How to get a data.frame with cases from a contingency table in r?

Question

I would like to reproduce some calculations from a book (logit regression). The book gives a contingency table and the results.

Here is the Table:

    .


    example <- matrix(c(21,22,6,51), nrow = 2, byrow = TRUE)
    #Labels:
    rownames(example) <- c("Present","Absent")
    colnames(example) <- c(">= 55", "<55")

It gives me this:

            >= 55 <55
    Present    21  22
    Absent      6  51

But to use the glm()-function the data has to be in the following way:

(two colums, one with "Age", and one with "Present", filled with 0/1)

    age <- c(rep(c(0),27), rep(c(1),73))
    present <- c(rep(c(0),21), rep(c(1),6), rep(c(0),22), rep(c(1),51))

    data <- data.frame(present, age)

    > data
        present age
    1         0   0
    2         0   0
    3         0   0
    .         .   .
    .         .   .
    .         .   .
    100       1   1

Is there a simple way to get this structure from the table/matrix?

Answer 1

So, glm is not quite that inflexible. In part ?glm reads

 For ‘binomial’ and ‘quasibinomial’ families the response can also
 be specified as a ‘factor’ (when the first level denotes failure
 and all others success) or as a two-column matrix with the columns
 giving the numbers of successes and failures.

I'll assume you want to test the effect of age on Present/Absent. The key is for to specify the response like (in psueudo-code) c(success, failure).

So you need data like data.frame(Age= ..., Present = ..., Absent). The easiest way to do this from your example is to transpose, then coerce to data.frame, and add a column:

example_t <- as.data.frame(t(example))
example_df <- data.frame(example_t, Age=factor(row.names(example_t)))

which gives you

      Present Absent   Age
>= 55      21      6 >= 55
<55        22     51   <55

Then, you can run the glm:

glm(cbind(Present, Absent) ~ Age, example_df, family = 'binomial')

to get

Call:  glm(formula = cbind(Present, Absent) ~ Age, family = "binomial",
    data = example_for_glm)

Coefficients:
(Intercept)       Age<55
      1.253       -2.094

Degrees of Freedom: 1 Total (i.e. Null);  0 Residual
Null Deviance:      18.7
Residual Deviance: -1.332e-15   AIC: 11.99

Addendum

You could also get here via the answer by @therimalaya. But it's just the first step

as.data.frame(as.table(example))

(only gets you part way there)

    Var1  Var2 Freq
1 Present >= 55   21
2  Absent >= 55    6
3 Present   <55   22
4  Absent   <55   51

but to actually have a column of successes and failures, you need to do something more. You could use tidyr to get there

as.data.frame(as.table(example)) %>% tidyr::spread(Var1, Freq)

is similar to my example_df above

  Var2 Present Absent
1 >= 55      21      6
2   <55      22     51

Answer 2

reshape2::melt(example)

This will give you,

     Var1  Var2 value
1 Present >= 55    21
2  Absent >= 55     6
3 Present   <55    22
4  Absent   <55    51

which you can easily use for glm

Answer 3

The code below might look long but only the group_by() and do() instruction deal with expanding the data. All the rest is about changing the data in long format and encoding character variables as 0 and 1. I tried to start from the exact matrix you gave in your question.

Load data manipulation packages

library(tidyr)
library(dplyr)

Create a data frame

Create a matrix as in your example, but avoid ">" signs in column names

example <- matrix(c(21,22,6,51), nrow = 2, byrow = TRUE)
rownames(example) <- c("Present","Absent")
colnames(example) <- c("above55", "below55")

Convert the matrix to a data frame

example <- data.frame(example) %>%
    add_rownames("chd")    

Or simply create a data frame directly

data.frame(chd = c("Present", "Absent"),
           above55 = c(21,6),
           below55 = c(22,51))

Reshape data

data2 <- example %>% 
    gather(age, nrow, -chd) %>%
    # Encode chd and age as 0 or 1
    mutate(chd = ifelse(chd=="Present",1,0),
           age = ifelse(age=="above55",1,0)) %>%
    group_by(chd, age) %>%
    # Expand each variable by nrow
    do(data.frame(chd = rep(.$chd,.$nrow),
                  age = rep(.$age,.$nrow)))

head(data2)
# Source: local data frame [6 x 2]
# Groups: chd, age [1]
# 
#     chd   age
#   (dbl) (dbl)
# 1     0     0
# 2     0     0
# 3     0     0
# 4     0     0
# 5     0     0
# 6     0     0
tail(data2)
# Source: local data frame [6 x 2]
# Groups: chd, age [1]
# 
#     chd   age
#   (dbl) (dbl)
# 1     1     1
# 2     1     1
# 3     1     1
# 4     1     1
# 5     1     1
# 6     1     1

table(data2)
#        age
# chd  0  1
#   0 51  6
#   1 22 21

Same as your example except for the age encoding issue mentioned in my comment above.

Answer 4

I would go for:

library(data.table)
tab <- data.table(AGED = c(1, 1, 0, 0),
                  CHD = c(1, 0, 1, 0),
                  Count = c(21, 6, 22, 51))

tabExp <- tab[rep(1:.N, Count), .(AGED, CHD)]

Edit: Quick explanation, as it took me some time to figure it out:

In data.table objects .N stores the number of rows of a group (if grouped with by) or just the number of rows of the whole data.table, so in this example:

tab[rep(1:.N, Count)]

and

tab[rep(1:4, Count)]

and finally

tab[rep(1:4, c(21, 6, 22, 51)]

are equivalent.

Same with base R:

tab2 <- data.frame(AGED = c(1, 1, 0, 0),
                   CHD = c(1, 0, 1, 0),
                   Count = c(21, 6, 22, 51))

tabExp2 <- tab2[rep(1:nrow(tab2), tab2$Count), c("AGED", "CHD")]

Answer 5

You could perhaps use the countsToCases function as defined here.

countsToCases(as.data.frame(as.table(example))) 
#        Var1  Var2
#1    Present >= 55
#1.1  Present >= 55
#1.2  Present >= 55
#1.3  Present >= 55
#1.4  Present >= 55
#1.5  Present >= 55
# ...

You can always recode the variables to numeric afterwards, if you prefer.