Basic examples

Like xtabs, crtabs takes a formula and a data argument. Dimensions of your crosstab go on the right side of the ~. For a univariate table of frequencies by education, we can do

tab1 <- crtabs(~ educ, data=ds)
tab1

## [1] 12 71 61 24 57 25

Additional dimensions are added with +. For a two-way table of education and gender,

tab2 <- crtabs(~ educ + gender, data=ds)
tab2

##      [,1] [,2]
## [1,]    6    6
## [2,]   33   38
## [3,]   26   35
## [4,]    6   18
## [5,]   25   32
## [6,]   15   10

Weighting

crtabs takes advantage of several Crunch features that xtabs does not support. First, it respects weight variables that have been set on the server. This dataset is not currently weighted

weight(ds)

## NULL

but we can very easily change that. Let’s use the “weight” variable that already exists in the dataset:

weight(ds) <- ds$weight

Now, if we request the same two-way table as before, we’ll get weighted results:

crtabs(~ educ + gender, data=ds)

##           [,1]      [,2]
## [1,] 12.628200  8.698227
## [2,] 43.315170 43.297542
## [3,] 31.612096 29.963579
## [4,]  8.567314 15.260707
## [5,] 16.492669 22.581293
## [6,]  8.935983  8.647220

If we want unweighted data, that’s easy enough:

crtabs(~ educ + gender, data=ds, weight=NULL)

##      [,1] [,2]
## [1,]    6    6
## [2,]   33   38
## [3,]   26   35
## [4,]    6   18
## [5,]   25   32
## [6,]   15   10

Proportion tables

As with any array data type, we can compute margin tables, and the prop.table function in R provides a convenient way for sweeping a table by a margin. These work on the output of crtabs, too:

prop.table(tab1)

## [1] 0.048 0.284 0.244 0.096 0.228 0.100

For column proportions, specify margin=2 (by rows, margin=1):

prop.table(tab2, 2)

##            [,1]       [,2]
## [1,] 0.05405405 0.04316547
## [2,] 0.29729730 0.27338129
## [3,] 0.23423423 0.25179856
## [4,] 0.05405405 0.12949640
## [5,] 0.22522523 0.23021583
## [6,] 0.13513514 0.07194245

Let’s make that more readable:

round(100*prop.table(tab2, 2))

##      [,1] [,2]
## [1,]    5    4
## [2,]   30   27
## [3,]   23   25
## [4,]    5   13
## [5,]   23   23
## [6,]   14    7

Complex data types

crtabs also comfortably handles the more complex data types that Crunch supports, including categorical array and multiple response variables. In the array variables vignette, we created a categorical array, “imiss”, for “Important issues”. We can crosstab with arrays just as we do non-arrays.

tab3 <- crtabs(~ imiss + gender, data=ds)
tab3

## , , 1
## 
##           [,1]     [,2]      [,3]      [,4]
##  [1,] 31.11036 27.53957 30.125371 32.776132
##  [2,] 47.47270 46.51134 11.613407 15.953981
##  [3,] 11.31668 28.19149 26.431299 55.117086
##  [4,] 75.85298 39.27766  3.819861  2.600933
##  [5,] 49.31502 37.34169 17.139246 17.755480
##  [6,] 59.80997 47.99707  9.550301  4.194091
##  [7,] 68.15899 41.79910  6.273460  5.319881
##  [8,] 65.01490 41.59154  6.653878  7.761953
##  [9,] 45.64391 42.62133 11.107822 19.924924
## [10,] 59.03394 30.34666 16.027038 16.143793
## [11,] 90.19129 18.19050 13.169648  0.000000
## [12,] 30.96798 59.36010 19.180623 12.042728
## [13,] 21.66667 51.95812 20.996176 25.220936
## 
## , , 2
## 
##           [,1]     [,2]      [,3]      [,4]
##  [1,] 52.59306 45.01694 17.535359 12.266433
##  [2,] 70.03272 45.04846  6.944584  6.422805
##  [3,] 33.97914 34.23703 24.418990 35.813411
##  [4,] 90.70215 29.57668  3.697671  3.856843
##  [5,] 48.19794 48.71002 17.758330 11.222931
##  [6,] 72.39412 38.22034 12.111045  4.282138
##  [7,] 73.35809 35.84414 13.522809  5.723524
##  [8,] 78.98925 29.93235 11.747300  7.779673
##  [9,] 63.89258 37.68492 14.613920 12.257150
## [10,] 58.46827 45.55364 15.087550  9.339109
## [11,] 93.86900 25.30076  5.421963  3.084749
## [12,] 53.05919 43.99564 15.071708 11.953823
## [13,] 48.27161 48.41640 17.997678 13.762882

Note that even though we specified two variables in our formula, because “imiss” itself is two dimensional, our result is a three-dimensional array.

To illustrate working with multiple response variables, let’s convert “imiss” to multiple response, selecting its positive categories as indicating selection:

ds$imiss <- dichotomize(ds$imiss, c("Very Important", "Somewhat Important"))

Now, when we crosstab it, we’ll get a two-dimensional table because multiple response variables present a one-dimensional interface:

tab3mr <- crtabs(~ imiss + gender, data=ds)
tab3mr

##            [,1]      [,2]
##  [1,]  58.64993  97.61001
##  [2,]  93.98404 115.08118
##  [3,]  39.50817  68.21617
##  [4,] 115.13064 120.27883
##  [5,]  86.65671  96.90796
##  [6,] 107.80704 110.61446
##  [7,] 109.95809 109.20223
##  [8,] 106.60644 108.92159
##  [9,]  88.26523 101.57750
## [10,]  89.38060 104.02191
## [11,] 108.38178 119.16976
## [12,]  90.32808  97.05483
## [13,]  73.62479  96.68801

It’s worth noting here that the result of crtabs isn’t an array object but a CrunchCube object.

class(tab3mr)

## [1] "CrunchCube"
## attr(,"package")
## [1] "crunch"

This allows us to do the appropriate calculations on arrays and multiple response variables when prop.table is called. To compute a margin table over a multiple response variable, summing along the dimension would give an incorrect value because the responses in a multiple response are not mutually exclusive–they can’t be assumed to sum to 100 percent. However, the margin.table method on CrunchCubes can compute the correct margin, so prop.table gives correct proportions:

round(100*prop.table(tab3mr, 2))

##       [,1] [,2]
##  [1,]   48   76
##  [2,]   77   90
##  [3,]   33   53
##  [4,]   95   94
##  [5,]   71   75
##  [6,]   89   86
##  [7,]   90   85
##  [8,]   88   85
##  [9,]   73   79
## [10,]   74   81
## [11,]   89   93
## [12,]   74   76
## [13,]   61   75

Finally, just as we saw in the array variables vignette, we can grab individual subvariables and crosstab with them:

crtabs(~ imiss$imiss_f + gender, data=ds)

##          [,1]      [,2]
## [1,] 47.47270 70.032722
## [2,] 46.51134 45.048457
## [3,] 11.61341  6.944584
## [4,] 15.95398  6.422805

N-way tables

It’s worth noting that we can extend the crosstabbing to higher dimensions, just by adding more terms on the right-hand side of the formula:

round(crtabs(~ imiss + educ + gender, data=ds))

## , , 1
## 
##       [,1] [,2] [,3] [,4] [,5] [,6]
##  [1,]    6   17   21    1    9    5
##  [2,]   13   25   27    9   13    8
##  [3,]    1   10   18    1    4    5
##  [4,]   12   43   28    9   15    8
##  [5,]   10   25   23    9   12    8
##  [6,]   12   39   27    8   14    7
##  [7,]   12   41   25    9   14    9
##  [8,]   13   31   31    9   15    8
##  [9,]   12   25   24    9   12    7
## [10,]   13   24   24    8   13    7
## [11,]   13   32   31    9   16    9
## [12,]   12   31   24    7    9    8
## [13,]   11   17   24    2   13    6
## 
## , , 2
## 
##       [,1] [,2] [,3] [,4] [,5] [,6]
##  [1,]    5   31   24   10   19    8
##  [2,]    9   32   28   15   23    9
##  [3,]    4   17   21    5   15    6
##  [4,]    9   38   29   15   21    9
##  [5,]    6   28   27   10   17    9
##  [6,]    9   34   26   15   19    7
##  [7,]    9   34   27   13   19    7
##  [8,]    9   32   24   14   22    8
##  [9,]    5   35   22   14   18    7
## [10,]    6   34   23   14   19    7
## [11,]    9   37   27   15   23    9
## [12,]    6   29   19   14   21    8
## [13,]    8   27   27   13   15    7

Numeric aggregations

crtabs can also compute quantities other than counts. Using the left-hand side of the formula, we can specify other aggregations to put in the cells of the table. For example, in the deriving variables vignette, we created an “age” variable. We can easily compute the average age by gender and education:

crtabs(mean(age) ~ educ + gender, data=ds)

##          [,1]     [,2]
## [1,] 54.00829 56.02205
## [2,] 50.31550 48.09241
## [3,] 40.84733 43.06316
## [4,] 55.25996 46.68702
## [5,] 50.14993 40.75736
## [6,] 50.85838 48.64874

Other supported aggregations include min, max, sd, and sum. For the minimum age by gender and education,

crtabs(min(age) ~ educ + gender, data=ds)

##      [,1] [,2]
## [1,]   42   45
## [2,]   35   27
## [3,]   22   24
## [4,]   35   26
## [5,]   32   24
## [6,]   26   27

We can get unconditional (univariate) statistics by making the right-hand side of your formula be just the number 1:

crtabs(min(age) ~ 1, data=ds)

## [1] 22

Numeric aggregation functions also work with categorical variables that have numeric values defined for their categories; this is the reason why numeric values for categories are defined, in fact. In the variables vignette, we worked with the “On the right track” question and set some numeric values:

categories(ds$track)

##   id                                    name value missing
## 1  1 Generally headed in the right direction     1   FALSE
## 2  3                                Not sure     0    TRUE
## 3  2                             Wrong track    -1   FALSE
## 4 -1                                 No Data    NA    TRUE

We can use these numeric values to compute an “on the right track index” by averaging them. If the index is greater than zero, more people thing things are going well, and if it is negative, more respondents are pessimistic.

round(crtabs(mean(track) ~ educ + gender, data=ds), 2)

##       [,1]  [,2]
## [1,] -0.39 -0.05
## [2,] -0.69 -0.22
## [3,] -0.05 -0.14
## [4,] -0.56 -0.40
## [5,] -0.57 -0.08
## [6,] -0.17  0.02

Looks like most people surveyed thought that the U.S. is on the wrong track, but that pessimism is less pronounced for women with higher levels of education.

Subsetting data

We can also specify a subset of ds to analyze, just as if it were a data.frame. Let’s do the same calculation for Democrats only:

round(crtabs(mean(track) ~ educ + gender, data=ds[ds$pid3 == "Democrat",]), 2)

##       [,1]  [,2]
## [1,]   NaN  1.00
## [2,]  0.64 -0.08
## [3,]  0.73  0.30
## [4,]  1.00  0.00
## [5,] -0.12  0.40
## [6,]  0.33  0.12

Not surprisingly, Democrats were less pessimistic about the direction of the country than the general population.

A few final observations about crtabs. First, all of these calculations have been weighted by the weight variable we set above. We set it and could then forget about it–we didn’t have to litter all of our expressions with ds$weight and extra arithmetic to do the weighting. Crunch handles this for us.

Second, none of these aggregations required pulling case-level data to your computer. crtabs sends Crunch expressions to the server and receives in return an n-D array of results. The only computations happening locally are the margin tables and sweeping in prop.table, computing on the aggregate results. Your computer would work exactly as hard with this example dataset of 1000 rows as it would with a dataset of 100 million rows.