Introduction
This article only requires the tidymodels package.
While the tidymodels package broom is useful for summarizing the result of a single analysis in a consistent format, it is really designed for high-throughput applications, where you must combine results from multiple analyses. These could be subgroups of data, analyses using different models, bootstrap replicates, permutations, and so on. In particular, it plays well with the nest()/unnest() functions from tidyr and the map() function in purrr.
Correlation analysis
Let’s demonstrate this with a simple data set, the built-in Orange. We start by coercing Orange to a tibble. This gives a nicer print method that will be especially useful later on when we start working with list-columns.
library(tidymodels)
data(Orange)
Orange <- as_tibble(Orange)
Orange
#> # A tibble: 35 × 3
#> Tree age circumference
#> <ord> <dbl> <dbl>
#> 1 1 118 30
#> 2 1 484 58
#> 3 1 664 87
#> 4 1 1004 115
#> 5 1 1231 120
#> 6 1 1372 142
#> 7 1 1582 145
#> 8 2 118 33
#> 9 2 484 69
#> 10 2 664 111
#> # … with 25 more rows
This contains 35 observations of three variables: Tree, age, and circumference. Tree is a factor with five levels describing five trees. As might be expected, age and circumference are correlated:
cor(Orange$age, Orange$circumference)
#> [1] 0.914
library(ggplot2)
ggplot(Orange, aes(age, circumference, color = Tree)) +
geom_line()
Suppose you want to test for correlations individually within each tree. You can do this with dplyr’s group_by:
Orange %>%
group_by(Tree) %>%
summarize(correlation = cor(age, circumference))
#> # A tibble: 5 × 2
#> Tree correlation
#> <ord> <dbl>
#> 1 3 0.988
#> 2 1 0.985
#> 3 5 0.988
#> 4 2 0.987
#> 5 4 0.984
(Note that the correlations are much higher than the aggregated one, and also we can now see the correlation is similar across trees).
Suppose that instead of simply estimating a correlation, we want to perform a hypothesis test with cor.test():
ct <- cor.test(Orange$age, Orange$circumference)
ct
#>
#> Pearson's product-moment correlation
#>
#> data: Orange$age and Orange$circumference
#> t = 13, df = 33, p-value = 2e-14
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#> 0.834 0.956
#> sample estimates:
#> cor
#> 0.914
This test output contains multiple values we may be interested in. Some are vectors of length 1, such as the p-value and the estimate, and some are longer, such as the confidence interval. We can get this into a nicely organized tibble using the tidy() function:
tidy(ct)
#> # A tibble: 1 × 8
#> estimate statistic p.value parameter conf.low conf.high method alternative
#> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <chr> <chr>
#> 1 0.914 12.9 1.93e-14 33 0.834 0.956 Pearson'… two.sided
Often, we want to perform multiple tests or fit multiple models, each on a different part of the data. In this case, we recommend a nest-map-unnest workflow. For example, suppose we want to perform correlation tests for each different tree. We start by nesting our data based on the group of interest:
nested <-
Orange %>%
nest(data = c(age, circumference))
Then we perform a correlation test for each nested tibble using purrr::map():
nested %>%
mutate(test = map(data, ~ cor.test(.x$age, .x$circumference)))
#> # A tibble: 5 × 3
#> Tree data test
#> <ord> <list> <list>
#> 1 1 <tibble [7 × 2]> <htest>
#> 2 2 <tibble [7 × 2]> <htest>
#> 3 3 <tibble [7 × 2]> <htest>
#> 4 4 <tibble [7 × 2]> <htest>
#> 5 5 <tibble [7 × 2]> <htest>
This results in a list-column of S3 objects. We want to tidy each of the objects, which we can also do with map().
nested %>%
mutate(
test = map(data, ~ cor.test(.x$age, .x$circumference)), # S3 list-col
tidied = map(test, tidy)
)
#> # A tibble: 5 × 4
#> Tree data test tidied
#> <ord> <list> <list> <list>
#> 1 1 <tibble [7 × 2]> <htest> <tibble [1 × 8]>
#> 2 2 <tibble [7 × 2]> <htest> <tibble [1 × 8]>
#> 3 3 <tibble [7 × 2]> <htest> <tibble [1 × 8]>
#> 4 4 <tibble [7 × 2]> <htest> <tibble [1 × 8]>
#> 5 5 <tibble [7 × 2]> <htest> <tibble [1 × 8]>
Finally, we want to unnest the tidied data frames so we can see the results in a flat tibble. All together, this looks like:
Orange %>%
nest(data = c(age, circumference)) %>%
mutate(
test = map(data, ~ cor.test(.x$age, .x$circumference)), # S3 list-col
tidied = map(test, tidy)
) %>%
unnest(cols = tidied) %>%
select(-data, -test)
#> # A tibble: 5 × 9
#> Tree estimate statistic p.value parameter conf.low conf.high method
#> <ord> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <chr>
#> 1 1 0.985 13.0 0.0000485 5 0.901 0.998 Pearson's pro…
#> 2 2 0.987 13.9 0.0000343 5 0.914 0.998 Pearson's pro…
#> 3 3 0.988 14.4 0.0000290 5 0.919 0.998 Pearson's pro…
#> 4 4 0.984 12.5 0.0000573 5 0.895 0.998 Pearson's pro…
#> 5 5 0.988 14.1 0.0000318 5 0.916 0.998 Pearson's pro…
#> # … with 1 more variable: alternative <chr>
Regression models
This type of workflow becomes even more useful when applied to regressions. Untidy output for a regression looks like:
lm_fit <- lm(age ~ circumference, data = Orange)
summary(lm_fit)
#>
#> Call:
#> lm(formula = age ~ circumference, data = Orange)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -317.9 -140.9 -17.2 96.5 471.2
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 16.604 78.141 0.21 0.83
#> circumference 7.816 0.606 12.90 1.9e-14 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 203 on 33 degrees of freedom
#> Multiple R-squared: 0.835, Adjusted R-squared: 0.83
#> F-statistic: 166 on 1 and 33 DF, p-value: 1.93e-14
When we tidy these results, we get multiple rows of output for each model:
tidy(lm_fit)
#> # A tibble: 2 × 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 16.6 78.1 0.212 8.33e- 1
#> 2 circumference 7.82 0.606 12.9 1.93e-14
Now we can handle multiple regressions at once using exactly the same workflow as before:
Orange %>%
nest(data = c(-Tree)) %>%
mutate(
fit = map(data, ~ lm(age ~ circumference, data = .x)),
tidied = map(fit, tidy)
) %>%
unnest(tidied) %>%
select(-data, -fit)
#> # A tibble: 10 × 6
#> Tree term estimate std.error statistic p.value
#> <ord> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 1 (Intercept) -265. 98.6 -2.68 0.0436
#> 2 1 circumference 11.9 0.919 13.0 0.0000485
#> 3 2 (Intercept) -132. 83.1 -1.59 0.172
#> 4 2 circumference 7.80 0.560 13.9 0.0000343
#> 5 3 (Intercept) -210. 85.3 -2.46 0.0574
#> 6 3 circumference 12.0 0.835 14.4 0.0000290
#> 7 4 (Intercept) -76.5 88.3 -0.867 0.426
#> 8 4 circumference 7.17 0.572 12.5 0.0000573
#> 9 5 (Intercept) -54.5 76.9 -0.709 0.510
#> 10 5 circumference 8.79 0.621 14.1 0.0000318
You can just as easily use multiple predictors in the regressions, as shown here on the mtcars dataset. We nest the data into automatic vs. manual cars (the am column), then perform the regression within each nested tibble.
data(mtcars)
mtcars <- as_tibble(mtcars) # to play nicely with list-cols
mtcars
#> # A tibble: 32 × 11
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 21 6 160 110 3.9 2.62 16.5 0 1 4 4
#> 2 21 6 160 110 3.9 2.88 17.0 0 1 4 4
#> 3 22.8 4 108 93 3.85 2.32 18.6 1 1 4 1
#> 4 21.4 6 258 110 3.08 3.22 19.4 1 0 3 1
#> 5 18.7 8 360 175 3.15 3.44 17.0 0 0 3 2
#> 6 18.1 6 225 105 2.76 3.46 20.2 1 0 3 1
#> 7 14.3 8 360 245 3.21 3.57 15.8 0 0 3 4
#> 8 24.4 4 147. 62 3.69 3.19 20 1 0 4 2
#> 9 22.8 4 141. 95 3.92 3.15 22.9 1 0 4 2
#> 10 19.2 6 168. 123 3.92 3.44 18.3 1 0 4 4
#> # … with 22 more rows
mtcars %>%
nest(data = c(-am)) %>%
mutate(
fit = map(data, ~ lm(wt ~ mpg + qsec + gear, data = .x)), # S3 list-col
tidied = map(fit, tidy)
) %>%
unnest(tidied) %>%
select(-data, -fit)
#> # A tibble: 8 × 6
#> am term estimate std.error statistic p.value
#> <dbl> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 1 (Intercept) 4.28 3.46 1.24 0.247
#> 2 1 mpg -0.101 0.0294 -3.43 0.00750
#> 3 1 qsec 0.0398 0.151 0.264 0.798
#> 4 1 gear -0.0229 0.349 -0.0656 0.949
#> 5 0 (Intercept) 4.92 1.40 3.52 0.00309
#> 6 0 mpg -0.192 0.0443 -4.33 0.000591
#> 7 0 qsec 0.0919 0.0983 0.935 0.365
#> 8 0 gear 0.147 0.368 0.398 0.696
What if you want not just the tidy() output, but the augment() and glance() outputs as well, while still performing each regression only once? Since we’re using list-columns, we can just fit the model once and use multiple list-columns to store the tidied, glanced and augmented outputs.
regressions <-
mtcars %>%
nest(data = c(-am)) %>%
mutate(
fit = map(data, ~ lm(wt ~ mpg + qsec + gear, data = .x)),
tidied = map(fit, tidy),
glanced = map(fit, glance),
augmented = map(fit, augment)
)
regressions %>%
select(tidied) %>%
unnest(tidied)
#> # A tibble: 8 × 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 4.28 3.46 1.24 0.247
#> 2 mpg -0.101 0.0294 -3.43 0.00750
#> 3 qsec 0.0398 0.151 0.264 0.798
#> 4 gear -0.0229 0.349 -0.0656 0.949
#> 5 (Intercept) 4.92 1.40 3.52 0.00309
#> 6 mpg -0.192 0.0443 -4.33 0.000591
#> 7 qsec 0.0919 0.0983 0.935 0.365
#> 8 gear 0.147 0.368 0.398 0.696
regressions %>%
select(glanced) %>%
unnest(glanced)
#> # A tibble: 2 × 12
#> r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.833 0.778 0.291 15.0 0.000759 3 -0.00580 10.0 12.8
#> 2 0.625 0.550 0.522 8.32 0.00170 3 -12.4 34.7 39.4
#> # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
regressions %>%
select(augmented) %>%
unnest(augmented)
#> # A tibble: 32 × 10
#> wt mpg qsec gear .fitted .resid .hat .sigma .cooksd .std.resid
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 2.62 21 16.5 4 2.73 -0.107 0.517 0.304 0.0744 -0.527
#> 2 2.88 21 17.0 4 2.75 0.126 0.273 0.304 0.0243 0.509
#> 3 2.32 22.8 18.6 4 2.63 -0.310 0.312 0.279 0.188 -1.29
#> 4 2.2 32.4 19.5 4 1.70 0.505 0.223 0.233 0.278 1.97
#> 5 1.62 30.4 18.5 4 1.86 -0.244 0.269 0.292 0.0889 -0.982
#> 6 1.84 33.9 19.9 4 1.56 0.274 0.286 0.286 0.125 1.12
#> 7 1.94 27.3 18.9 4 2.19 -0.253 0.151 0.293 0.0394 -0.942
#> 8 2.14 26 16.7 5 2.21 -0.0683 0.277 0.307 0.00732 -0.276
#> 9 1.51 30.4 16.9 5 1.77 -0.259 0.430 0.284 0.263 -1.18
#> 10 3.17 15.8 14.5 5 3.15 0.0193 0.292 0.308 0.000644 0.0789
#> # … with 22 more rows
By combining the estimates and p-values across all groups into the same tidy data frame (instead of a list of output model objects), a new class of analyses and visualizations becomes straightforward. This includes:
- sorting by p-value or estimate to find the most significant terms across all tests,
- p-value histograms, and
- volcano plots comparing p-values to effect size estimates.
In each of these cases, we can easily filter, facet, or distinguish based on the term column. In short, this makes the tools of tidy data analysis available for the results of data analysis and models, not just the inputs.
Session information
#> ─ Session info ─────────────────────────────────────────────────────
#> setting value
#> version R version 4.2.1 (2022-06-23)
#> os macOS Big Sur ... 10.16
#> system x86_64, darwin17.0
#> ui X11
#> language (EN)
#> collate en_US.UTF-8
#> ctype en_US.UTF-8
#> tz America/Los_Angeles
#> date 2022-12-07
#> pandoc 2.19.2 @ /Applications/RStudio.app/Contents/MacOS/quarto/bin/tools/ (via rmarkdown)
#>
#> ─ Packages ─────────────────────────────────────────────────────────
#> package * version date (UTC) lib source
#> broom * 1.0.1 2022-08-29 [1] CRAN (R 4.2.0)
#> dials * 1.1.0 2022-11-04 [1] CRAN (R 4.2.0)
#> dplyr * 1.0.10 2022-09-01 [1] CRAN (R 4.2.0)
#> ggplot2 * 3.4.0 2022-11-04 [1] CRAN (R 4.2.0)
#> infer * 1.0.4 2022-12-02 [1] CRAN (R 4.2.1)
#> parsnip * 1.0.3 2022-11-11 [1] CRAN (R 4.2.0)
#> purrr * 0.3.5 2022-10-06 [1] CRAN (R 4.2.0)
#> recipes * 1.0.3 2022-11-09 [1] CRAN (R 4.2.0)
#> rlang 1.0.6 2022-09-24 [1] CRAN (R 4.2.0)
#> rsample * 1.1.1 2022-12-07 [1] CRAN (R 4.2.1)
#> tibble * 3.1.8 2022-07-22 [1] CRAN (R 4.2.0)
#> tidymodels * 1.0.0 2022-07-13 [1] CRAN (R 4.2.0)
#> tune * 1.0.1 2022-10-09 [1] CRAN (R 4.2.0)
#> workflows * 1.1.2 2022-11-16 [1] CRAN (R 4.2.0)
#> yardstick * 1.1.0 2022-09-07 [1] CRAN (R 4.2.0)
#>
#> [1] /Library/Frameworks/R.framework/Versions/4.2/Resources/library
#>
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