# tidyCat: Tidy Methods For Categorical Data Analysis

#### Michael Friendly

#### 2026-03-17

> Frequency tables need some Tidy Love ❤️

Tidy methods for quantitative data & models have advanced considerably, but there hasn’t been much development of similar ideas for “categorical data”, by which I mean data that is often compactly represented as \(n\)-way frequency tables, cross classified by one or more discrete factors.

What would it take to implement a tidy framework for such data? These notes are, in effect, a call for participation in developing a `tidyCat` package for this purpose. Other possible names for this: `tidyCDA`, `tidyfreq` but `tidyCat` makes for a nice logo!

    library(MASS)
    library(vcdExtra)

I see three areas that could be developed here:

## Constructing categorical data sets

Current non-tidy data forms and operations, following (Friendly & Meyer, 2016) are described in the vignette Creating and manipulating frequency tables

It seems clear that the most flexible and general form, and one that most closely matches a tidy data frame is case form, because this allows for numeric variables as well. Thus:

> Among these, tidy categorical data should best be represented as a `tibble` in case form. A tibble is convenient for its’ printing.

### Manipulating categorical data sets

The methods `xtabs()`, `table()` and `expand.dft()` described in that vignette allow conversion from one form to another. Tidy equivalents might be:

- `as_table()`, `as_matrix()`, `as_array()` to convert from any form to table/array form

- Similarly, perhaps `as_caseform()`, `as_freqform()` to convert to those. There is already `as.data.frame(table)` to convert to frequency form, and `expand.dft()` converts that to case form

    data("HairEyeColor")
    hec.df <- as.data.frame(HairEyeColor)
    head(hec.df)
    ##    Hair   Eye  Sex Freq
    ## 1 Black Brown Male   32
    ## 2 Brown Brown Male   53
    ## 3   Red Brown Male   10
    ## 4 Blond Brown Male    3
    ## 5 Black  Blue Male   11
    ## 6 Brown  Blue Male   50
    # expand to case form
    expand.dft(hec.df) |> head()
    ##    Hair   Eye  Sex
    ## 1 Black Brown Male
    ## 2 Black Brown Male
    ## 3 Black Brown Male
    ## 4 Black Brown Male
    ## 5 Black Brown Male
    ## 6 Black Brown Male

- `vcd::structable()` (and `stats::ftable()`) produce a ‘flat’ representation of a high-dimensional contingency table constructed by recursive splits (similar to the construction of mosaic displays). One can be constructed from a table or from a data frame with a formula method,

    structable(Titanic)
    ##             Sex      Male     Female
    ##             Survived   No Yes     No Yes
    ## Class Age
    ## 1st   Child             0   5      0   1
    ##       Adult           118  57      4 140
    ## 2nd   Child             0  11      0  13
    ##       Adult           154  14     13  80
    ## 3rd   Child            35  13     17  14
    ##       Adult           387  75     89  76
    ## Crew  Child             0   0      0   0
    ##       Adult           670 192      3  20
    structable(Sex + Class ~ Survived + Age, data = Titanic)
    ##                Sex   Male              Female
    ##                Class  1st 2nd 3rd Crew    1st 2nd 3rd Crew
    ## Survived Age
    ## No       Child          0   0  35    0      0   0  17    0
    ##          Adult        118 154 387  670      4  13  89    3
    ## Yes      Child          5  11  13    0      1  13  14    0
    ##          Adult         57  14  75  192    140  80  76   20

and there are a suite of methods for indexing and selecting parts of an \(n\)-way table.

- The methods in the `plyr` package (now retired) provided a coherent set of tools for a split-apply-combine strategy that works nicely with multidimensional arrays. Perhaps there are some useful ideas for frequency tables that could be resurrected here.

- There is also a role for `purrr` methods and thinking here: \(n\)-way tables as nested lists/arrays? The ideas of mapping over these?

## Manipulating factor levels

Also needed:

- methods for recoding and collapsing the levels of a factor: `forcats::fct_recode()`, `forcats::fct_collapse()`, `forcats::fct_lump_min()` are useful here.

- methods for reordering the levels of a factor, either manually or for some analysis purpose. For example, Data from Glass (1954) gave this 5 x 5 table on the occupations of 3500 British fathers and their sons, where the occupational categories are listed in alphabetic order.

    data(Glass, package="vcdExtra")
    str(Glass)
    ## 'data.frame':    25 obs. of  3 variables:
    ##  $ father: Factor w/ 5 levels "Managerial","Professional",..: 2 2 2 2 2 1 1 1 1 1 ...
    ##  $ son   : Factor w/ 5 levels "Managerial","Professional",..: 2 1 4 3 5 2 1 4 3 5 ...
    ##  $ Freq  : int  50 45 8 18 8 28 174 84 154 55 ...
    (glass.tab <- xtabs(Freq ~ father + son, data=Glass))
    ##               son
    ## father         Managerial Professional Skilled Supervisory Unskilled
    ##   Managerial          174           28     154          84        55
    ##   Professional         45           50      18           8         8
    ##   Skilled             150           14     714         185       447
    ##   Supervisory          78           11     223         110        96
    ##   Unskilled            42            3     320          72       411

This can be reordered manually by indexing, to arrange the categories by status, giving an order `Professional` down to `Unskilled`:

    # reorder by status
    ord <- c(2, 1, 4, 3, 5)
    glass.tab[ord, ord]
    ##               son
    ## father         Professional Managerial Supervisory Skilled Unskilled
    ##   Professional           50         45           8      18         8
    ##   Managerial             28        174          84     154        55
    ##   Supervisory            11         78         110     223        96
    ##   Skilled                14        150         185     714       447
    ##   Unskilled               3         42          72     320       411

A more general method is to permute the row and column categories in the order implied by correspondence analysis dimensions. This is implemented in the `seriation` package using the `CA` method of `seriation::seriate()` and applying `permute()` to the result.

    library(seriation)
    order <- seriate(glass.tab, method = "CA")
    # the permuted row and column labels
    rownames(glass.tab)[order[[1]]]
    ## [1] "Professional" "Managerial"   "Supervisory"  "Skilled"      "Unskilled"

    # reorder rows and columns
    permute(glass.tab, order)
    ##               son
    ## father         Professional Managerial Supervisory Skilled Unskilled
    ##   Professional           50         45           8      18         8
    ##   Managerial             28        174          84     154        55
    ##   Supervisory            11         78         110     223        96
    ##   Skilled                14        150         185     714       447
    ##   Unskilled               3         42          72     320       411

What are tidy ways to do these things?

## Models

The standard analysis of frequency data is in the form of loglinear models fit by `MASS::loglm()` or with more flexible versions fit with `glm()` or `gnm::gnm()`. These are essentially linear models for the log of frequency. In `vcdExtra`, there are several methods for a list of such models, of class `"glmlist"` and `"loglmlist"`, and these should be accommodated in tidy methods.

What is needed are `broom` methods for `loglm` models. The information required is accessible from standard functions, but not in a tidy form.

- `glance.loglm()` – model level statistics. These are given in the output of the `print()` method, and available from the `print()` method. A complication is both LR and Pearson \(\chi^2\) are reported, so these would need to be made to appear in separate columns. There are also related `LRstats()` functions in `vcdExtra`, which report `AIC` and `BIC`.

    hec.indep <- loglm(~Hair+Eye+Sex, data=HairEyeColor)
    hec.indep
    ## Call:
    ## loglm(formula = ~Hair + Eye + Sex, data = HairEyeColor)
    ##
    ## Statistics:
    ##                       X^2 df P(> X^2)
    ## Likelihood Ratio 166.3001 24        0
    ## Pearson          164.9247 24        0
    # extract test statistics
    summary(hec.indep)$tests
    ##                       X^2 df P(> X^2)
    ## Likelihood Ratio 166.3001 24        0
    ## Pearson          164.9247 24        0
    LRstats(hec.indep)
    ## Likelihood summary table:
    ##              AIC   BIC LR Chisq Df Pr(>Chisq)
    ## hec.indep 321.18 332.9    166.3 24  < 2.2e-16 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

- `tidy.loglm()` — coefficient level statistics. These are available from `coef.loglm()`. They would need to assembled into a long format. Standard errors & p-values might be a problem.

    coef(hec.indep)
    ## $`(Intercept)`
    ## [1] 2.646879
    ##
    ## $Hair
    ##       Black       Brown         Red       Blond
    ## -0.17911627  0.79474431 -0.59856762 -0.01706041
    ##
    ## $Eye
    ##      Brown       Blue      Hazel      Green
    ##  0.5296905  0.5067010 -0.3313375 -0.7050540
    ##
    ## $Sex
    ##       Male     Female
    ## -0.0574957  0.0574957

- `augment.loglm()` — should give case level statistics: fitted values, residuals, …

    fitted(hec.indep)
    ## Re-fitting to get fitted values
    ## , , Sex = Male
    ##
    ##        Eye
    ## Hair       Brown     Blue     Hazel     Green
    ##   Black 18.91504 18.48515  7.995903  5.502557
    ##   Brown 50.08982 48.95142 21.174335 14.571585
    ##   Red   12.43489 12.15228  5.256566  3.617421
    ##   Blond 22.24268 21.73717  9.402589  6.470599
    ##
    ## , , Sex = Female
    ##
    ##        Eye
    ## Hair       Brown     Blue     Hazel     Green
    ##   Black 21.22010 20.73782  8.970314  6.173119
    ##   Brown 56.19396 54.91682 23.754719 16.347334
    ##   Red   13.95025 13.63320  5.897151  4.058254
    ##   Blond 24.95326 24.38614 10.548424  7.259131
    residuals(hec.indep)
    ## Re-fitting to get frequencies and fitted values
    ## , , Sex = Male
    ##
    ##        Eye
    ## Hair         Brown       Blue      Hazel      Green
    ##   Black  2.7349421 -1.8843321  0.6818522 -1.1685504
    ##   Brown  0.4073036  0.1493413  0.8080654  0.1116873
    ##   Red   -0.7150915 -0.6371217  0.7233138  1.5738248
    ##   Blond -5.1444108  1.6747424 -1.5778804  0.5796238
    ##
    ## , , Sex = Female
    ##
    ##        Eye
    ## Hair         Brown       Blue      Hazel      Green
    ##   Black  2.9150045 -2.9069608 -1.4476878 -1.9590840
    ##   Brown  1.2726041 -3.0381608  1.0398490 -0.5953638
    ##   Red    0.5361173 -1.9834384  0.4409912  1.3223880
    ##   Blond -5.2211917  6.6539759 -1.9056398  0.2704898

What about `hatvalues`? Not implemented, but shouldn’t be too hard.

    hatvalues(hec.indep)
    ## Error in `UseMethod()`:
    ## ! no applicable method for 'hatvalues' applied to an object of class "loglm"

## Graphical methods

The most common graphical methods are those implemented in `vcd`: `mosaic()` association plots (`assoc()`), …, which rely on `vcd::strucplot()` described in (Meyer, Zeileis, & Hornik, 2006).

Is there a tidy analog that might work with `ggplot2`? The `ggmosaic` package implements basic marimeko-style mosaic plots. They are not very general, in that they cannot do residual-based shading to show the patterns of association.

However, they are based on a productplots package by Hadley, which seems to provide some basic structure for constructing such displays of nested rectangles.

## Some tidy stuff

- The infer package has some interesting stuff for CDA. The vignette Tidy Chi-Squared Tests with infer expresses do a Chisq test of independences as:

    observed_indep_statistic <- gss |>
      specify(college ~ finrela) |>
      hypothesize(null = "independence") |>
      calculate(stat = "Chisq")

You can do simulation tests like this:

    null_dist_sim <- gss |>
      specify(college ~ finrela) |>
      hypothesize(null = "independence") |>
      generate(reps = 1000, type = "permute") |>
      calculate(stat = "Chisq")

## References

Friendly, M., & Meyer, D. (2016). Discrete data analysis with R: Visualization and modeling techniques for categorical and count data. Boca Raton, FL: Chapman & Hall/CRC.
Glass, D. V. (1954). Social mobility in britain. Glencoe, IL: The Free Press.
Meyer, D., Zeileis, A., & Hornik, K. (2006). The strucplot framework: Visualizing multi-way contingency tables with. Journal of Statistical Software, 17(3), 1–48. Retrieved from https://www.jstatsoft.org/v17/i03/