# Regression Tables with huxreg

#### David Hugh-Jones

#### 2023-12-09

## Regression tables with `huxreg`

Huxtable includes the function `huxreg` to build a table of regressions.

You call `huxreg` with a list of models. These models can be of any class which has a `tidy` method defined in the broom package. The method should return a list of regression coefficients with names `term`, `estimate`, `std.error` and `p.value`. That covers most standard regression packages.

Let’s start by running some regressions to predict a diamond’s price.

    data(diamonds, package = "ggplot2")
    diamonds <- diamonds[1:100,]

    lm1 <- lm(price ~ carat + depth, diamonds)
    lm2 <- lm(price ~ depth + factor(color, ordered = FALSE), diamonds)
    lm3 <- lm(log(price) ~ carat + depth, diamonds)

Now, we use `huxreg` to display the regression output side by side.

    huxreg(lm1, lm2, lm3)

| (1) | (2) | (3)
--- | --- | --- | ---
(Intercept) | 981.607 | 900.067 | 6.269 ***
| (720.175) | (2431.815) | (0.782)
carat | 4328.324 *** |  | 3.531 ***
| (136.755) |  | (0.149)
depth | -27.785 * | -6.804 | -0.019
| (11.656) | (39.293) | (0.013)
factor(color, ordered = FALSE)E |  | 449.490 |
|  | (239.388) |
factor(color, ordered = FALSE)F |  | 391.705 |
|  | (290.880) |
factor(color, ordered = FALSE)G |  | 583.111 |
|  | (308.513) |
factor(color, ordered = FALSE)H |  | 126.916 |
|  | (256.367) |
factor(color, ordered = FALSE)I |  | -47.220 |
|  | (253.092) |
factor(color, ordered = FALSE)J |  | -123.430 |
|  | (269.157) |
N | 100 | 100 | 100
R2 | 0.912 | 0.123 | 0.854
logLik | -675.703 | -790.788 | 6.822
AIC | 1359.405 | 1599.576 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

The basic output includes estimates, standard errors and summary statistics.

Some of those variable names are hard to read. We can change them by providing a named vector of variables in the `coefs` argument.

    color_names <- grep("factor", names(coef(lm2)), value = TRUE)
    names(color_names) <- gsub(".*)(.)", "Color: \\1", color_names)

    huxreg(lm1, lm2, lm3, coefs = c("Carat" = "carat", "Depth" = "depth", color_names))

| (1) | (2) | (3)
--- | --- | --- | ---
Carat | 4328.324 *** |  | 3.531 ***
| (136.755) |  | (0.149)
Depth | -27.785 * | -6.804 | -0.019
| (11.656) | (39.293) | (0.013)
Color: E |  | 449.490 |
|  | (239.388) |
Color: F |  | 391.705 |
|  | (290.880) |
Color: G |  | 583.111 |
|  | (308.513) |
Color: H |  | 126.916 |
|  | (256.367) |
Color: I |  | -47.220 |
|  | (253.092) |
Color: J |  | -123.430 |
|  | (269.157) |
N | 100 | 100 | 100
R2 | 0.912 | 0.123 | 0.854
logLik | -675.703 | -790.788 | 6.822
AIC | 1359.405 | 1599.576 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

Or, since the output from `huxreg` is just a huxtable, we could just edit its contents directly.

    diamond_regs <- huxreg(lm1, lm2, lm3)
    diamond_regs[seq(8, 18, 2), 1] <- paste("Color:", LETTERS[5:10])

    # prints the same as above

Of course, we aren’t limited to just changing names. We can also make our table prettier. Let’s put our footnote in italic, add a caption, and highlight the cell background of significant coefficients. All of these are just standard huxtable commands.

    suppressPackageStartupMessages(library(dplyr))

    diamond_regs %>%
          map_background_color(-1, -1, by_regex(
            "\\*" = "yellow"
          )) %>%
          set_italic(final(1), 1) %>%
          set_caption("Linear regressions of diamond prices")

Linear regressions of diamond prices
| (1) | (2) | (3)
--- | --- | --- | ---
(Intercept) | 981.607 | 900.067 | 6.269 ***
| (720.175) | (2431.815) | (0.782)
carat | 4328.324 *** |  | 3.531 ***
| (136.755) |  | (0.149)
depth | -27.785 * | -6.804 | -0.019
| (11.656) | (39.293) | (0.013)
Color: E |  | 449.490 |
|  | (239.388) |
Color: F |  | 391.705 |
|  | (290.880) |
Color: G |  | 583.111 |
|  | (308.513) |
Color: H |  | 126.916 |
|  | (256.367) |
Color: I |  | -47.220 |
|  | (253.092) |
Color: J |  | -123.430 |
|  | (269.157) |
N | 100 | 100 | 100
R2 | 0.912 | 0.123 | 0.854
logLik | -675.703 | -790.788 | 6.822
AIC | 1359.405 | 1599.576 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

By default, standard errors are shown below coefficient estimates. To display them in a column to the right, use `error_pos = "right"`:

    huxreg(lm1, lm3, error_pos = "right")

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 | (720.175) | 6.269 *** | (0.782)
carat | 4328.324 *** | (136.755) | 3.531 *** | (0.149)
depth | -27.785 * | (11.656) | -0.019 | (0.013)
N | 100 |  | 100 |
R2 | 0.912 |  | 0.854 |
logLik | -675.703 |  | 6.822 |
AIC | 1359.405 |  | -5.644 |
*** p < 0.001; ** p < 0.01; * p < 0.05.

This will give column headings a column span of 2.

To display standard errors in the same cell as estimates, use `error_pos = "same"`:

    huxreg(lm1, lm3, error_pos = "same")

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 (720.175) | 6.269 *** (0.782)
carat | 4328.324 *** (136.755) | 3.531 *** (0.149)
depth | -27.785 * (11.656) | -0.019 (0.013)
N | 100 | 100
R2 | 0.912 | 0.854
logLik | -675.703 | 6.822
AIC | 1359.405 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

You can change the default column headings by naming the model arguments:

    huxreg("Price" = lm1, "Log price" = lm3)

| Price | Log price
--- | --- | ---
(Intercept) | 981.607 | 6.269 ***
| (720.175) | (0.782)
carat | 4328.324 *** | 3.531 ***
| (136.755) | (0.149)
depth | -27.785 * | -0.019
| (11.656) | (0.013)
N | 100 | 100
R2 | 0.912 | 0.854
logLik | -675.703 | 6.822
AIC | 1359.405 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

To display a particular row of summary statistics, use the `statistics` parameter. This should be a character vector. Valid values are anything returned from your models by `broom::glance`:

    gl <- as_hux(broom::glance(lm1))

    gl %>%
          restack_down(cols = 3, on_remainder = "fill") %>%
          set_bold(odds, everywhere)

r.squared | adj.r.squared | sigma
--- | --- | ---
0.912 | 0.91 | 211
statistic | p.value | df
504 | 5.65e-52 | 2
logLik | AIC | BIC
-676 | 1.36e+03 | 1.37e+03
deviance | df.residual | nobs
4.33e+06 | 97 | 100

Another value you can use is `"nobs"`, which returns the number of observations from the regression. If the `statistics` vector has names, these will be used for row headings:

    huxreg(lm1, lm3, statistics = c("N. obs." = "nobs",
          "R squared" = "r.squared", "F statistic" = "statistic",
          "P value" = "p.value"))

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 | 6.269 ***
| (720.175) | (0.782)
carat | 4328.324 *** | 3.531 ***
| (136.755) | (0.149)
depth | -27.785 * | -0.019
| (11.656) | (0.013)
N. obs. | 100 | 100
R squared | 0.912 | 0.854
F statistic | 504.082 | 283.881
P value | 0.000 | 0.000
*** p < 0.001; ** p < 0.01; * p < 0.05.

By default, `huxreg` displays significance stars. You can alter the symbols used and significance levels with the `stars` parameter, or set `stars = NULL` to turn off significance stars completely.

    huxreg(lm1, lm3, stars = c(`*` = 0.1, `**` = 0.05, `***` = 0.01)) # a little boastful?

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 | 6.269 ***
| (720.175) | (0.782)
carat | 4328.324 *** | 3.531 ***
| (136.755) | (0.149)
depth | -27.785 ** | -0.019
| (11.656) | (0.013)
N | 100 | 100
R2 | 0.912 | 0.854
logLik | -675.703 | 6.822
AIC | 1359.405 | -5.644
*** p < 0.01; ** p < 0.05; * p < 0.1.

You aren’t limited to displaying standard errors of the estimates. If you prefer, you can display t statistics or p values, using the `error_format` option. Any column from `tidy` can be used by putting it in curly brackets:

    # Another useful column: p.value
    huxreg(
            lm1, lm3,
            error_format = "[{statistic}]",
            note         = "{stars}. T statistics in brackets."
          )

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 | 6.269 ***
| [1.363] | [8.016]
carat | 4328.324 *** | 3.531 ***
| [31.650] | [23.773]
depth | -27.785 * | -0.019
| [-2.384] | [-1.499]
N | 100 | 100
R2 | 0.912 | 0.854
logLik | -675.703 | 6.822
AIC | 1359.405 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05. T statistics in brackets.

Here we also changed the footnote, using `note`. If `note` contains the string `"{stars}"` it will be replaced by a description of the significance stars used. If you don’t want a footnote, just set `note = NULL`.

Alternatively, you can display confidence intervals. Use `ci_level` to set the confidence level for the interval, then use `{conf.low}` and `{conf.high}` in `error_format`:

    huxreg(lm1, lm3, ci_level = .99, error_format = "({conf.low} -- {conf.high})")

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 | 6.269 ***
| (-910.629 -- 2873.844) | (4.214 -- 8.324)
carat | 4328.324 *** | 3.531 ***
| (3969.004 -- 4687.643) | (3.140 -- 3.921)
depth | -27.785 * | -0.019
| (-58.411 -- 2.842) | (-0.052 -- 0.014)
N | 100 | 100
R2 | 0.912 | 0.854
logLik | -675.703 | 6.822
AIC | 1359.405 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

To change number formatting, set the `number_format` parameter. This works the same as the `number_format` property for a huxtable - if it is numeric, numbers will be rounded to that many decimal places; if it is character, it will be taken as a format to the base R `sprintf` function. `huxreg` tries to be smart and to format summary statistics like `nobs` as integers.

    huxreg(lm1, lm3, number_format = 2)

| (1) | (2)
--- | --- | ---
(Intercept) | 981.61 | 6.27 ***
| (720.17) | (0.78)
carat | 4328.32 *** | 3.53 ***
| (136.75) | (0.15)
depth | -27.78 * | -0.02
| (11.66) | (0.01)
N | 100 | 100
R2 | 0.91 | 0.85
logLik | -675.70 | 6.82
AIC | 1359.41 | -5.64
*** p < 0.001; ** p < 0.01; * p < 0.05.

Lastly, if you want to bold all significant coefficients, set the parameter `bold_signif` to a maximum significance level:

    huxreg(lm1, lm3, bold_signif = 0.05)

| (1) | (2)
--- | --- | ---
(Intercept) | 981.607 | 6.269 ***
| (720.175) | (0.782)
carat | 4328.324 *** | 3.531 ***
| (136.755) | (0.149)
depth | -27.785 * | -0.019
| (11.656) | (0.013)
N | 100 | 100
R2 | 0.912 | 0.854
logLik | -675.703 | 6.822
AIC | 1359.405 | -5.644
*** p < 0.001; ** p < 0.01; * p < 0.05.

## Altering data

Sometimes, you want to report different statistics for a model. For example, you might want to use robust standard errors.

One way to do this is to pass a `tidy`-able test object into `huxreg`. The function `coeftest` in the “lmtest” package has `tidy` methods defined:

    library(lmtest)

    ## Loading required package: zoo

    ##
    ## Attaching package: 'zoo'

    ## The following objects are masked from 'package:base':
    ##
    ##     as.Date, as.Date.numeric

    library(sandwich)
    lm_robust <- coeftest(lm1, vcov = vcovHC, save = TRUE)
    huxreg("Normal SEs" = lm1, "Robust SEs" = lm_robust)

| Normal SEs | Robust SEs
--- | --- | ---
(Intercept) | 981.607 | 981.607
| (720.175) | (1117.654)
carat | 4328.324 *** | 4328.324 ***
| (136.755) | (293.929)
depth | -27.785 * | -27.785
| (11.656) | (17.995)
N | 100 | 100
R2 | 0.912 | 0.912
logLik | -675.703 | -675.703
AIC | 1359.405 | 1359.405
*** p < 0.001; ** p < 0.01; * p < 0.05.

If that is not possible, you can compute statistics yourself and add them to your model using the `tidy_override` function:

    lm_fixed <- tidy_override(lm1, p.value = c(0.5, 0.2, 0.06))
    huxreg("Normal p values" = lm1, "Supplied p values" = lm_fixed)

| Normal p values | Supplied p values
--- | --- | ---
(Intercept) | 981.607 | 981.607
| (720.175) | (720.175)
carat | 4328.324 *** | 4328.324
| (136.755) | (136.755)
depth | -27.785 * | -27.785
| (11.656) | (11.656)
N | 100 | 100
R2 | 0.912 | 0.912
logLik | -675.703 | -675.703
AIC | 1359.405 | 1359.405
*** p < 0.001; ** p < 0.01; * p < 0.05.

You can override any statistics returned by `tidy` or `glance`.

If you want to completely replace the output of tidy, use the `tidy_replace()` function. For example, here’s how to print different coefficients for a multinomial model.

    mnl <- nnet::multinom(gear ~ mpg, mtcars)

    ## # weights:  9 (4 variable)
    ## initial  value 35.155593
    ## iter  10 value 23.131901
    ## final  value 23.129234
    ## converged

    tidied <- broom::tidy(mnl)
    models <- list()
    models[["4 gears"]] <- tidy_replace(mnl, tidied[tidied$y.level == 4, ])
    models[["5 gears"]] <- tidy_replace(mnl, tidied[tidied$y.level == 5, ])
    huxreg(models, statistics = "AIC")

| 4 gears | 5 gears
--- | --- | ---
(Intercept) | -9.502 ** | -7.691 *
| (3.262) | (3.232)
mpg | 0.475 ** | 0.358 *
| (0.168) | (0.168)
AIC | 54.258 | 54.258
*** p < 0.001; ** p < 0.01; * p < 0.05.