R Data Types - Part 2: Factors

摘抄自 Factors in R，部分删改和注释。

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1. Basis

Factors are used to represent categorical data. Factors can be unordered or ordered. One can think of a factor as an integer vector where each integer has a label.

One of the most important uses of factors is in statistical modeling (e.g. linear modelling); since categorical variables enter into statistical models differently than continuous variables, storing data as factors insures that the modeling functions will treat such data correctly.

Factors in R are stored as a vector of integer values with a corresponding set of character values (labels) to use when the factor is displayed. The factor function is used to create a factor. The only required argument to factor is a vector of values which will be returned as a vector of factor values. Both numeric and character variables can be made into factors, but a factor’s levels will always be character values. You can see the possible levels for a factor through the levels command.

Factors represent a very efficient way to store character values, because each unique character value is stored only once, and the data itself is stored as a vector of integers. Because of this, read.table will automatically convert character variables to factors unless the as.is= argument is specified.

2. Levels and Labels

下面介绍下 levels 和 labels 参数。假设有：

> data = c(1,1,1,1,2,2,2,2,2,3,3,3,3,3,3) # 4个1，5个2，6个3

2.1 “levels=” is for input

默认情况下，level 值就是元素 toString()，然后顺序也是自然顺序:

> fdata = factor(data)
> fdata
 [1] 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3
Levels: 1 2 3

可以指定 levels=xxx 指定 factor 按这个顺序去分类。下面这个还是指定按正常顺序分类，和默认的效果一样：

> fdata = factor(data, levels=c(1, 2, 3))
> fdata
 [1] 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3
Levels: 1 2 3

这里指定按 (2, 1, 3) 这样的顺序去分类：

> fdata = factor(data, levels=c(2, 1, 3))
> fdata
 [1] 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3
Levels: 2 1 3

转成 table 可能更能说明问题一些：

> table(fdata)
fdata
2 1 3 
5 4 6 

你看表头的排序就是 (2, 1, 3)

如果指定的 levels 和实际的 level 值不符，则会得到 NA

> fdata = factor(data, levels=c("a", "b", "c"))
> fdata
 [1] <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA>
[15] <NA>
Levels: a b c

ordered：logical flag to determine if the levels should be regarded as ordered (in the order given). 感觉就是是标记参数，为 TRUE 时就好像在宣称：我这个 factor 是 Ordered 的哟

> fdata = factor(data, levels=c(2, 1, 3), ordered=TRUE)
> fdata
 [1] 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3
Levels: 2 < 1 < 3

这个 2 < 1 < 3 是逻辑排序，并不是表示大小关系，你可以理解为是一种人为定的 sequence。

2.2 “labels=” is for output

labels 参数是用来给 levels 附新值的，但是要注意这样会实际改掉 factor 元素的值：

> fdata = factor(data, labels=c("I", "II", "III"))
> fdata
 [1] I   I   I   I   II  II  II  II  II  III III III III III III
Levels: I II III

它和下面这种方式是等价的：

> levels(fdata) = c('I','II','III')
> fdata
 [1] I   II  II  III I   II  III III I   II  III III I
Levels: I II III

fdata = factor(data, labels=c("I", "II", "III")) 应该这么理解：按默认的 level=c(1, 2, 3) 给 data 分类，然后得到的三个类别再分别改名为 (“I”, “II”, “III”)，顺带把元素值也改了。

3. More on “ordered=TRUE”

As an example of an ordered factor, consider data consisting of the names of months:

> mons = c("March","April","January","November","January",
+ "September","October","September","November","August",
+ "January","November","November","February","May","August",
+ "July","December","August","August","September","November",
+ "February","April")
> mons = factor(mons)
> table(mons)
mons
	April    August  December  February   January      July
	2         4         1         2         3         1
	March       May  November   October September
	1         1         5         1         3

Although the months clearly have an ordering, this is not reflected in the output of the table function. Additionally, comparison operators are not supported for unordered factors. Creating an ordered factor solves these problems:

> mons = factor(mons,levels=c("January","February","March",
+               "April","May","June","July","August","September",
+               "October","November","December"),ordered=TRUE)
> mons[1] < mons[2]
[1] TRUE
> table(mons)
mons
	January  February     March     April       May      June
	3         2         1         2         1         0
	July    August September   October  November  December
	1         4         3         1         5         1

4. Covert Factor to Numeric

While it may be necessary to convert a numeric variable to a factor for a particular application, it is often very useful to convert the factor back to its original numeric values, since even simple arithmetic operations will fail when using factors. Since the as.numeric function will simply return the internal integer values of the factor, the conversion must be done using the levels attribute of the factor. Suppose we are studying the effects of several levels of a fertilizer on the growth of a plant. For some analyses, it might be useful to convert the fertilizer levels to an ordered factor:

> fert = c(10,20,20,50,10,20,10,50,20)
> fert = factor(fert,levels=c(10,20,50),ordered=TRUE)
> fert
[1] 10 20 20 50 10 20 10 50 20
Levels: 10 < 20 < 50

If we wished to calculate the mean of the original numeric values of the fert variable, we would have to convert the values using the levels function:

> mean(fert)
[1] NA
Warning message:
argument is not numeric or logical: 
	  returning NA in: mean.default(fert)
> mean(as.numeric(levels(fert)[fert]))
[1] 23.33333

Indexing the return value from the levels function is the most reliable way to convert numeric factors to their original numeric values.

5. Exclude Elements

When a factor is first created, all of its levels are stored along with the factor, and if subsets of the factor are extracted, they will retain all of the original levels. This can create problems when constructing model matrices and may or may not be useful when displaying the data using, say, the table function. As an example, consider a random sample from the letters vector, which is part of the base R distribution.

> lets = sample(letters,size=100,replace=TRUE)
> lets = factor(lets)
> table(lets[1:5])

a b c d e f g h i j k l m n o p q r s t u v w x y z
1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1

Even though only five of the levels were actually represented, the table function shows the frequencies for all of the levels of the original factors. To change this, we can simply use another call to factor

> table(factor(lets[1:5]))

a k q s z
1 1 1 1 1

To exclude certain levels from appearing in a factor, the exclude= argument can be passed to factor. By default, the missing value (NA) is excluded from factor levels; to create a factor that inludes missing values from a numeric variable, use exclude=NULL.

6. Combine 2 Factors

Care must be taken when combining variables which are factors, because the c function will interpret the factors as integers. To combine factors, they should first be converted back to their original values (through the levels function), then catenated and converted to a new factor:

> l1 = factor(sample(letters,size=10,replace=TRUE))
> l2 = factor(sample(letters,size=10,replace=TRUE))
> l1
 [1] o b i v q n q w e z
Levels: b e i n o q v w z
> l2
 [1] b a s b l r g m z o
Levels: a b g l m o r s z
> l12 = factor(c(levels(l1)[l1],levels(l2)[l2]))
> l12
 [1] o b i v q n q w e z b a s b l r g m z o
Levels: a b e g i l m n o q r s v w z

7. Cut a vector into a factor

The cut function is used to convert a numeric vector into a factor. The breaks= argument to cut is used to describe how ranges of numbers will be converted to factor values. If a number is provided through the breaks= argument, the resulting factor will be created by dividing the range of the variable into that number of equal length intervals; if a vector of values is provided, the values in the vector are used to determine the breakpoint. Note that if a vector of values is provided, the number of levels of the resultant factor will be one less than the number of values in the vector.

(更多示例可以参考 example(cut))

For example, consider the women data set, which contains height and weights for a sample of women. If we wanted to create a factor corresponding to weight, with three equally-spaced levels, we could use the following:

> wfact = cut(women$weight,3)
> table(wfact)
wfact
(115,131] (131,148] (148,164]
	6         5         4

Notice that the default label for factors produced by cut contains the actual range of values that were used to divide the variable into factors. The pretty function can be used to make nicer default labels, but it may not return the number of levels that’s actually desired:

> wfact = cut(women$weight,pretty(women$weight,3))
> wfact
 [1] (100,120] (100,120] (100,120] (120,140] (120,140] (120,140] (120,140]
 [8] (120,140] (120,140] (140,160] (140,160] (140,160] (140,160] (140,160]
[15] (160,180]
Levels: (100,120] (120,140] (140,160] (160,180]
> table(wfact)
wfact
(100,120] (120,140] (140,160] (160,180]
	3         6         5         1

The labels= argument to cut allows you to specify the levels of the factors:

> wfact = cut(women$weight,3,labels=c('Low','Medium','High'))
> table(wfact)
wfact
	Low	Medium	High
	6	5	4

To produce factors based on percentiles of your data (for example quartiles or deciles), the quantile function can be used to generate the breaks= argument, insuring nearly equal numbers of observations in each of the levels of the factor:

> wfact = cut(women$weight,quantile(women$weight,(0:4)/4))
> table(wfact)
wfact
(115,124] (124,135] (135,148] (148,164]
	3         4         3         4

As mentioned in Section , there are a number of ways to create factors from date/time objects. If you wish to create a factor based on one of the components of that date, you can extract it with strftime and convert it to a factor directly. For example, we can use the seq function to create a vector of dates representing each day of the year:

> everyday = seq(from=as.Date('2005-1-1'),to=as.Date('2005-12-31'),by='day')

To create a factor based on the month of the year in which each date falls, we can extract the month name (full or abbreviated) using format:

> cmonth = format(everyday,'%b')
> months = factor(cmonth,levels=unique(cmonth),ordered=TRUE)
> table(months)
months
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
 31  28  31  30  31  30  31  31  30  31  30  31

Since unique returns unique values in the order they are encountered, the levels argument will provide the month abbreviations in the correct order to produce an properly ordered factor.

Sometimes more flexibility can be acheived by using the cut function, which understands time units of months, days, weeks and years through the breaks= argument. (For date/time values, units of hours, minutes, and seconds can also be used.) For example, to format the days of the year based on the week in which they fall, we could use cut as follows:

> wks = cut(everyday,breaks='week')
> head(wks)
[1] 2004-12-27 2004-12-27 2005-01-03 2005-01-03 2005-01-03 2005-01-03
53 Levels: 2004-12-27 2005-01-03 2005-01-10 2005-01-17 ... 2005-12-26

Note that the first observation had a date earlier than any of the dates in the everyday vector, since the first date was in middle of the week. By default, cut starts weeks on Mondays; to use Sundays instead, pass the start.on.monday=FALSE argument to cut.

Multiples of units can also be specified through the breaks= argument. For example, create a factor based on the quarter of the year an observation is in, we could use cut as follows:

> qtrs = cut(everyday,"3 months",labels=paste('Q',1:4,sep=''))
> head(qtrs)
[1] Q1 Q1 Q1 Q1 Q1 Q1
Levels: Q1 Q2 Q3 Q4