Category: teaching

Comment on Sustainability and innovation in staple crop production in the US Midwest

After writing a blog post about the paper “Sustainability and innovation in staple crop production in the US Midwest” I decided to submit a formal comment to the International Journal of Agricultural Sustainability in July 2013, which was published today. As far as I know, Heinemann et al. provided a rebuttal to my comments, which I have not seen but that should be published soon. This post is an example on how we can use open data (in this case from the USDA and FAO) and free software (R) to participate in scientific discussion (see supplementary material below).

The text below the *** represents my author’s version provided as part of my Green Access rights. The article published in the International Journal of Agricultural Sustainability [copyright Taylor & Francis]; is freely available online at http://dx.doi.org/10.1080/14735903.2014.939842).

While I had many issues with the original article, I decided to focus on three problems—to make the submission brief and fit under the 1,000 words limit enforced by the journal editor. The first point I make is a summary of my previous post on the article, and then move on to two big problems: assuming that only the choice of biotechnology affects yield (making the comparison between USA and Western Europe inadequate) and comparing use of agrochemicals at the wrong scale (national- versus crop-level).

PS 2014-08-05 16:30: Heinemann et al.’s reply to my comment is now available.

  • They state that “Apiolaza did not report variability in the annual yield data” and that they had to ‘reconstruct’ my figure. Firstly, the published figure 2 does include error bars and, secondly, the data and R code are available as supplementary information (in contrast to their original paper). Let’s blame the journal for not passing this information to them.
  • They also include 2 more years of data (2011 & 2012), although the whole point of my comment is that the conclusions they derived with the original data set were not justified. Heinemann et al. are right in that yields in 2011 & 2012 were higher in Western Europe than in the USA (the latter suffering a huge drought); however, in 2013 it was the opposite: 99,695 Hg/ha for USA vs 83,724 Hg/ha for Western Europe.
  • They question that I commented only on one crop, although I did cover another crop (wheat) quickly with respect to the use of pesticides—but not with the detail I wanted, as there was a 1,000 words limit. I would have also mentioned the higher variability for Western European wheat production, as it is weird that they pointed out that high variability is a problems for USA maize production but said nothing for wheat in Europe.
  • Furthermore, they also claimed “There is no statistically significant difference in the means over the entire 50-year period” however, a naive paired t-test t.test(FAOarticle$Yield[1:50], FAOarticle$Yield[51:100], paired = TRUE) (see full code below) says otherwise.

***

Abstract

This comment highlight issues when comparing genetically modified (GM) crops to non-GM ones across countries. Ignoring structural differences between agricultural sectors and assuming common yield trajectories before the time of introduction of GM crops results on misestimating the effect of GM varieties. Further data collection and analyses should guide policy-makers to encourage diverse approaches to agriculture, rather than excluding specific technologies (like GM crops) from the onset.

Keywords: genetic modification; biotechnology; productivity; economics

In a recent article Heinemann et al. (2013) focused “on the US staple crop agrobiodiversity, particularly maize” using the contrast between the yield of Western Europe and United States as a proxy for the comparison between genetically modified (GM) maize versus non-GM maize. They found no yield benefit from using GM maize when comparing the United States to Western Europe.

In addition, Heinemann et al. contrasted wheat yields across United States and Western Europe to highlight the superiority of the European biotechnological package from a sustainability viewpoint.

I am compelled to comment on two aspects that led the authors to draw incorrect conclusions on these issues. My statistical code and data are available as supplementary material.

1. Misestimating the effect of GM maize varieties

Heinemann et al. used FAO data[↓], from 1961 to 2010 inclusive, to fit linear models with yield as the response variable, country and year as predictors. Based on this analysis they concluded, “W. Europe has benefitted from the same, or marginally greater, yield increases without GM”. However, this assumes a common yield trajectory for United States and Western Europe before significant commercial use of GM maize, conflating GM and non-GM yields. GM maize adoption in United States has continually increased from 25% of area of maize planted in 2000 to the current 90% (Figure 1, United States Department of Agriculture 2013[↓]).

Figure 1: Adoption of GM maize in United States, expressed as percentage of planted area.
Figure 1: Adoption of GM maize in United States, expressed as percentage of total maize planted area (click to enlarge).

If we fit a linear model from 1961 to 1999 (last year with less than 25% area of GM maize) we obtain the following regression equations \(y = 1094.8 x + 39895.6\) (United States, R2 = 0.80) and \(y = 1454.5 x + 29802.2\) (W. Europe, R2 = 0.90). This means that Western Europe started with a considerably lower yield than the USA (29,802.2 vs 39,895.6 hg/ha) in 1961 but increased yields faster than USA (1,454.5 vs 1,094.8 hg/ha per year) before substantial use of GM maize. By 1999 yield in Western Europe was superior to that in United States.

This is even more evident in Figure 2, which shows average yield per decade, removing year-to-year extraneous variation (e.g. due to weather). Western European yields surpassed United States’s during the 1990s (Figure 2). This trend reverses in the 2000s, while United States simultaneously increased the percentage of planted area with GM maize, directly contradicting Heinemann et al.’s claim.

Figure 2: Average maize yield (and standard error) per decade for United States and Western Europe. The 2010s include a single year to replicate the original data set (click to enlarge).
Figure 2: Average maize yield (and standard error) per decade for United States and Western Europe. The 2010s include a single year to replicate the original data set (click to enlarge).

2. Ignoring structural differences between agricultural sectors

When discussing non-GM crops using wheat the authors state, “the combination of biotechnologies used by W. Europe is demonstrating greater productivity than the combination used by the United States”. This sentence summarizes one of the central problems of their article: assuming that, if it were not for the choice of biotechnology bundle, the agricultural sectors would have the same intrinsic yield, making them comparable. However, many inputs beside biotechnology affect yield. For example, Neumann et al. (2010) studied the spatial distribution of yield and found that in the Unites States “access can explain most of the variability in wheat efficiency. In the more remote regions land prices are lower and inputs are therefore often substituted by land leading to lower efficiencies”. Lower yields in United States make sense from an economic point of view, as land replaces more expensive inputs like agrochemicals.

Heinemann et al. support their case by comparing pesticide use between United States and France across all crops. However, what is relevant to the discussion is pesticide use for the crops being compared. European cereals, and wheat in particular, are the most widely fungicide-treated group of crops worldwide (Kucket al. 2012). For example, 27% of the wheat planted area in France was already treated with fungicides by 1979 (Jenkins and Lescar 1980). More than 30 years later in the United States this figure has reached only 19% for winter wheat (which accounts for 70% of planted area, NASS 2013). Fungicide applications result on higher yield responses (Oerke 2006).

Final remarks

Heinemann et al. ignored available data on GM adoption when analysing maize yields. They also mistakenly treated biotechnological bundles as the only/main explanation for non-GMO yield differences between United States and Western Europe. These issues mean that the thrust of their general conclusion is unsupported by the available evidence. Nevertheless, their article also raised issues that deserve more consideration; e.g. the roles of agricultural subsidies and market concentration on food security.

Agricultural sustainability requires carefully matching options in the biotechnology portfolio to site-specific economic, environmental and cultural constraints. Further data collection and analyses should lead policy makers to encourage diverse approaches to agriculture, rather than excluding specific technologies (like GMOs and pesticides) from the onset.

References

Heinemann, J. A., Massaro, M., Coray, D. S., Agapito-Tenfen, S. Z. and Wen, J. D. 2013. Sustainability and innovation in staple crop production in the US Midwest. International Journal of Agricultural Sustainability (available here).

Jenkins, J. E. E. and Lescar, L. 1980. Use of foliar fungicides on cereals in Western Europe. Plant Disease, 64(11): 987-994 (behind paywall).

Kuck, K. H., Leadbeater, A. and Gisi, U. 2012. FRAC Mode of Action Classification and Resistance Risk of Fungicides. In: Krämer, W., Schirmer, U., Jeschke, P. and Witschel, M., eds., Modern Crop Protection Compounds. Wiley. 539-567.

NASS, 2013. Highlights: 2012 Agricultural Chemical Use Survey. Wheat. United States Department of Agriculture (available here).

Neumann, K., Verburg, P. H., Stehfest, E., and Müller, C. 2010. The yield gap of global grain production: a spatial analysis. Agricultural Systems, 103(5), 316–326 (behind paywall).

Oerke E. 2006. Crop losses to pests. Journal of Agriculture Science, 144: 31-43 (behind paywall, or Free PDF).

United States Department of Agriculture. 2013. Adoption of Genetically Engineered Crops in the U.S. USDA Economic Research Service (available here).

Supplementary material

You can replicate the analyses and plots produced in this comment using the following files:

  • Maize production data for United States and Western Europe (csv, extracted from FAO). [↑]
  • GMO maize penetration data (csv, extracted from USDA). [↑]
  • R code for analyses (R file, changed extension to .txt so WordPress would not complain).

Sometimes I feel (some) need for speed

I’m the first to acknowledge that most of my code could run faster. The truth of the matter is that, in essence, I write ‘quickies’: code that will run once or twice, so there is no incentive to spend days or hours in shaving seconds of a computation. Most analyses of research data fall in to this approach: read data-clean data-fit model-check model-be happy-write article-(perhaps) make data and code available-move on with life.

One of the reasons why my code doesn’t run faster or uses less memory is the trade-off between the cost of my time (very high) compared to the cost of more memory or faster processors (very cheap) and the gains of shaving a few seconds or minutes of computer time, which tend to be fairly little.

In R vectorization is faster than working with each vector element, although it implies allocating memory for whole vectors and matrices, which for large-enough problems may become prohibitively expensive. On the other hand, not vectorizing some operations may turn your problem into an excruciatingly slow exercise and, for example in large simulations, in practice intractable in a useful timeframe.

Dealing with vectors and matrices is like dealing with many chairs simultaneously. Some patterns and operations are easier and faster than others. (Photo: Luis, click to enlarge).
Dealing with vectors and matrices is like dealing with many chairs simultaneously. Some patterns and operations are easier and faster than others. (Photo: Luis, click to enlarge).

John Muschelli wrote an interesting post reimplementing 2×2 frequency tables for a highly specific use, comparing the results of image processing algorithms. In John’s case, there are two greater-than-9-million-long-elements logical vectors, and when comparing vectors for many images the process becomes very slow. He explains part of his rationale in his blog (go and read it), but say that his solution can be expressed like this:

which uses 1/4 of the time used by table(manual, auto). Mission accomplished! However, if I stopped here this blog post would not make much sense, simply rehashing (pun intended) John’s code. The point is to explain what is going on and, perhaps, to find even faster ways of performing the calculations. As a start, we have to be aware that the calculations in logical.tab() rely on logical (boolean) operations and on the coercion of logical vectors to numerical values, as stated in the documentation:

Logical vectors are coerced to integer vectors in contexts where a numerical value is required, with TRUE being mapped to 1L, FALSE to 0L and NA to NA_integer_.

In R Logical operations can be slower than mathematical ones, a consideration that may guide us to think of the problem in a slightly different way. For example, take the difference between the vectors (dif = x - y), so both TRUE-TRUE (1-1) and FALSE-FALSE (0-0) are 0, while TRUE - FALSE (1-0) is 1 and FALSE - TRUE (0-1) is -1. Therefore:

  • the sum of positive values (sum(dif > 0)) is the frequency of TRUE & FALSE,
  • while the sum of negative values (sum(dif < 0)) is the frequency of FALSE & TRUE.

The values for TRUE & TRUE can be obtained by adding up the element-wise multiplication of the two vectors, as TRUE*TRUE (1*1) is the only product that's different from zero. A vectorized way of performing this operation would be to use t(x) %*% y; however, for large vectors the implementation crossprod(x, y) is faster. The values for FALSE & FALSE are simply the difference of the length of the vectors and the previously calculated frequencies length(dif) - tt - tf - ft. Putting it all together:

This code takes 1/20 of the time taken by table(x, y). An interesting result is that the crossproduct crossprod(x, y) can also be expressed as sum(x * y), which I didn't expect to be faster but, hey, it is. So we can express the code as:

to get roughly 1/22 of the time. The cost of logical operations is easier to see if we isolate particular calculations in logical.tab and basic.tab; for example,

is slower than

This also got me thinking of the cost of coercion: Would it take long? In fact, coercing logical vectors to numeric has little (at least I couldn't see from a practical viewpoint) if any cost. In some cases relying on logical vectors converted using as.numeric() seems to be detrimental on terms of speed.

As I mentioned at the beginning, vectorization uses plenty of memory, so if we were constrained in that front and we wanted to do a single pass on the data we could write an explicit loop:

The loopy.tab does only one pass over the vectors and should use less memory as it doesn't need to create those huge 10M elements vectors all the time (at least it would if we used a proper iterator in the loop instead of iterating on a vector of length 10M (that's 40 MB big in this case). The iterators package may help here). We save room/memory at the expense of speed, as loopy.tab is ten times slower than the original table() function. Of course one could run it a lot faster if implemented in another language like C++ or Fortran and here Rcpp or Rcpp11 would come handy (updated! See below).

This is only a not-so-short way of reminding myself what's going on when trading-off memory, execution speed and my personal time. Thus, I am not saying that any of these functions is the best possible solution, but playing with ideas and constraints that one often considers when writing code. Incidentally, an easy way to compare the execution time of these functions is using the microbenchmark library. For example:

will spit numbers when running a couple of functions 1,000 times with results that apply to your specific system.

PS 2014-07-12 11:08 NZST Hadley Wickham suggests using tabulate(manual + auto * 2 + 1, 4) as a fast alternative. Nevertheless, I would like to point out that i- the initial tabulation problem is only an excuse to discuss a subset of performance issues when working with R and ii- this post is more about the journey than the destination.

PS 2014-07-13 20:32 NZST Links to two posts related to this one:

  • Wiekvoet's work which i- relies on marginals and ii- reduces the use of logical operators even more than my basic.tab2(), simultaneously taking around 1/4 of the time.
  • Yin Zhu's post describing vectors is a handy reminder of the basic building blocks used in this post.

Updated with Rcpp goodness!

PS 2014-07-13 21:45 NZST I browsed the Rcpp Gallery and Hadley Wickham's Rcpp tutorial and quickly converted loopy.tab() to C++. Being a bit of an oldie I've used Fortran (90, not that old) before but never C++, so the following code is probably not very idiomatic.

Loops and all it runs roughly twice as fast as basic.tab2() but it should also use much less memory.

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’.

How apply loops around a matrix or data frame (Shaky handwriting and all).
How apply loops around a matrix or data frame, doing its business for all rows [1] or columns [2] (Shaky handwriting and all).

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 \(X\).

Gliding in a hierarchy of models (Photo: Luis, click to enlarge).
Gliding in a hierarchy of models (Photo: Luis, click to enlarge).

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:

Seven-week growth of native grasses with three proportions of liquefied soil.
Seven-week growth of native grasses with three proportions of liquefied soil. T1: pure liquefaction, T2: 50% liquefaction, 50% normal soil, T3: pure normal soil.

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:

Typical simple linear regression scatterplot.
Typical simple linear regression scatterplot.

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

Typical diagnostic plot for simple linear regression model. What's the meaning of the fourth plot (lower right)?
Typical diagnostic plot for simple linear regression model. What’s the meaning of the fourth plot (lower right)?

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.

Compulsory seesaw picture (source Wikipedia).
Compulsory seesaw picture (source Wikipedia).

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.
  3. Run your code

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.

A 'hello world' of the calling R from Processing world.
A ‘hello world’ of the calling R from Processing world.

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.

Suggested sane data setup in a spreadsheet.
Suggested sane data setup in a spreadsheet.

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.

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:

Figure 1. Corn yield per year for USA and Western Europe (click to enlarge).
Figure 1. Corn yield per year for USA and Western Europe (click to enlarge).

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):

GM corn percentage by state in the USA.
Figure 2. GM corn percentage by state in the USA (click to enlarge).

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:

Figure 3. Corn yield by decade (click to enlarge).
Figure 3. Corn yield by decade (click to enlarge).

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.

Historic average yield per decade for USA (click to enlarge).
Figure 4. Historic average yield per decade for USA (click to enlarge).

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.

Drought’s Footprint map produced by The New York Times (click on graph to view larger version in the NYT).
Drought’s Footprint map produced by The New York Times (click on graph to view larger version in the NYT). This can help to understand the Decade patterns in previous figures.

‡ 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.

GM-fed pigs, chance and how research works

Following my post on GM-fed pigs I received several comments, mostly through Twitter. Some people liked having access to an alternative analysis, while others replied with typical anti-GM slogans, completely ignoring that I was posting about the technical side of the paper. This post is not for the slogan crowd (who clearly are not interested in understanding), but for people that would like to know more about how one would evaluate claims from a scientific article. While I refer to the pig paper, most issues apply to any paper that uses statistics.

In general, researchers want to isolate the effect of the treatments under study (diets in this case) from any other extraneous influence. We want control over the experimental conditions, so we can separate the effects of interest from all other issues that could create differences between our experimental units (pigs in this case). What could create ‘noise’ in our results? Animals could have different genetic backgrounds (for example with different parents), they could be exposed to different environmental conditions, they could be treated differently (more kindly or harshly), etc.

Once we control those conditions as much as possible we would randomly assign animals to each of the treatments (diets). The rationale behind random allocation is easy to follow. Let’s say that we can see that some animals are healthier than others before starting the trial. If I had a pro-GM agenda, I could assign the healthiest animals to the GM-diet and we would not be able to separate the effect of the treatment from the initial difference. To avoid this, we could have many labels in a hat, shake the hat, and for each pig take a label that randomly assigns the pig to a diet so the comparison is fair.

Researchers also like to have a baseline of the conditions before the treatments are applied. This way we can ‘adjust’ the results by any pre-existing differences. For example, there could be measurable differences on health, size, etc. I normally work with trees in experiments and we routinely assess the height of the trees just planted, so we can establish a baseline.

Finally, we often have a ‘default’ treatment which represents the status quo and acts as a comparison point for the new treatments. In the GM pig case, the default is a non-GM diet and the new treatment is the GM-diet.

The paper on GM fed pigs states that they tried to have as much control as possible of the growing conditions and that they used random allocation to the two feeding treatments. I have no problems with the paper up to this point.

When doing research it is good manners to state one’s expectations before the start of the trial. Doing this provides the experimenter with guidance about how to proceed with the evaluation of the experiment:

  1. What are the characteristics under study? Both the response variables (in the past called ‘dependent variables’) and the predictors (old name ‘independent variables’).
  2. What is the magnitude of the differences between groups that we would consider practically significant? Put another way, what would be the size of the difference that one would care about? For example, if we have two groups of pigs and the difference on weight between them is 1 g (0.035 ounces for people with funny units), who cares? If the difference was 5 kg (11 pounds, funny units again) then, perhaps, we are in to something.
  3. What level of statistical significance we consider appropriate? Even if we assume that truly there is no difference between the two diets, we would expect to see small differences between the two groups just by chance. Big differences are more unlikely. It is common in research to state that a difference is statistically significant if the probability of observing the difference is smaller than, say, 0.05 (or 1 in 20). There is nothing sacred about the number but just a convention.

By this stage one would expect a researcher to state one or more hypotheses to be tested. For example, ‘I expect that the GM diet will increase [condition here] by [number here] percent’. One can run an experiment ignoring ‘good manners’, but (and this is a big but) an informed reader will become suspicious if suddenly one starts testing hypotheses like there is no tomorrow. Why? Because if one conducts too many tests one is bound to find statistically significant results even when there are none.

The comic below presents a brief example with jelly beans assuming that we claim significance for an event occurring with probability 0.05 (1 in 20) or less. Notice that the scientists use 20 colors of jelly beans and find that green ones ’cause’ acne. Running so many tests—without adjusting down the probability of the event that we would call significant, so p needs to be much smaller than 0.05 to be significant—results in wrong conclusions.

XKCD explaining significance (click for original, larger version). p refers to the probability of observing that result if jelly beans have no effect on acne.
XKCD explaining significance (click for original, larger version).

In the pig paper there are 8 tests in Table 2, 18 (or 15 with some value) in Table 3, 8 in Table 4 and 17 in Table 5 for a total of 49 (or 46 with some testable values). In fact one would expect to find a couple of significant results (at 0.05 or 1 in 20) by chance even if there are absolutely no differences in reality.

Add to this that many of the tests are unnecessary, because they are performing the wrong type of analysis. For example, there are four separate analyses for stomach inflammation; however, the analysis ignores the type of variable one is testing as I point out in a previous post.

This is why, if I were Monsanto, I would use the paper as evidence supporting the idea that there is no difference between the two diets:

  1. the paper was ‘independent’ (although the authors have a clear anti-GM bias) and
  2. when running proper analyses (accounting for the type of variable and the number of tests that one is running) no difference is statistically significant.

P.S. 2013-06-21. 15:38 NZST A footnote about data availability: it is becoming increasingly common to make both the data and code used to analyze the data available when publishing (part of Open Science). I would expect that a paper that is making bold claims that could have policy implications would provide those, which does not happens in this case. However, the publication does include part of the data in results Tables 3 & 4, in the counts of pigs under different classes of inflammation.

Subsetting data

At School we use R across many courses, because students are supposed to use statistics under a variety of contexts. Imagine their disappointment when they pass stats and discovered that R and statistics haven’t gone away!

When students start working with real data sets one of their first stumbling blocks is subsetting data. We have data sets and either they are required to deal with different subsets or there is data cleaning to do. For some reason, many students struggle with what should be a simple task.

If one thinks of data as as a matrix/2-dimensional array, subsetting boils down to extracting the needed rows (cases) and columns (variables). In the R world one can do this in a variety of ways, ranging from the cryptic to the explicit and clear. For example, let’s assume that we have a dataset called alltrials with heights and stem diameters for a number of trees in different trials (We may have a bunch of additional covariates and experimental design features that we’ll ignore for the moment). How do we extract all trees located in Christchurch?

Two common approaches are:

While both expressions are equivalent, the former reads like Klingon to students, while the latter makes explicit that we are obtaining a subset of the original data set. This can easily be expanded to more complex conditions; for example to include all trees from Christchurch that are taller than 10 m:

I think the complication with the Klingonian notation comes mostly from two sources:

  • Variable names for subsetting the data set are not directly accessible, so we have to prefix them with the NameOfDataset$, making the code more difficult to read, particularly if we join several conditions with & and |.
  • Hanging commas: if we are only working with rows or columns we have to acknowledge it by suffixing or prefixing with a comma, which are often forgotten.

Both points result on frustrating error messages like

  • Error in [.data.frame(alltrials, location == 'Christchurch', ) : object 'location' not found for the first point or
  • Error in [.data.frame(alltrials, alltrials$location == 'Christchurch') undefined columns selected for the second point.

The generic forms of these two notations are:

We often want to keep a subset of the observed cases and keep (or drop) specific variables. For example, we want to keep trees in ‘Christchurch’ and we want to ignore diameter, because the assessor was ‘high’ that day:

There are, however, situations where Klingon is easier or more efficient. For example, to take a random sample of 100 trees from the full dataset:

If you are interested in this issue Quick-R has a good description of subsetting. I’m sure this basic topic must has been covered many times, although I doubt anyone used Klingon in the process.

Gratuitous picture: building blocks for research (Photo: Luis).
Gratuitous picture: building blocks for R (Photo: Luis).