In elmstedt/UCLAstats20: Stats 20 Homework Templates
source("../../setup.R")
group <- c("control", "treatment", "control", "treatment", "treatment")
group <- factor(group)
hurricanes <- factor(c(3, 1, 2, 5, 3, 3, 5), levels = c(1, 2, 3, 4, 5))
month_day <- rep(month.name, c(31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31))
f_month_day <- factor(month_day)
# load("hurricanes.RData")
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## Learning Objectives {-}
After studying this chapter, you should be able to:
* Identify when to use factors.
* Create factors using `factor()`.
* Differentiate between character vectors and factors.
* Understand how R stores factors.
* Summarize a categorical variable using `table()`.
* Assign and reassign levels to a factor.
* Order the levels of a factor.
## Basic Definitions
In experimental design (the process of designing experiments), a **factor** is an explanatory variable controlled by the experimenter. The different values the factor can take are called **levels**. For example, if we are designing an experiment to understand differences in efficacy between several headache medications, the medication is a factor, and the types of medication (e.g., acetaminophen, ibuprofen, naproxen, etc.) are the levels of the factor. More generally, we can think of categorical variables as synonymous with factors, where the categories are the levels.
The levels (categories) of a factor are sometimes represented (coded) as numbers, often to denote an ordering to the levels. For example, the Saffir-Simpson hurricane wind scale (SSHWS) classifies hurricanes into five categories, labeled Category 1, Category 2, etc., based on the maximum sustained wind speed of the hurricane. If we had data on hurricanes and input the category classifications as a numeric vector, R would not recognize that the vector represents categorical data.
We typically analyze categorical variables and numerical variables using different methods. For example, the mean classification for a sample of hurricanes in a given year would not make much sense. Instead, we might be interested in the relative frequencies of each classification.
**Factors** in R are an alternative way to store character vectors, particularly when the vector represents categories (levels) from a categorical variable (factor). The **`factor()`** and **`as.factor()`** functions can be used to create or coerce a vector into a factor.
As an example, suppose we have five subjects who are assigned into control or treatment groups. We can create a factor of the group variable:
```r
group <- c("control", "treatment", "control", "treatment", "treatment")
group # This is a character vector
## Convert the group vector into a factor and overwrite the original vector by the factor.
group <- factor(group)
group
Note: The values of the factor vector are not in quotation marks. This highlights the fact that the vector does not contain character values.
Note: Because factors represent categorical data, we cannot apply the usual arithmetic operations on them, even though the values of factors are stored as integers. Attempting to apply numeric operations to factors will cause R to throw a warning and produce a vector of NA values.
group + 1
Working with Levels
The levels() Function
Because the values of a factor are limited to just the levels, there are often many repeated values. R more efficiently stores factors than character vectors with repeated values by internally storing and coding the levels of a factor as integers. Put group in each of the parentheses to see how R works with factors.
typeof() # Internal storage type of the factor vector
as.integer() # How the levels of group are coded/stored in R
The labels for the levels of a factor are only stored once, rather than being repeated. The levels() function accesses the levels attribute of a factor vector. The levels themselves are characters. The integer codes are indices of the levels vector.
levels(group)
levels(group)[as.integer(group)]
The levels() function can also be used to change the factor labels by using the assignment <- operator. For example, we can change the "control" label to"placebo"`:
levels(group)[1] <- "placebo"
group
The nlevels() function returns the number of levels in the factor. The table() function will output a frequency table that summarizes the factor.
nlevels(group)
table(group)
Caution: Changing an element of a factor to a new value will not change or add the factor label. If the new value is not already a level, R will replace the value by an NA and throw a warning.
\newpage
levels(group)[1] <- "placebo"
group[5] <- "control" # Change the value from placebo to control (Warning!)
group
group[5] <- "placebo" # Change the value to placebo (No warning)
group
Write the hurricanes factor with each element being the factor level.
hurricanes <- factor(c(1, 3, 2, 3, 2, 1, 3, 5, 1, 9, 5, "super hurricane"))
hurricanes <- factor(c(1, 3, 2, 3, 2, 1, 3, 5, 1, 9, 5))
as.integer(hurricanes)
The levels Argument
The levels argument in the factor() function can be used to specify all possible levels of a factor, even if some are not observed in the data itself.
## Sample hurricane category data
hurricanes <- factor(c(3, 1, 2, 5, 3, 3, 5), levels = c(1, 2, 3, 4, 5))
hurricanes
This can also be done by adding an element to the levels attribute through the levels() function.
## Sample self-identified gender data
gender <- factor(c("M", "F", "F", "M", "M"))
levels(gender) # Currently 2 levels
levels(gender)[3] <- "X"
levels(gender) # Now has 3 levels
gender
Extracting Values from Factors
Because a factor is a special type of vector, we can still use square brackets to extract values. However, extracting a subset of values from a factor will retain the levels attribute of the original factor, even if the subset of values does not contain all the levels.
hurricanes[1:3] # Only contains 1, 2, 3
To remove the unobserved levels, we could invoke the factor() function again to reset the levels attribute.
factor(hurricanes[1:3])
A more direct way to remove levels when subsetting values is to use the argument drop=TRUE in the square brackets.
hurricanes[1:3, drop = TRUE]
Ordered Levels
Categorical variables which have a natural ordering to the categories (like hurricane categories or coffee cup sizes) are called ordinal variables. Ones which do not have a natural ordering (like gender or eye color) are called nominal variables.
By default, the factor() function will order the character levels in alphabetical (lexicographic) order and numeric levels in numerical (increasing) order. Lowercase will be ordered before their uppercase versions (so a < A).
For example, if we had data consisting of the names of the months, the natural ordering in the months would not be preserved. We will illustrate this with the built-in vector in base R called month.name that contains the names of the months.
month.name # Built-in character vector of the month names
## Create a vector of month names for each day of the year
month_day <- rep(month.name, c(31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31))
f_month_day <- factor(month_day) # Convert into a factor
levels(f_month_day)
To specify the ordering of the levels, we can input the levels in the correct order in the levels argument of the factor() function and also set the argument ordered to be TRUE.
f_month_day <- factor(month_day, levels = month.name, ordered = TRUE)
f_month_day[1:10]
levels(f_month_day)
Operations on Subsets of Data
The tapply() Function
Recall that subsetting and logical indexing allow us to extract subsets of an object based on a condition or criterion. A natural application is to extract subsets of an object based on the levels of a factor (i.e., the categories of a categorical variable).
The tapply() function is used to apply a function to subsets of a vector.
The syntax of tapply() is tapply(X, INDEX, FUN, ..., simplify = TRUE), where the arguments are:
-
X: A numeric or logical vector
-
INDEX: A factor or list of factors that identifies the subsets. Non-factors will be coerced into factors.
-
FUN: The function to be applied.
-
...: Any optional arguments to be passed to the FUN function.
-
simplify: Logical value that specifies whether to simplify the output to a matrix or array.
The tapply() function splits the values of the vector X into groups, each group corresponding to a level of the INDEX factor, then applies the function in FUN to each group.
As an example, we will consider the hurricanes.RData file, which has four objects category, pressure, wind, and year, containing measurements on 455 hurricanes that occurred between 2006 and 2011.
# load("hurricanes.RData") # Load the objects in the hurricanes data
category[1:10] # The Saffir-Simpson classification
pressure[1:10] # Air pressure at the hurricane's center (in millibars)
wind[1:10] # Hurricane's maximum sustained wind speed (in knots)
year[1:10] # Year of hurricane
Side Note: The hurricanes.RData data was extracted from the storms dataset in the dplyr package, which itself is a subset of the NOAA Atlantic hurricane database best track data (HURDAT2),\linebreak http://www.nhc.noaa.gov/data/#hurdat.
Note that the corresponding entry of each object refers to the same hurricane. For example, the 5th hurricane in the data was a Category category[5] hurricane, with air pressure of pressure[5], maximum windspeed of wind[5], and occurred in the year year[5].
Suppose we are interested in whether the mean air pressure at a hurricane's center is related to the category of the hurricane. The tapply() function can split the pressures based on the category and compute the mean of each subset.
## Compute the mean pressure, grouped by category
tapply(pressure, category, mean)
From the output, we see that the mean pressure at a hurricane's center is lower for higher category hurricanes.
question("How would you find the mean maximum sustained wind speed in each year?",
answer("tapply(wind, year, max)", correct = TRUE),
answer("tapply(year, wind, mean)"),
answer("tapply(year, wind, max)"),
answer("tapply(wind, year, mean)"),
random_answer_order = TRUE,
allow_retry = TRUE)
Suppose we want to know the mean pressure for each category/year combination. The tapply() function can also group values based on combinations of levels from multiple factors. When using multiple factors in the INDEX argument, the factors need to be put into a list.
## Compute the mean pressure for each category/year combination
tapply(pressure, list(category, year), mean)
question("How would you find out how many observations are in each category?",
answer("tapply(category, category, length)", correct = TRUE),
answer("table(length)"),
answer("tapply(category, as.integer(category), length)", correct = TRUE),
answer("tapply(category, category, table)", correct = TRUE),
answer("table(category)", correct = TRUE),
random_answer_order = TRUE,
allow_retry = TRUE)
Chapter 6 Final Quiz
question("If numbers were a factor (made by: numbers <- factor(10:1)), what is the result of: numbers + 1?",
answer("No output; an error results"),
answer("11 10 9 8 7 6 5 4 3 2"),
answer("2 3 4 5 6 7 8 9 10 11"),
answer("NA NA NA NA NA NA NA NA NA NA (with a warning message)", correct = TRUE),
random_answer_order = TRUE,
allow_retry = TRUE)
fac <- factor(c("a", 2, 1, 3, "c"), levels = c("a", "b", "c", "d", 1, 2, 3))
fac
question("How many levels are in fac (as defined above)?",
answer("3"),
answer("2"),
answer("5"),
answer("6"),
answer("7", correct = TRUE),
answer("11"),
random_answer_order = TRUE,
allow_retry = TRUE)
elmstedt/UCLAstats20 documentation built on Oct. 24, 2020, 8:55 p.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
source("../../setup.R") group <- c("control", "treatment", "control", "treatment", "treatment") group <- factor(group) hurricanes <- factor(c(3, 1, 2, 5, 3, 3, 5), levels = c(1, 2, 3, 4, 5)) month_day <- rep(month.name, c(31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)) f_month_day <- factor(month_day) # load("hurricanes.RData")
```{js, echo=FALSE} $(function() { $('.ace_editor').each(function( index ) { ace.edit(this).setFontSize("20px"); }); })
## Learning Objectives {-} After studying this chapter, you should be able to: * Identify when to use factors. * Create factors using `factor()`. * Differentiate between character vectors and factors. * Understand how R stores factors. * Summarize a categorical variable using `table()`. * Assign and reassign levels to a factor. * Order the levels of a factor. ## Basic Definitions In experimental design (the process of designing experiments), a **factor** is an explanatory variable controlled by the experimenter. The different values the factor can take are called **levels**. For example, if we are designing an experiment to understand differences in efficacy between several headache medications, the medication is a factor, and the types of medication (e.g., acetaminophen, ibuprofen, naproxen, etc.) are the levels of the factor. More generally, we can think of categorical variables as synonymous with factors, where the categories are the levels. The levels (categories) of a factor are sometimes represented (coded) as numbers, often to denote an ordering to the levels. For example, the Saffir-Simpson hurricane wind scale (SSHWS) classifies hurricanes into five categories, labeled Category 1, Category 2, etc., based on the maximum sustained wind speed of the hurricane. If we had data on hurricanes and input the category classifications as a numeric vector, R would not recognize that the vector represents categorical data. We typically analyze categorical variables and numerical variables using different methods. For example, the mean classification for a sample of hurricanes in a given year would not make much sense. Instead, we might be interested in the relative frequencies of each classification. **Factors** in R are an alternative way to store character vectors, particularly when the vector represents categories (levels) from a categorical variable (factor). The **`factor()`** and **`as.factor()`** functions can be used to create or coerce a vector into a factor. As an example, suppose we have five subjects who are assigned into control or treatment groups. We can create a factor of the group variable: ```r group <- c("control", "treatment", "control", "treatment", "treatment") group # This is a character vector ## Convert the group vector into a factor and overwrite the original vector by the factor. group <- factor(group) group
Note: The values of the factor vector are not in quotation marks. This highlights the fact that the vector does not contain character values.
Note: Because factors represent categorical data, we cannot apply the usual arithmetic operations on them, even though the values of factors are stored as integers. Attempting to apply numeric operations to factors will cause R to throw a warning and produce a vector of NA values.
group + 1
Working with Levels
The levels() Function
Because the values of a factor are limited to just the levels, there are often many repeated values. R more efficiently stores factors than character vectors with repeated values by internally storing and coding the levels of a factor as integers. Put group in each of the parentheses to see how R works with factors.
typeof() # Internal storage type of the factor vector as.integer() # How the levels of group are coded/stored in R
The labels for the levels of a factor are only stored once, rather than being repeated. The levels() function accesses the levels attribute of a factor vector. The levels themselves are characters. The integer codes are indices of the levels vector.
levels(group) levels(group)[as.integer(group)]
The levels() function can also be used to change the factor labels by using the assignment <- operator. For example, we can change the "control" label to"placebo"`:
levels(group)[1] <- "placebo" group
The nlevels() function returns the number of levels in the factor. The table() function will output a frequency table that summarizes the factor.
nlevels(group) table(group)
Caution: Changing an element of a factor to a new value will not change or add the factor label. If the new value is not already a level, R will replace the value by an NA and throw a warning.
\newpage
levels(group)[1] <- "placebo" group[5] <- "control" # Change the value from placebo to control (Warning!) group group[5] <- "placebo" # Change the value to placebo (No warning) group
Write the hurricanes factor with each element being the factor level.
hurricanes <- factor(c(1, 3, 2, 3, 2, 1, 3, 5, 1, 9, 5, "super hurricane"))
hurricanes <- factor(c(1, 3, 2, 3, 2, 1, 3, 5, 1, 9, 5)) as.integer(hurricanes)
The levels Argument
The levels argument in the factor() function can be used to specify all possible levels of a factor, even if some are not observed in the data itself.
## Sample hurricane category data hurricanes <- factor(c(3, 1, 2, 5, 3, 3, 5), levels = c(1, 2, 3, 4, 5)) hurricanes
This can also be done by adding an element to the levels attribute through the levels() function.
## Sample self-identified gender data gender <- factor(c("M", "F", "F", "M", "M")) levels(gender) # Currently 2 levels levels(gender)[3] <- "X" levels(gender) # Now has 3 levels gender
Extracting Values from Factors
Because a factor is a special type of vector, we can still use square brackets to extract values. However, extracting a subset of values from a factor will retain the levels attribute of the original factor, even if the subset of values does not contain all the levels.
hurricanes[1:3] # Only contains 1, 2, 3
To remove the unobserved levels, we could invoke the factor() function again to reset the levels attribute.
factor(hurricanes[1:3])
A more direct way to remove levels when subsetting values is to use the argument drop=TRUE in the square brackets.
hurricanes[1:3, drop = TRUE]
Ordered Levels
Categorical variables which have a natural ordering to the categories (like hurricane categories or coffee cup sizes) are called ordinal variables. Ones which do not have a natural ordering (like gender or eye color) are called nominal variables.
By default, the factor() function will order the character levels in alphabetical (lexicographic) order and numeric levels in numerical (increasing) order. Lowercase will be ordered before their uppercase versions (so a < A).
For example, if we had data consisting of the names of the months, the natural ordering in the months would not be preserved. We will illustrate this with the built-in vector in base R called month.name that contains the names of the months.
month.name # Built-in character vector of the month names ## Create a vector of month names for each day of the year month_day <- rep(month.name, c(31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)) f_month_day <- factor(month_day) # Convert into a factor levels(f_month_day)
To specify the ordering of the levels, we can input the levels in the correct order in the levels argument of the factor() function and also set the argument ordered to be TRUE.
f_month_day <- factor(month_day, levels = month.name, ordered = TRUE) f_month_day[1:10] levels(f_month_day)
Operations on Subsets of Data
The tapply() Function
Recall that subsetting and logical indexing allow us to extract subsets of an object based on a condition or criterion. A natural application is to extract subsets of an object based on the levels of a factor (i.e., the categories of a categorical variable).
The tapply() function is used to apply a function to subsets of a vector.
The syntax of tapply() is tapply(X, INDEX, FUN, ..., simplify = TRUE), where the arguments are:
-
X: A numeric or logical vector -
INDEX: A factor or list of factors that identifies the subsets. Non-factors will be coerced into factors. -
FUN: The function to be applied. -
...: Any optional arguments to be passed to theFUNfunction. -
simplify: Logical value that specifies whether to simplify the output to a matrix or array.
The tapply() function splits the values of the vector X into groups, each group corresponding to a level of the INDEX factor, then applies the function in FUN to each group.
As an example, we will consider the hurricanes.RData file, which has four objects category, pressure, wind, and year, containing measurements on 455 hurricanes that occurred between 2006 and 2011.
# load("hurricanes.RData") # Load the objects in the hurricanes data
category[1:10] # The Saffir-Simpson classification pressure[1:10] # Air pressure at the hurricane's center (in millibars) wind[1:10] # Hurricane's maximum sustained wind speed (in knots) year[1:10] # Year of hurricane
Side Note: The hurricanes.RData data was extracted from the storms dataset in the dplyr package, which itself is a subset of the NOAA Atlantic hurricane database best track data (HURDAT2),\linebreak http://www.nhc.noaa.gov/data/#hurdat.
Note that the corresponding entry of each object refers to the same hurricane. For example, the 5th hurricane in the data was a Category category[5] hurricane, with air pressure of pressure[5], maximum windspeed of wind[5], and occurred in the year year[5].
Suppose we are interested in whether the mean air pressure at a hurricane's center is related to the category of the hurricane. The tapply() function can split the pressures based on the category and compute the mean of each subset.
## Compute the mean pressure, grouped by category tapply(pressure, category, mean)
From the output, we see that the mean pressure at a hurricane's center is lower for higher category hurricanes.
question("How would you find the mean maximum sustained wind speed in each year?", answer("tapply(wind, year, max)", correct = TRUE), answer("tapply(year, wind, mean)"), answer("tapply(year, wind, max)"), answer("tapply(wind, year, mean)"), random_answer_order = TRUE, allow_retry = TRUE)
Suppose we want to know the mean pressure for each category/year combination. The tapply() function can also group values based on combinations of levels from multiple factors. When using multiple factors in the INDEX argument, the factors need to be put into a list.
## Compute the mean pressure for each category/year combination tapply(pressure, list(category, year), mean)
question("How would you find out how many observations are in each category?", answer("tapply(category, category, length)", correct = TRUE), answer("table(length)"), answer("tapply(category, as.integer(category), length)", correct = TRUE), answer("tapply(category, category, table)", correct = TRUE), answer("table(category)", correct = TRUE), random_answer_order = TRUE, allow_retry = TRUE)
Chapter 6 Final Quiz
question("If numbers were a factor (made by: numbers <- factor(10:1)), what is the result of: numbers + 1?", answer("No output; an error results"), answer("11 10 9 8 7 6 5 4 3 2"), answer("2 3 4 5 6 7 8 9 10 11"), answer("NA NA NA NA NA NA NA NA NA NA (with a warning message)", correct = TRUE), random_answer_order = TRUE, allow_retry = TRUE)
fac <- factor(c("a", 2, 1, 3, "c"), levels = c("a", "b", "c", "d", 1, 2, 3)) fac question("How many levels are in fac (as defined above)?", answer("3"), answer("2"), answer("5"), answer("6"), answer("7", correct = TRUE), answer("11"), random_answer_order = TRUE, allow_retry = TRUE)
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