# Analyzing Crunch Data

Previous: transform and derive

With `crunch`, you can harness the power of R to do computations with your datasets in Crunch that would be difficult or impossible to accomplish in a graphical user interface.

## Crosstabbing

While the web application certainly supports crosstabbing, you may want to do aggregations like this in R. Crosstabbing in R with `crunch` may allow you to easily do additional computations on the result, for example.

`crunch` contains the `crtabs` (Crunch-tabs) function, which largely emulates the design of the `xtabs` function in base R. In essence, you define a formula and provide data in which to evaluate it. In this case, we’ll be providing a `CrunchDataset`.

### 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

    ## educ
    ##                No HS High school graduate         Some college               2-year               4-year
    ##                   12                   71                   61                   24                   57
    ##            Post-grad
    ##                   25

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

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

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   6      6
    ##   High school graduate   33     38
    ##   Some college           26     35
    ##   2-year                  6     18
    ##   4-year                 25     32
    ##   Post-grad              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)

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   6      6
    ##   High school graduate   33     38
    ##   Some college           26     35
    ##   2-year                  6     18
    ##   4-year                 25     32
    ##   Post-grad              15     10

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

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

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   6      6
    ##   High school graduate   33     38
    ##   Some college           26     35
    ##   2-year                  6     18
    ##   4-year                 25     32
    ##   Post-grad              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)

    ## educ
    ##                No HS High school graduate         Some college               2-year               4-year
    ##                0.048                0.284                0.244                0.096                0.228
    ##            Post-grad
    ##                0.100

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

    prop.table(tab2, 2)

    ##                       gender
    ## educ                         Male     Female
    ##   No HS                0.05405405 0.04316547
    ##   High school graduate 0.29729730 0.27338129
    ##   Some college         0.23423423 0.25179856
    ##   2-year               0.05405405 0.12949640
    ##   4-year               0.22522523 0.23021583
    ##   Post-grad            0.13513514 0.07194245

Let’s make that more readable:

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

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   5      4
    ##   High school graduate   30     27
    ##   Some college           23     25
    ##   2-year                  5     13
    ##   4-year                 23     23
    ##   Post-grad              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

    ## , , gender = Male
    ##
    ##                         imiss
    ## imiss                    Very Important Somewhat Important Not very Important Unimportant
    ##   Abortion                           32                 31                 26          22
    ##   Education                          49                 44                 12           6
    ##   Gay rights                         18                 25                 21          46
    ##   Health care                        79                 23                  5           4
    ##   Immigration                        51                 38                 14           8
    ##   Medicare                           58                 35                 12           6
    ##   Social security                    67                 33                  5           6
    ##   Taxes                              75                 29                  5           1
    ##   Terrorism                          44                 38                 17          11
    ##   The budget deficit                 60                 26                 16           9
    ##   The economy                        93                 14                  4           0
    ##   The environment                    35                 42                 20          14
    ##   The war in Afghanistan             24                 51                 25          10
    ##
    ## , , gender = Female
    ##
    ##                         imiss
    ## imiss                    Very Important Somewhat Important Not very Important Unimportant
    ##   Abortion                           63                 42                 24           9
    ##   Education                          87                 41                  7           4
    ##   Gay rights                         41                 36                 25          37
    ##   Health care                       102                 30                  4           2
    ##   Immigration                        56                 53                 20           9
    ##   Medicare                           80                 41                 15           2
    ##   Social security                    82                 41                 14           2
    ##   Taxes                              85                 35                 15           4
    ##   Terrorism                          68                 44                 18           9
    ##   The budget deficit                 65                 50                 17           7
    ##   The economy                       103                 30                  4           1
    ##   The environment                    64                 45                 16          11
    ##   The war in Afghanistan             49                 57                 20          13

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

    ##                         gender
    ## imiss                         Male    Female
    ##   Abortion                58.64993  97.61001
    ##   Education               93.98404 115.08118
    ##   Gay rights              39.50817  68.21617
    ##   Health care            115.13064 120.27883
    ##   Immigration             86.65671  96.90796
    ##   Medicare               107.80704 110.61446
    ##   Social security        109.95809 109.20223
    ##   Taxes                  106.60644 108.92159
    ##   Terrorism               88.26523 101.57750
    ##   The budget deficit      89.38060 104.02191
    ##   The economy            108.38178 119.16976
    ##   The environment         90.32808  97.05483
    ##   The war in Afghanistan  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))

    ##                         gender
    ## imiss                    Male Female
    ##   Abortion                 48     77
    ##   Education                77     90
    ##   Gay rights               33     53
    ##   Health care              95     94
    ##   Immigration              71     77
    ##   Medicare                 89     87
    ##   Social security          90     85
    ##   Taxes                    88     85
    ##   Terrorism                74     79
    ##   The budget deficit       74     81
    ##   The economy              89     93
    ##   The environment          74     78
    ##   The war in Afghanistan   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)

    ##                     gender
    ## imiss_f              Male Female
    ##   Very Important       44     68
    ##   Somewhat Important   38     44
    ##   Not very Important   17     18
    ##   Unimportant          11      9

### 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))

    ## , , gender = Male
    ##
    ##                         educ
    ## imiss                    No HS High school graduate Some college 2-year 4-year Post-grad
    ##   Abortion                   3                   19           18      1     14         8
    ##   Education                  6                   23           22      6     23        13
    ##   Gay rights                 1                   11           12      1      8        10
    ##   Health care                5                   33           22      6     22        14
    ##   Immigration                4                   26           20      6     20        13
    ##   Medicare                   5                   29           21      5     21        12
    ##   Social security            5                   31           22      6     21        15
    ##   Taxes                      6                   30           25      6     23        14
    ##   Terrorism                  5                   24           19      6     16        12
    ##   The budget deficit         6                   25           20      5     18        12
    ##   The economy                6                   31           25      6     24        15
    ##   The environment            5                   22           16      4     17        13
    ##   The war in Afghanistan     5                   17           20      3     20        10
    ##
    ## , , gender = Female
    ##
    ##                         educ
    ## imiss                    No HS High school graduate Some college 2-year 4-year Post-grad
    ##   Abortion                   4                   26           27     12     27         9
    ##   Education                  6                   31           32     17     32        10
    ##   Gay rights                 3                   15           23      9     21         6
    ##   Health care                6                   35           33     18     30        10
    ##   Immigration                5                   27           30     13     24        10
    ##   Medicare                   6                   32           30     18     27         8
    ##   Social security            6                   33           33     16     27         8
    ##   Taxes                      6                   30           29     15     31         9
    ##   Terrorism                  4                   32           27     16     25         8
    ##   The budget deficit         5                   32           28     16     26         8
    ##   The economy                6                   34           33     18     32        10
    ##   The environment            5                   25           24     16     30         9
    ##   The war in Afghanistan     5                   26           31     15     22         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)

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   6      6
    ##   High school graduate   33     38
    ##   Some college           26     35
    ##   2-year                  6     18
    ##   4-year                 25     32
    ##   Post-grad              15     10

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

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

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   6      6
    ##   High school graduate   33     38
    ##   Some college           26     35
    ##   2-year                  6     18
    ##   4-year                 25     32
    ##   Post-grad              15     10

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] 250

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)

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   6      6
    ##   High school graduate   33     38
    ##   Some college           26     35
    ##   2-year                  6     18
    ##   4-year                 25     32
    ##   Post-grad              15     10

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)

    ##                       gender
    ## educ                   Male Female
    ##   No HS                   0      3
    ##   High school graduate    7     17
    ##   Some college            8     16
    ##   2-year                  1      6
    ##   4-year                  9     19
    ##   Post-grad               5      5

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.

## Statistical modeling

Any statistical modeling function that takes a `data` argument should happily accept a `CrunchDataset` and just do the right thing–no extra effort or thought required.

Let’s fit a basic Ordinary Least Squares (OLS) model. In our dataset, we have a few questions about Edward Snowden, such as:

    ds$snowdenleakapp

    ## Approval of Snowden's Leak (categorical)
    ##
    ##                        Count
    ## Strongly disapprove 86.00644
    ## Not sure            55.82542
    ## Somewhat approve    43.19385
    ## Somewhat disapprove 40.26587
    ## Strongly approve    24.70842

We can use `lm` to fit our model. Let’s explore the relationship between approval of Snowden’s leak and respondents’ interest in current events, party identification, gender, and age.

    ols1 <- lm(I(snowdenleakapp == "Strongly approve") ~ newsint2 + pid3 + gender + age,
        data=ds)
    summary(ols1)

    ##
    ## Call:
    ## lm(formula = I(snowdenleakapp == "Strongly approve") ~ newsint2 +
    ##     pid3 + gender + age, data = ds)
    ##
    ## Residuals:
    ##      Min       1Q   Median       3Q      Max
    ## -0.33261 -0.15753 -0.12930 -0.06006  0.94924
    ##
    ## Coefficients:
    ##                            Estimate Std. Error t value Pr(>|t|)
    ## (Intercept)                0.133723   0.093700   1.427    0.155
    ## newsint2Some of the time   0.016157   0.050750   0.318    0.750
    ## newsint2Only now and then -0.007068   0.074048  -0.095    0.924
    ## newsint2Hardly at all     -0.058744   0.091630  -0.641    0.522
    ## pid3Republican            -0.088822   0.058002  -1.531    0.127
    ## pid3Independent            0.022139   0.052650   0.420    0.675
    ## pid3Other                  0.185892   0.198541   0.936    0.350
    ## pid3Not sure              -0.049288   0.103442  -0.476    0.634
    ## genderFemale              -0.019411   0.045856  -0.423    0.672
    ## age                        0.000361   0.001651   0.219    0.827
    ##
    ## Residual standard error: 0.3366 on 240 degrees of freedom
    ## Multiple R-squared:  0.02533,    Adjusted R-squared:  -0.01122
    ## F-statistic: 0.6931 on 9 and 240 DF,  p-value: 0.7149

Looks like partisanship is weakly associated with approval of the NSA leak, but overall the model isn’t a great fit, given our data. (For what it’s worth, we’re working on a randomly drawn subset of the survey so that the size of data included with package is small. Results are more meaningful with the full dataset.) Nevertheless, this example illustrates how straightforward it is to do statistical analysis with data in Crunch. Even though your dataset lives on the server, you can think of it like a local `data.frame`. Note, for example, that our categorical variables (News Interest, Party ID, and Gender) expand their categories out as dichotomous indicators, just as if they were `factor` variables in a `data.frame`.

Given that we’re estimating a model with a dichotomous dependent variable, perhaps a logit would be more appropriate than a strict linear predictor. We can use `glm` instead:

    logit1 <- glm(I(snowdenleakapp == "Strongly approve") ~ newsint2 + pid3 + gender + age,
        family=binomial(link="logit"), data=ds)
    summary(logit1)

    ##
    ## Call:
    ## glm(formula = I(snowdenleakapp == "Strongly approve") ~ newsint2 +
    ##     pid3 + gender + age, family = binomial(link = "logit"), data = ds)
    ##
    ## Coefficients:
    ##                            Estimate Std. Error z value Pr(>|z|)
    ## (Intercept)               -1.883494   0.847876  -2.221   0.0263 *
    ## newsint2Some of the time   0.141215   0.439458   0.321   0.7480
    ## newsint2Only now and then -0.075103   0.700499  -0.107   0.9146
    ## newsint2Hardly at all     -0.734607   1.084190  -0.678   0.4980
    ## pid3Republican            -1.077062   0.673224  -1.600   0.1096
    ## pid3Independent            0.156299   0.439101   0.356   0.7219
    ## pid3Other                  1.056509   1.273998   0.829   0.4069
    ## pid3Not sure              -0.535621   1.119244  -0.479   0.6323
    ## genderFemale              -0.176401   0.410364  -0.430   0.6673
    ## age                        0.003547   0.015024   0.236   0.8134
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ##
    ## (Dispersion parameter for binomial family taken to be 1)
    ##
    ##     Null deviance: 191.28  on 249  degrees of freedom
    ## Residual deviance: 184.52  on 240  degrees of freedom
    ## AIC: 204.52
    ##
    ## Number of Fisher Scoring iterations: 5

As before, not a particularly interesting result, but this is just the beginning of the analysis process. Using `crunch`, you can keep exploring the data and perhaps find a better fit.

Unlike the previous examples, these modeling functions do have to pull columns of data from the server to your local machine. However, only the columns of data you reference in your formula are copied, and if you specify a subset of the dataset to regress on (as we did above with `crtabs` when we looked at just Democrats), only those rows are retrieved. This helps minimize the time spent shipping data across the network. Moreover, because of the `crunch` package’s query cache, subsequent models that incorporate any of those variables will not have to go to the server to get them.

Next: filtering datasets