I just read about a website, accidental aRt, that shows how artistic R graphics can look when things go bad. Wonderful!
When I first heard of SSA (Singular Spectrum Analysis) and the EMD (Empirical Mode Decomposition) I though surely I’ve found a couple of magical methods for decomposing a time series into component parts (trend, various seasonalities, various cycles, noise). And joy of joys, it turns out that each of these methods is implemented in R packages:
In this posting, I’m going to document some of my explorations of the two methods, to hopefully paint a more realistic picture of what the packages and the methods can actually do. (At least in the hands of a non-expert such as myself.)
In a previous series of postings, I described a model that I developed to predict monthly electricity usage and expenditure for a condo association. I based my model on the average monthly temperature at a nearby NOAA weather station at Ronald Reagan Airport (DCA), because the results are reasonable and more importantly because I can actually obtain forecasts from NOAA up to a year out.
The small complication is that the NOAA forecasts cover three-month periods rather than single month: JFM (Jan-Feb-Mar), FMA (Feb-Mar-Apr), MAM (Mar-Apr-May), etc. So, in this posting, we’ll briefly describe how to turn a series of these overlapping three-month forecasts into a series of monthly approximations.
I’m always intrigued by techniques that have cool names: Support Vector Machines, State Space Models, Spectral Clustering, and an old favorite Hidden Markov Models (HMM’s). While going through some of my notes, I stumbled onto a fun experiment with HMM’s where you feed a bunch of English text into a two-state HMM and it will (tend to) discover what letters are vowels.
I did a quick Google search on “Stata for R users” (both as separate words and as a quoted phrase) and there really isn’t much out there. At best, there are a couple of equivalence guides that show you how to do certain tasks in both programs. (Plus a whole lot of “R for (ex-) Stata users” articles.) I’m writing this post, as a long-term R user who recently bought Stata, because I believe that Stata is a good complement to R, and many R users should consider adding it to their toolbox.
I’m going to write this in two parts. Part one will describe why an R user might be interested in Stata — with various Stata examples. Part Two will give specific tips and warnings to R users who do decide to use Stata.
In Part 4 of this series, I created a Bayesian model in Stan. A member of the Stan team, Bob Carpenter, has been so kind as to send me some comments via email, and has given permission to post them on the blog. This is a great opportunity to get some expert insights! I’ll put his comments as block quotes:
That’s a lot of iterations! Does the data fit the model well?
I hadn’t thought about this. Bob noticed in both the call and the summary results that I’d run Stan for 300,000 iterations, and it’s natural to wonder, “Why so many iterations? Was it having trouble converging? Is something wrong?” The
stan command defaults to four chains, each with 2,000 iterations, and one of the strengths of
Stan‘s HMC algorithm is that the iterations are a bit slower than other methods but it mixes much faster so you don’t need nearly as many iterations. So 300,000 is a bit excessive. It turns out that if I run for 2,000 iterations, it takes 28 seconds on my laptop and mixes well. Most of the 28 seconds is taken up by compiling the model, since I can get 10,000 iterations in about 40 seconds.
So why 300,000 iterations? For the silly reason that I wanted lots of samples to make the CI’s in my plot as smooth as possible. Stan is pretty fast, so it only took a few minutes, but I hadn’t thought of implication of appearing to need that many iterations to converge.
Last time, we modeled the Association’s electricity expenditure using Bayesian Analysis. Besides the fact that MCMC and Bayesian are sexy and resume-worthy, what have we gained by using
Stan? MCMC runs more slowly than alternatives, so it had better be superior in other ways, and in this posting, we’ll look at an example of how. I’d recommend pulling the previous posting up in another browser window or tab, and position the “Inference for Stan model” table so that you can quickly consult it in the following discussion.
If you look closely at the numbers, you may notice that the high season (warmer-high, ratetemp 3, beta) appears to have a lower slope than the mid season (warmer-low, ratetemp 2, beta), as was the case in an earlier model. This seems backwards: the high season should cost more per additional kWh, and thus should have a higher slope. This raises two questions: 1) is the apparent slope difference real, and 2) if it is real, is there some real-world basis for this counter-intuitive result?
There’s a new R-related website out there: Rdocumentation, which gathers the documentation for most R packages (that are hosted on CRAN) in one place and allows you to search through it.
There are a couple major benefits to the site:
- It also provides a comments area where you can share thoughts, questions, and tips on various packages or even individual functions. (Though we’ll have to see if a critical mass builds for this.)
- If you search in your own R installation with ?? you will only search the packages you have installed. I’m a package junkie, so have a huge number installed, but it’s still nice to have a place where I can discover new packages more easily.
So check it out and make suggestions to the creators. This should really be rolled into CRAN at some point.
This is the fourth article in the series, where the techiness builds to a crescendo. If this is too statistical/programming geeky for you, the next posting will return to a more investigative and analytical flavor. Last time, we looked at a fixed-effects model:
m.fe <- lm (dollars ~ 1 + regime + ratetemp * I(dca - 55))
which looks like a plausible model and whose parameters are all statistically significant. A question that might arise is: why not use a hierarchical (AKA multilevel, mixed-effects) model instead? While we’re at it, why not go full-on Bayesian as well? It just so happens that there is a great new tool called
Stan which fits the bill and which also has an
rstan package for
In a previous installment, we looked at modeling electricity usage for the infrastructure and common areas of a condo association, and a fairly simple model was reasonably accurate. This makes sense in a large system such as mid-sized, high-rise condo building, which has a lot of electricity-usage inertia. The cost of that electricity has a lot more variability, however, because of rate changes (increases and decreases), refunds, high/low seasons, and other factors that affect the bottom line.
In a previous installment, we described a condo association that needed to know what its electricity budget should be for an upcoming budget. In this posting, we’ll develop a model for electricity utilization, leaving electricity expenses for the next installment.
I like to have pretty pictures above the fold, so let’s take a look at the data and the resulting model, all in one convenient and colorful graph. The graph shows each month’s average daily electricity usage (in kilowatt hours, kWh) versus the month’s average temperature at nearby Ronald Reagan Airport (DCA). Each month’s bill is a point at the center of the month name:
This is the story of a condominium association in Northern Virginia, which was in the midst of transforming their budget. In the early days of the association they didn’t have an operational cash reserve built up, so they had to make budget categories a bit oversized, “just in case”. As time went on, they saved the cash from their over-estimates, and eventually arrived at the place where they could set tighter budgets and depend on their cash savings if the budget were exceeded.
In the process of reviewing various categories, they came to “Utilities”, which lumped water, sewage, gas, and electricity all together. They decided to break it down into individual utilities, but when they started with electricity, no one actually knew how much was used nor how much it cost. The General Manager had dutifully filed away monthly bills from Dominion, but didn’t have a spreadsheet. They needed a data analyst, and I was all over it.
In the next four or five postings, I want to show some of the details of my investigation of electricity expenses. I hope it will be an interesting look at the kinds of things that happen in the real world, not just textbooks. Oh, by the way, it turns out that electricity was the single largest operating expense of the association. Here’s a graph of average expenditures, brought up to the present:
The reshape function in R is very useful, but poorly documented. Wingfeet, over at Wiekvoet, has written a well-illustrated article on reshape that steps through SAS’ transpose examples and shows how that’s done with R’s reshape.
This is a quick introduction to using R, the R package `knitr`, and the markdown language to automatically generate monthly reports.
Let’s say I track electricity usage and expenses for a client. I initially spent a lot of time analyzing and making models for the data, but at this point I’m now in more of a maintenance mode and simply want an updated report to email each month. So, when their new electricity bill arrives I scrape the data into R, save the data in an R workspace, and then use knitr to generate a simplistic HTML report.
Good news about R is it has thousands of packages. Bad news about R is that it has thousands of packages, and often it’s difficult to know which wavelet packages, for example, do what.
On his blog, Wes has provided a concise, illustrated tour of the major tree/forest packages in R. Go and gain clarity.
Everyone’s interested in the global climate these days, so I’ve been looking at the GISTEMP temperature series, from the GISS (NASA’s Goddard Institute for Space Studies). I was recently analyzing the data and it turned into an interesting data forensics operation that I hope will inspire you to dig a little deeper into your data.
Let’s start with the data. GISS has a huge selection of data for the discerning data connoisseur, so which to choose? The global average seems too coarse — the northern and southern hemispheres are out of phase and dominated by different geography. On the other hand, the gridded data is huge and requires all kinds of spatially-saavy processing to be useful. (We may go there in a future post, but not today.) So let’s start with the two hemisphere monthly average datasets, which I’ll refer to as GISTEMP NH and GISTEMP SH.
To be specific, these time series are GISTEMP LOTI (Land Ocean Temperature Index) which means that they cover both land and sea. GISS has land-only data and combines this with NOAA’s sea-only data from ERSST (Extended Reconstructed Sea Surface Temperature). I’d also point out that all of the temperature data I’ll use is measured as an anomaly from the average temperature over the years 1951-1980, which was approximately 14 degrees Celsius (approximately 57 degrees Farenheit). So let’s plot the GISTEMP LOTI NH and SH data and see what we have.