Simple Functions

In previous chapters, we demonstrated how to enter data; read data from a spreadsheet, ascii file, or a database; and extract subsets of data. In this chapter, we discuss applying some simple functions to the data, such as the mean or the mean of a single data subset. These are functions that may be useful; however, they are not the tools that will convince you to become an R user. Use them when it is convenient. Upon first reading of the book, you may skip this chapter.

4.1 The tapply Function

R provides functions for calculating the mean, length, standard deviation, minimum, maximum, variance, and any other function of a single variable, multiple variables, or on subsets of observations. For illustration, we use a vegetation dataset. Sikkink et al. (2007) analysed grassland data from a monitoring program conducted in two temperate communities, Yellowstone National Park and the National Bison Range, USA. The aim of the study was to determine whether the biodiversity of these bunchgrass communities changed over time, and, if so, whether the changes in biodiversity related to particular environmental factors. For our purposes we use only the Yellowstone National Park data. To quantify biodiversity, the researchers calculated species richness, defined as the number of different species per site. The study identified about 90 species. The data were measured in 8 transects, with each transect being assessed at intervals of 4–10 years, for a total of 58 observations.

The following code can be used to import the data and gain basic information on the variables.

> setwd("C:/RBook/") > Veg <- read.table(file= "Vegetation2.txt", header= TRUE) > names(Veg) [1] "TransectName" "Samples" "Transect" [4] "Time"         "R" "ROCK" [7] "LITTER" "ML" "BARESOIL" [10] "FallPrec" "SprPrec" "SumPrec" [13] "WinPrec" "FallTmax" "SprTmax" [16] "SumTmax" "WinTmax" "FallTmin" [19] "SprTmin" "SumTmin" "WinTmin" [22] "PCTSAND" "PCTSILT" "PCTOrgC" > str(Veg) ‘data.frame’: 58 obs. of 24 variables: $ TransectName: Factor w/ 58 levels ... $ Samples : int 1 2 3 4 5 6 7 8 9 10 ... $ Transect : int 1 1 1 1 1 1 1 2 2 2 ... $ Time : int 1958 1962 1967 1974 1981 1994... $ R : int 8 6 8 8 10 7 6 5 8 6 ... $ ROCK : num 27 26 30 18 23 26 39 25 24 21 ... $ LITTER : num 30 20 24 35 22 26 19 26 24 16 ... <Cut to reduce space>

The data are stored in the ascii file “Vegetation2.txt.” Once the read.table function has been executed, we need to ensure that richness is indeed a numerical vector or integer. If, for some reason, R imports richness as a factor (e.g., because there is an alphanumerical in the column, or there are problems with the decimal separator), functions such as mean, sd, and the like will give an error message¹.

4.1.1 Calculating the Mean Per Transect

One of the first things we would like to know is whether the mean richness per transect differs. The code below calculates the mean richness, as well as mean richness for each transect (see Chapter 3 for selecting subsets of data):

> m <- mean(Veg$R) > m1<- mean(Veg$R[Veg$Transect == 1]) > m2<- mean(Veg$R[Veg$Transect == 2]) > m3<- mean(Veg$R[Veg$Transect == 3]) > m4<- mean(Veg$R[Veg$Transect == 4]) > m5<- mean(Veg$R[Veg$Transect == 5]) > m6<- mean(Veg$R[Veg$Transect == 6]) > m7<- mean(Veg$R[Veg$Transect == 7]) > m8<- mean(Veg$R[Veg$Transect == 8]) > c(m, m1, m2, m3, m4, m5, m6, m7, m8) [1] 9.965517 7.571429 6.142857 10.375000 9.250000 [6] 12.375000 11.500000 10.500000 11.833333

The variable m contains the mean richness of all 8 transects, and m1 through m8 show the mean richness values per transect. Note that the mean command is applied to Veg $R, which is a vector of data. It is not a matrix; hence there is no need for a comma between the square brackets.

4.1.2 Calculating the Mean Per Transect More Efficiently

It is cumbersome to type eight commands to calculate the mean value per transect. The R function tapply performs the same operation as the code above (for m1 through m8 ), but with a single line of code:

> tapply(Veg$R, Veg$Transect, mean) 1 2 3 4 5 7.571429 6.142857 10.375000 9.250000 12.375000 6 7 8 11.500000 10.500000 11.833333

You can also run this code as

> tapply(X = Veg$R, INDEX = Veg$Transect, FUN = mean)

The tapply function splits the data of the first variable (R), based on the levels of the second variable (Transect). To each subgroup of data, it applies a function, in this case the mean, but we can also use the standard deviation (function sd), variance (function var), length (function length), and so on. The following lines of code calculate some of these functions for the vegetation data.

> Me <- tapply(Veg$R, Veg$Transect, mean) > Sd <- tapply(Veg$R, Veg$Transect, sd) > Le <- tapply(Veg$R, Veg$Transect, length) > cbind(Me, Sd, Le) Me Sd Le 1  7.571429 1.3972763 7 2  6.142857 0.8997354 7 3 10.375000 3.5831949 8 4  9.250000 2.3145502 8 5 12.375000 2.1339099 8 6 11.500000 2.2677868 8 7 10.500000 3.1464265 6 8 11.833333 2.7141604 6

Each row in the output gives the mean richness, standard deviation, and number of observations per transect. In a later chapter we discuss graphic tools to visualise these values.

4.2 The sapply and lapply Functions

To calculate the mean, minimum, maximum, standard deviation, and length of the full series, we still need to use mean (Veg$R), min (Veg$R), max (Veg$R), sd (Veg$R), and length (Veg$R). This is laborious if we wish to calculate the mean of a large number of variables such as all the numerical variables of the vegetation data. We specifically say “numerical” as one cannot calculate the mean of a factor. There are 20 numerical variables in the vegetation dataset, columns 5–25 of the data frame Veg. However, we do not need to type in the mean command 20 times. R provides other functions similar to the tapply to address this situation: the lapply and the sapply. The use of sapply and its output is given below:

> sapply(Veg[, 5:9], FUN= mean) R ROCK LITTER ML BARESOIL 9.965517 20.991379 22.853448 1.086207 17.594828

To save space, we only present the results of the first five variables. It is important to realise that tapply calculates the mean (or any other function) for subsets of observations of a variable, whereas lapply and sapply calculate the mean (or any other function) of one or more variables, using all observations.

The word FUN stands for function, and must be written in capitals. Instead of the mean, you can use any other function as an argument for FUN, and you can write your own functions. So what is the difference between sapply and lapply? The major differences lie in the presentation of output, as can be seen in the following example.

> lapply(Veg[, 5:9], FUN= mean) $R [1] 9.965517 $ROCK [1] 20.99138 $LITTER [1] 22.85345 $ML [1] 1.086207 $BARESOIL [1] 17.59483

The output of lapply is presented as a list, whereas sapply gives it as a vector. The choice depends on the format in which you would like the output.

The variable that contains the data in lapply and sapply needs to be a data frame. This will not work:

> sapply(cbind(Veg$R, Veg$ROCK, Veg$LITTER, Veg$ML, Veg$BARESOIL), FUN = mean)

It will produce one long vector of data, because the output of the cbind command is not a data frame. It can easily be changed to a data frame:

> sapply(data.frame(cbind(Veg$R, Veg$ROCK, Veg$LITTER, Veg$ML, Veg$BARESOIL)), FUN = mean) X1 X2 X3 X4 X5 9.965517 20.991379 22.853448 1.086207 17.594828

Note that we have lost the variable labels. To avoid this, make a proper data frame (Chapter 2) before running the sapply function. Alternatively, use the colnames function after combining the data with the cbind function.

 Do Exercise 1 in Section 4.6. This is an exercise in the use of the tapply, sapply, and lapply functions with a temperature dataset.

4.3 The summary Function

Another function that gives basic information on variables is the summary command. The argument can be a variable, the output from a cbind command, or a data frame. It is run by the following commands.

> Z <-cbind(Veg$R, Veg$ROCK, Veg$LITTER) > colnames(Z) <- c("R", "ROCK", "LITTER") > summary(Z) R ROCK LITTER Min. : 5.000 Min. : 0.00 Min. : 5.00 1st Qu. : 8.000 1st Qu. : 7.25 1st Qu. :17.00 Median :10.000 Median :18.50 Median :23.00 Mean : 9.966 Mean :20.99 Mean :22.85 3rd Qu. :12.000 3rd Qu. :27.00 3rd Qu. :28.75 Max. :18.000 Max. :59.00 Max. :51.00

The summary command gives the minimum, first quartile, median, mean, third quartile, and maximum value of the variable. An alternative R code gives the same result:

> summary(Veg[ , c("R","ROCK","LITTER")])

or

> summary(Veg[ , c(5, 6, 7)])

Output is not presented here.

4.4 The table Function

In Exercises 1 and 7 in Section 2.4, we introduced the deer data from Vicente et al. (2006). The data were from multiple farms, months, years, and sexes. One of the aims of the study was to find a relationship between length of the animal and the number of E. cervi parasites. It may be the case that this relationship changes with respect to sex, year, month, farm, or even year and month. To test this, one needs to include interactions in the statistical models. However, problems may be encountered if there are no sampled females in some years, or if some farms were not sampled in every year. The table function can be used to learn how many animals per farm were sampled, as well as the number of observations per sex and year. The following code imports the data, and shows the results.

> setwd("c:/RBook/") > Deer <- read.table(file="Deer.txt", header= TRUE) > names (Deer) [1] "Farm" "Month" "Year" "Sex" "clas1_4" [6] "LCT" "KFI" "Ecervi" "Tb" > str(Deer) [1] "Farm" "Month" "Year" "Sex" "clas1_4" [6] "LCT" "KFI" "Ecervi" "Tb" > str(Deer) ‘data.frame’: 1182 obs. of 9 variables: $ Farm : Factor w/ 27 levels"AL","AU","BA",..: 1... $ Month : int 10 10 10 10 10 10 10 10 10 10 ... $ Year : int 0 0 0 0 0 0 0 0 0 0 ... $ Sex : int 1 1 1 1 1 1 1 1 1 1 ... $ clas1_4 : int 4 4 3 4 4 4 4 4 4 4 ... $ LCT : num 191 180 192 196 204 190 196 200 19 ... $ KFI : num 20.4 16.4 15.9 17.3 NA ... $ Ecervi : num 0 0 2.38 0 0 0 1.21 0 0.8 0 ... $ Tb : int 0 0 0 0 NA 0 NA 1 0 0 ...

Farm has been coded as AL, AU, and so on, and is automatically imported as a factor. The other variables are all vectors of numerical or integer values. The number of observations per farm is obtained by

> table(Deer$Farm) AL AU BA BE CB CRC HB LCV LN MAN MB 15 37 98 19 93 16 35 2 34 76 41 MO NC NV PA PN QM RF RÑ RO SAL SAU 278 32 35 11 45 75 34 25 44 1 3 SE TI TN VISO VY 26 21 31 15 40

At one farm, 278 animals were sampled and, at others, only one. This dataset typically requires a mixed effects modelling² approach in which “farm” is used as a random effect (see Zuur et al., 2009). This method can cope with unbalanced designs. However, the inclusion of a sex/year interaction term³ in such models for these data will give an error message. This is because both sexes were not measured in every year, as can be seen from the following contingency table. (The labels 0, 1, 2, 3, 4, 5, and 99 in the horizontal direction refer to 2000, 2001, 2002, 2003, 2004, 2005, and 1999, respectively. In the vertical direction 1 and 2 indicate sex).

> table(Deer$Sex, Deer$Year) 0 1 2 3 4 5 99 1 115 85 154 75 78 34 21 2 76 40 197 123 60 35 0

In 1999, animals of only one sex were measured. We recommend always using the table command before including interactions between two categorical variables in regression type models.

 Do Exercise 2 in Section 4.6. This is an exercise in using the table function with a temperature dataset.

4.5 Which R Functions Did We Learn?

Table 4.1 shows the R functions that were introduced in this chapter.

Table 4.1 R functions introduced in this chapter

4.6 Exercises

Exercise 1. The use of the tapply, sapply, and lapply functions to calculate mean temperature per month.

The file temperature.xls contains temperature observations made at 31 locations along the Dutch coastline. The data were collected and provided by the Dutch institute RIKZ (under the monitoring program MWTL; Monitoring Waterstaatkundige Toestand des Lands). Sampling began in 1990, and the final measurements in the spreadsheet were taken in December 2005, a period of 16 years. Sampling frequency was 0–4 times per month, depending on the season.

Calculate a one-time series of monthly averages using data from all stations. The end result should be a variable of dimension 16 × 12. Also calculate the standard deviation and number of observations per month.

Exercise 2. The use of the table function for the temperature data.

Using the data in Exercise 1, determine the number of observations per station. How many observations were made per year? How many observations were made at each station per year?