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Now, on to today's main course.

For cyclical data, it's sometimes useful to generate rolling averages-- the average of some number of recent measurements, usually one full cycle. For example, for retail sales, one might want the rolling average of the most recent week. The rolling average will dampen the effects of repeated patterns but still show the location of the data.

In keeping with our habit of plotting personal data (e.g.,

Example 8.11,

Example 8.12,

example 10.1,

Example 10.2), I'll use my own weight recorded over the past 6 months. After reading about "alternate day dieting" in

The Atlantic, I decided to try the diet described in the book by

Varady. I've never really tried to diet for weight loss before, but this diet has worked really well for me over the past six months. The basics are that you eat 500 calories every other day (diet days) and on the non-diet days you eat what you want. There's a little science supporting the approach. I can't really recommend the book, unfortunately, unless you're a fan of the self-help style.

As you can imagine, one's weight tends to fluctuate pretty wildly between diet days and non-diet days. The cycle is just two days, but to get a sense of my weight at any given time, it might be best to use the rolling average of the past, say, four days.

The beginning of the data, available from

http://www.amherst.edu/~nhorton/sasr2/datasets/weight.txt, follows.

1/11/14 219

1/12/14 NA

1/13/14 219

1/14/14 NA

1/15/14 221.8

1/16/14 218

...

**R**As you can tell from the

`NA`s, I compiled the data with the intent to read it into R.

> weights = read.table("c:/temp/weight.txt")

> head(weights)

V1 V2

1 1/11/14 219.0

2 1/12/14 NA

3 1/13/14 219.0

4 1/14/14 NA

5 1/15/14 221.8

6 1/16/14 218.0

Note, though, that the date values are just character strings (read in as a factor variable), and not so useful as read in.

> str(weights)

'data.frame': 161 obs. of 2 variables:

$ V1: Factor w/ 161 levels "1/11/14","1/12/14",..: 1 2 3 4 5 6 7 8 9 10 ...

$ V2: num 219 NA 219 NA 222 ...

The

`lubridate` package contributed by the invaluable

Hadley Wickham contains functions to make it easier to use dates in R. Here, I use its

`mdy()` function to convert characters values into R dates.

library(lubridate)

with(weights, plot(V2 ~ mdy(V1),

xlim = c(mdy("1/1/14"),mdy("6/30/14")),

ylab="Weight", xlab="Date"))

The simple plot has enough values that you can clearly see the trend of weight loss over time, and perhaps the rolling average exercise is somewhat misplaced, here. To calculate the rolling average, I adapted (below) the lag function from section 2.2.18 (2nd edition; 1.4.17 in the 1st ed.)-- this is a simpler version that does not check for errors. The result of

`lag(x,k)` is a vector with the first

`k` values missing and with the remaining values being the beginning values of

`x`. Thus the

*i*th value of

`lag(x,k)` is

`x[i-k]`. To get the rolling average, I just take the mean of several lags. Here I use the

`rowMeans()` function to do it for all the values at once. The

`lines()` function adds the rolling average to the plot.

lag = function(x,k) {

return( c(rep(NA,k), x[1:(length(x)-k)]) )

}

y = weights$V2

ra = rowMeans(

matrix(c(y,lag(y,1),lag(y,2),lag(y,3)),ncol=4,byrow=F),

na.rm=T)

lines(mdy(weights$V1),ra)

The final plot is shown above. Note that the the initial values of the lagged vector are missing, as are weights for several dates throughout this period. The

`na.rm=T` option causes

`rowMeans()` to return the mean of the observed values-- equivalent to a single

imputation of the mean of the observed values, which perhaps Nick will allow me in this setting (note from NH: I don't have major issues with this). There are also two periods where I failed to record weights for four days running. For these periods,

`rowMeans()` returns NaN, or "Not a Number". This is usefully converted to regions in the plot where the running average line is not plotted. Compare, for instance, with the default SAS behavior shown below. For the record, I was ill in early May and had little appetite regardless of my dieting schedule.

**SAS**The data can be easily read with the

`input` statement. The

`mmddyy7.` informat tells SAS that the data in the first field are as many as 7 characters long and should be read as dates. SAS will store them as SAS dates (section 2.4 in the 2nd edition; 1.6 in the 1st edition). As the data are read in, I use the

`lagk` functions (section 2.2.18 2nd edition; 1.4.17 in the 1st ed.) to recall the values from recent days and calculate the rolling average as I go.

data weights;

infile "c:tempweight.txt";

input date mmddyy7. weight;

ra = mean(weight,lag(weight), lag2(weight), lag3(weight));

run;

Note that the

`input` statement expects the weight values to be numbers, and interprets the

`NA`s in the data as "Invalid data". It inserts missing values into the data set, which is what we desire. The

`mean` function provides the mean of the non-missing values. When the weight and all of the lagged values of weight are missing, it will return a missing value. With the rolling average in hand, I can plot the observed weights and the rolling average. To print Julian dates rather than SAS dates, use the

`format` statement to tell SAS that the

`date` variable should be printed using the

`date.` format.

symbol1 i = none v=dot c = blue;

symbol2 i = j v = none c = black w=5;

proc gplot data = weights;

plot (weight ra)*date /overlay;

format date date.;

run;

The results are shown below. The main difference from the R plot is that the gaps in my recording do not appear in the line. The SAS

`symbol` statement, the equivalent of the

`lines()` function, more or less, does not encounter NaNs, but only missing values, and so it connects the points. I think R's behavior is more appropriate here-- there's no particular reason to suppose a linear interpolation between the observed data points is best, and so the line ought to be missing.

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