages for each decade and see how the two ‘countries’ are performing:

This last figure requires more attention. We can again see that Western Europe starts with lower yields than the USA; however, it keeps on increasing those yields faster than USA, overtaking it during the 1990s. Again, all this change happened while both USA and Western Europe were not using GM corn. The situation reverses in the 2000s, when the USA overtakes Western Europe, while the USA continuously increased the percentage of GM corn. The last bar in Figure 3 is misleading because it includes a single year (2010) and we know that yields in USA went down in 2011 and 2012, affected by a very large drought (see Figure 4).

At least when looking at corn, I can’t say (with the same data available to Heinemann) that there is no place or need for GM genotypes. I do share some of his concerns with respect to the low level of diversity present in staple crops but, in contrast to his opinion, I envision a future for agriculture that includes large-scale operations (either GM or no-GM), as well as smaller operations (including organic ones). I’d like to finish with some optimism looking further back to yield, because the USDA National Agricultural Statistics Service keeps yield statistics for corn since 1866(!) (csv file), although it uses bizarre non-metric units (bushels/acre). As a metric boy, I converted to kilograms per hectare (multiplying by 62.77 from this page) and then to hectograms (100 g) multiplying by 10.

It is interesting to see that there was little change until the 1940s, with the advent of the Green Revolution (modern breeding techniques, fertilization, pesticides, etc.). The 2010s decade in Figure 4 includes 2010, 2011 and 2012, with the last two years reflecting extensive droughts. Drought tolerance is one of the most important traits in modern breeding programs.

While Prof. Heinemann and myself work for the same university I don’t know him in person.

P.S. Did you know that Norman Borlaug (hero of mine) studied forestry?
P.S.2 Time permitting I’ll have a look at other crops later. I would have liked to test a regression with dummy variables for corn to account for pre-2000 and post-1999, but there are not yet many years to fit a decent model (considering natural variability between years). We’ll have to wait for that one.
P.S.3 I share some of Heinemann’s concerns relating to subsidies and other agricultural practices.
P.S.4 In case anyone is interested, I did write about a GM-fed pigs study not long ago.
P.S.5 2013-07-05 20:10 NZST. I updated Figures 1 and 3 to clearly express that yield was in hectograms/ha and recalculated average decade yield because it was originally averaging yields rather calculating total production and area for the decade and then calculating average yield. The discussion points I raised are still completely valid.
P.S.6 2013-07-07 11:30 NZST. The inclusion of Canadian canola does not make any sense because, as far as I know, Canada is not part of Western Europe or the US Midwest. This opens the inclusion of crops from any origin as far as the results are convenient for one’s argument.
P.S.7 2014-08-06 13:00 NZST My comment was expanded and published in the journal (or here for HTML version with comments on the authors’ reply to my comment.

## Flotsam 12: early June linkathon

A list of interesting R/Stats quickies to keep the mind distracted:

• A long draft Advanced Data Analysis from an Elementary Point of View by Cosma Shalizi, in which he uses R to drive home the message. Not your average elementary point of view.
• Good notes by Frank Davenport on starting using R with data from a Geographic Information System (GIS). Read this so you get a general idea of how things fit together.
• If you are in to maps, Omnia sunt Communia! provides many good tips on producing them using R.
• Mark James Adams reminded us that Prediction ? Understanding, probably inspired by Dan Gianola‘s course on Whole Genome Prediction. He is a monster of Bayesian applications to genetic evaluation.
• If you are in to data/learning visualization you have to watch Bret Victor’s presentation on Media for thinking the unthinkable. He is so far ahead what we normally do that it is embarrassing.
• I follow mathematician Atabey Kaygun in twitter and since yesterday I’ve been avidly reading his coverage of the protests in Turkey. Surely there are more important things going on in the world than the latest R gossip.

I’m marking too many assignments right now to have enough time to write something more substantial. I can see the light at the end of the tunnel though.

## Analyzing a simple experiment with heterogeneous variances using asreml, MCMCglmm and SAS

I was working with a small experiment which includes families from two Eucalyptus species and thought it would be nice to code a first analysis using alternative approaches. The experiment is a randomized complete block design, with species as fixed effect and family and block as a random effects, while the response variable is growth strain (in $$mu epsilon$$).

When looking at the trees one can see that the residual variances will be very different. In addition, the trees were growing in plastic bags laid out in rows (the blocks) and columns. Given that trees were growing in bags siting on flat terrain, most likely the row effects are zero.

Below is the code for a first go in R (using both MCMCglmm and ASReml-R) and SAS. I had stopped using SAS for several years, mostly because I was running a mac for which there is no version. However, a few weeks ago I started accessing it via their OnDemand for Academics program via a web browser.

The R code using REML looks like:

While using MCMC we get estimates in the ballpark by using:

The SAS code is not that disimilar, except for the clear demarcation between data processing (data step, for reading files, data transformations, etc) and specific procs (procedures), in this case to summarize data, produce a boxplot and fit a mixed model.

I like working with multiple languages and I realized that, in fact, I missed SAS a bit. It was like meeting an old friend; at the beginning felt strange but we were quickly chatting away after a few minutes.