This is a collection of tools that the author (Jacob) has written for the purpose of more efficiently understanding and sharing the results of (primarily) regression analyses. There are a number of functions focused specifically on the interpretation and presentation of interactions. Just about everything supports models from the survey package.

This package consists of a series of functions created by the author
(Jacob) to automate otherwise tedious research tasks. At this juncture,
the unifying theme is the more efficient presentation of regression
analyses. There are a number of functions for visualizing and doing
inference for interaction terms. Support for the `survey`

package’s
`svyglm`

objects as well as weighted regressions is a common theme
throughout.

**Note**: This is beta software. Bugs are possible, both in terms of
code-breaking errors and more pernicious errors of mistaken computation.

For the most stable version, simply install from CRAN.

install.packages("jtools")

If you want the latest features and bug fixes (and perhaps the latest
bugs, too) then you can download from Github. To do that you will need
to have `devtools`

installed if you don’t already:

install.packages("devtools")

Then install the package from Github.

devtools::install_github("jacob-long/jtools")

Here’s a brief synopsis of the current functions in the package:

`summ`

, `plot_summs`

, `export_summs`

)`summ`

is a replacement for `summary`

that provides the user several
options for formatting regression summaries. It supports `glm`

,
`svyglm`

, and `merMod`

objects as input as well. It supports calculation
and reporting of robust standard errors via the `sandwich`

package.

Basic use:

fit <- lm(mpg ~ hp + wt, data = mtcars)summ(fit)

```
#> MODEL INFO:
#> Observations: 32
#> Dependent Variable: mpg
#>
#> MODEL FIT:
#> F(2,29) = 69.21, p = 0
#> R-squared = 0.83
#> Adj. R-squared = 0.81
#>
#> Standard errors: OLS
#> Est. S.E. t val. p
#> (Intercept) 37.23 1.6 23.28 0 ***
#> hp -0.03 0.01 -3.52 0 **
#> wt -3.88 0.63 -6.13 0 ***
```

It has several conveniences, like re-fitting your model with scaled
variables (`scale = TRUE`

). You have the option to leave the outcome
variable in its original scale (`scale.response = TRUE`

), which is the
default for scaled models. I’m a fan of Andrew Gelman’s 2 SD
standardization method, so you can specify by how many standard
deviations you would like to rescale (`n.sd = 2`

).

You can also get variance inflation factors (VIFs) and partial/semipartial (AKA part) correlations. Partial correlations are only available for OLS models. You may also substitute confidence intervals in place of standard errors and you can choose whether to show p values.

summ(fit, scale = TRUE, vifs = TRUE, part.corr = TRUE, confint = TRUE,pvals = FALSE)

```
#> MODEL INFO:
#> Observations: 32
#> Dependent Variable: mpg
#>
#> MODEL FIT:
#> F(2,29) = 69.21, p = 0
#> R-squared = 0.83
#> Adj. R-squared = 0.81
#>
#> Standard errors: OLS
#> Est. 2.5% 97.5% t val. VIF partial.r part.r
#> (Intercept) 20.09 19.19 20.99 43.82
#> hp -2.18 -3.39 -0.97 -3.52 1.77 -0.55 -0.27
#> wt -3.79 -5.01 -2.58 -6.13 1.77 -0.75 -0.47
#>
#> All continuous predictors are mean-centered and scaled by 1 s.d.
```

Cluster-robust standard errors:

data("PetersenCL", package = "sandwich")fit2 <- lm(y ~ x, data = PetersenCL)summ(fit2, robust = TRUE, cluster = "firm", robust.type = "HC3")

```
#> MODEL INFO:
#> Observations: 5000
#> Dependent Variable: y
#>
#> MODEL FIT:
#> F(1,4998) = 1310.74, p = 0
#> R-squared = 0.21
#> Adj. R-squared = 0.21
#>
#> Standard errors: Cluster-robust, type = HC3
#> Est. S.E. t val. p
#> (Intercept) 0.03 0.07 0.44 0.66
#> x 1.03 0.05 20.36 0 ***
```

Of course, `summ`

like `summary`

is best-suited for interactive use.
When it comes to share results with others, you want sharper output and
probably graphics. `jtools`

has some options for that, too.

First, for tabular output, `export_summs`

is an interface to the
`huxtable`

package’s `huxreg`

function that preserves the niceties of
`summ`

, particularly its facilities for robust standard errors and
standardization. It also concatenates multiple models into a single
table.

fit <- lm(mpg ~ hp + wt, data = mtcars)fit_b <- lm(mpg ~ hp + wt + disp, data = mtcars)fit_c <- lm(mpg ~ hp + wt + disp + drat, data = mtcars)export_summs(fit, fit_b, fit_c, scale = TRUE, scale.response = TRUE,note = "")

1 | 2 | 3 | |
---|---|---|---|

(Intercept) | 5.27e-17.00 | 4.98e-17.00 | 1.02e-16.00 |

(0.08) | (0.08) | (0.08) | |

hp | -0.36 ** | -0.35 * | -0.40 ** |

(0.10) | (0.13) | (0.13) | |

wt | -0.63 *** | -0.62 ** | -0.56 ** |

(0.10) | (0.17) | (0.18) | |

disp | -0.02 | 0.08 | |

(0.21) | (0.22) | ||

drat | 0.16 | ||

(0.12) | |||

N | 32 | 32 | 32 |

R 2 | 0.83 | 0.83 | 0.84 |

In RMarkdown documents, using `export_summs`

and the chunk option
`results = 'asis'`

will give you nice-looking tables in HTML and PDF
output. Using the `to.word = TRUE`

argument will create a Microsoft Word
document with the table in it.

Another way to get a quick gist of your regression analysis is to plot
the values of the coefficients and their corresponding uncertainties
with `plot_summs`

(or the closely related `plot_coefs`

). `jtools`

has
made some slight changes to `ggplot2`

geoms to make everything look
nice; and like with `export_summs`

, you can still get your scaled models
and robust standard errors.

plot_summs(fit, fit_b, fit_c, scale = TRUE, robust = TRUE,coefs = c("Horsepower" = "hp", "Weight (tons)" = "wt","Displacement" = "disp", "Rear axle ratio" = "drat"))

And since you get a `ggplot`

object in return, you can tweak and theme
as you wish.

`plot_coefs`

works much the same way, but without support for `summ`

arguments like `robust`

and `scale`

. This enables a wider range of
models that have support from the `broom`

package but not for `summ`

.
And you can give `summ`

objects to `plot_coefs`

since this package
defines tidy methods for `summ`

objects.

For instance, I could compare the confidence bands with different robust
standard error specifications using `plot_coefs`

by giving the `summ`

objects as arguments.

summ_fit_1 <- summ(fit_b, scale = TRUE)summ_fit_2 <- summ(fit_b, scale = TRUE, robust = TRUE,robust.type = "HC0")summ_fit_3 <- summ(fit_b, scale = TRUE, robust = TRUE,robust.type = "HC3")plot_coefs(summ_fit_1, summ_fit_2, summ_fit_3,model.names = c("OLS","HC0","HC3"),coefs = c("Horsepower" = "hp", "Weight (tons)" = "wt","Displacement" = "disp"))

Unless you have a really keen eye and good familiarity with both the underlying mathematics and the scale of your variables, it can be very difficult to look at the ouput of regression model that includes an interaction and actually understand what the model is telling you.

This package contains several means of aiding understanding and doing statistical inference with interactions.

The “classic” way of probing an interaction effect is to calculate the slope of the focal predictor at different values of the moderator. When the moderator is binary, this is especially informative—e.g., what is the slope for men vs. women? But you can also arbitrarily choose points for continuous moderators.

With that said, the more statistically rigorous way to explore these effects is to find the Johnson-Neyman interval, which tells you the range of values of the moderator in which the slope of the predictor is significant vs. nonsignificant at a specified alpha level.

The `sim_slopes`

function will by default find the Johnson-Neyman
interval and tell you the predictor’s slope at specified values of the
moderator; by default either both values of binary predictors or the
mean and the mean +/- one standard deviation for continuous moderators.

fiti <- lm(mpg ~ hp * wt, data = mtcars)sim_slopes(fiti, pred = hp, modx = wt, jnplot = TRUE)

```
#> JOHNSON-NEYMAN INTERVAL
#>
#> The slope of hp is p < .05 when wt is OUTSIDE this interval:
#> [3.69, 5.9]
#> Note: The range of observed values of wt is [1.51, 5.42]
```

```
#> SIMPLE SLOPES ANALYSIS
#>
#> Slope of hp when wt = 4.2 (+ 1 SD):
#> Est. S.E. p
#> 0.00 0.01 0.76
#>
#> Slope of hp when wt = 3.22 (Mean):
#> Est. S.E. p
#> -0.03 0.01 0.00
#>
#> Slope of hp when wt = 2.24 (- 1 SD):
#> Est. S.E. p
#> -0.06 0.01 0.00
```

The Johnson-Neyman plot can really help you get a handle on what the
interval is telling you, too. Note that you can look at the
Johnson-Neyman interval directly with the `johnson_neyman`

function.

The above all generalize to three-way interactions, too.

This function plots two- and three-way interactions using `ggplot2`

with
a similar interface to the aforementioned `sim_slopes`

function. Users
can customize the appearance with familiar `ggplot2`

commands. It
supports several customizations, like confidence intervals.

interact_plot(fiti, pred = hp, modx = wt, interval = TRUE)

You can also plot the observed data for comparison:

interact_plot(fiti, pred = hp, modx = wt, plot.points = TRUE)

The function also supports categorical moderators—plotting observed data in these cases can reveal striking patterns.

fitiris <- lm(Petal.Length ~ Petal.Width * Species, data = iris)interact_plot(fitiris, pred = Petal.Width, modx = Species, plot.points = TRUE)

You may also combine the plotting and simple slopes functions by using
`probe_interaction`

, which calls both functions simultaneously.
Categorical by categorical interactions can be investigated using the
`cat_plot`

function.

`theme_apa`

This will format your `ggplot2`

graphics to make them (mostly)
appropriate for APA style publications. There’s no drop-in, perfect way
to get plots into APA format sight unseen, but this gets you close and
returns a `ggplot`

object that can be further tweaked to your
specification.

The plots produced by other functions in this package use `theme_apa`

,
but use its options to position the plots and alter other details to
make them more in line with `ggplot2`

defaults than APA norms.

You might start with something like the above interaction plots and then
use `theme_apa`

to tune it to APA specification. Note the `legend.pos`

option:

p <- interact_plot(fitiris, pred = "Petal.Width", modx = "Species", plot.points = TRUE)p + theme_apa(legend.pos = "topleft")

You may need to make further changes to please your publisher, of
course. Since these are regular `ggplot`

theme changes, it shouldn’t be
a problem.

`svycor`

This function extends the `survey`

package by calculating correlations
with complex survey designs, a feature absent from `survey`

. Users may
request significance tests, which are calculated via bootstrap by
calling the `weights`

package.

library(survey)data(api)dstrat <- svydesign(id = ~1, strata = ~stype, weights = ~pw, data = apistrat, fpc = ~fpc)svycor(~ api00 + api99 + dnum, design = dstrat, sig.stats = TRUE)

```
#> api00 api99 dnum
#> api00 1 0.98* 0.25*
#> api99 0.98* 1 0.24*
#> dnum 0.25* 0.24* 1
```

In keeping with the package’s attention to users of survey data, I’ve implemented a couple of tests that help to check whether your model is specified correctly without survey weights. It goes without saying that you shouldn’t let statistical tests do your thinking for you, but they can provide useful info.

The first is `wgttest`

, which implements the DuMouchel-Duncan (1983)
procedure and is meant in part to duplicate the user-written Stata
procedure of the same name. It can both test whether the model fit
overall is changed with the addition of weights as well as show you
which coefficients are most affected.

The next is `pf_sv_test`

, short for Pfeffermann-Sverchkov (1999) test,
which focuses on residual correlation with weights. You’ll need the
`boot`

package for this one.

To run both at once, you can use `weights_tests`

.

`gscale`

, `center_lm`

, `scale_lm`

, and `svysd`

each do some of the
behind the scenes computation in the above functions, but could do well
for end users as well. See the documentation for more.

Details on the arguments can be accessed via the R documentation
(`?functionname`

). There are now vignettes documenting just about
everything you can do as well.

I’m happy to receive bug reports, suggestions, questions, and (most of all) contributions to fix problems and add features. I prefer you use the Github issues system over trying to reach out to me in other ways. Pull requests for contributions are encouraged.

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.

The source code of this package is licensed under the MIT License.

Bugfixes:

`johnson_neyman`

and`sim_slopes`

were both encountering errors with`merMod`

input. Thanks to Seongho Bae for reporting these issues and testing out development versions.- An upcoming version of R will change a common warning to an error, causing
a need to change the internals of
`gscale`

. - The default model names in
`export_summs`

had an extra space (e.g.,`( 1)`

) due to changes in`huxtable`

. The defaults are now just single numbers.

Bugfix:

- Johnson-Neyman plots misreported the alpha level if
`control.fdr`

was`TRUE`

. It was reporting`alpha * 2`

in the legend, but now it is accurate again.

Feature update:

`johnson_neyman`

now handles multilevel models from`lme4`

.

Bugfix update:

Jonas Kunst helpfully pointed out some odd behavior of `interact_plot`

with
factor moderators. No longer should there be occasions in which you have two
different legends appear. The linetype and colors also should now be consistent
whether there is a second moderator or not. For continuous moderators, the
darkest line should also be a solid line and it is by default the highest
value of the moderator.

Other fixes:

- An update to
`huxtable`

broke`export_summs`

, but that has been fixed.

Feature updates:

- You can now manually provide colors to
`interact_plot`

and`cat_plot`

by providing a vector of colors (any format that`ggplot2`

accepts) for the`color.class`

argument. - Noah Greifer wrote up a tweak to
`summ`

that formats the output in a way that lines up the decimal points. It looks great.

This may be the single biggest update yet. If you downloaded from CRAN, be sure to check the 0.8.1 update as well.

New features are organized by function.

johnson_neyman:

- A new
`control.fdr`

option is added to control the false discovery rate, building on new research. This makes the test more conservative but less likely to be a Type 1 error. - A
`line.thickness`

argument has been added after Heidi Jacobs pointed out that it cannot be changed after the fact. - The construction of the multiple plots when using
`sim_slopes`

for 3-way interactions is much-improved. - The critical test statistic used by default has been slightly altered. It
previously used a normal approximation; i.e., if
`alpha = .05`

the critical test statistic was always 1.96. Now, the residual degrees of freedom are used with the t distribution. You can do it the old way by setting`df = "normal"`

or any arbitrary number.

interact_plot:

- More improvements to
`plot.points`

(see 0.8.1 for more). You can now plot observed data with 3-way interactions. - Another pre-set
`modxvals`

and`mod2vals`

specification has been added:`"terciles"`

. This splits the observed data into 3 equally sized groups and chooses as values the mean of each of those groups. This is especially good for skewed data and for second moderators. - A new
`linearity.check`

option for two-way interactions. This facets by each level of the moderator and lets you compare the fitted line with a loess smoothed line to ensure that the interaction effect is roughly linear at each level of the (continuous) moderator. - When the model used weights, like survey sampling weights, the observed data
points are resized according to the observation's weight when
`plot.points = TRUE`

. - New
`jitter`

argument added for those using`plot.points`

. If you don't want the points jittered, you can set`jitter = 0`

. If you want more or less, you can play with the value until it looks right. This applies to`effect_plot`

as well.

summ:

- Users are now informed why the function is taking so long if
`r.squared`

or`pbkrtest`

are slowing things down.`r.squared`

is now set to FALSE by default.

New functions!

`plot_summs`

: A graphic counterpart to `export_summs`

, which was introduced in
the 0.8.0 release. This plots regression coefficients to help in visualizing
the uncertainty of each estimate and facilitates the plotting of nested models
alongside each other for comparison. This allows you to use `summ`

features
like robust standard errors and scaling with this type of plot that you could
otherwise create with some other packages.

`plot_coefs`

: Just like `plot_summs`

, but no special `summ`

features. This
allows you to use models unsupported by `summ`

, however, and you can provide
`summ`

objects to plot the same model with different `summ`

argument alongside
each other.

`cat_plot`

: This was a long time coming. It is a complementary function to
`interact_plot`

, but is designed to deal with interactions between
categorical variables. You can use bar plots, line plots, dot plots, and
box and whisker plots to do so. You can also use the function to plot the effect
of a single categorical predictor without an interaction.

Thanks to Kim Henry who reported a bug with `johnson_neyman`

in the case that
there is an interval, but the entire interval is outside of the plotted area:
When that happened, the legend wrongly stated the plotted line was
non-significant.

Besides that bugfix, some new features:

- When
`johnson_neyman`

fails to find the interval (because it doesn't exist), it no longer quits with an error. The output will just state the interval was not found and the plot will still be created. - Much better support for plotting observed data in
`interact_plot`

has been added. Previously, if the moderator was a factor, you would get very nicely colored plotted points when using`plot.points = TRUE`

. But if the moderator was continuous, the points were just black and it wasn't very informative beyond examining the main effect of the focal predictor. With this update, the plotted points for continous moderators are shaded along a gradient that matches the colors used for the predicted lines and confidence intervals.

Not many user-facing changes since 0.7.4, but major refactoring internally should speed things up and make future development smoother.

Bugfixes:

- interact_plot and effect_plot would trip up when one of the focal predictors had a name that was a subset of a covariate (e.g., pred = "var" but a covariate is called "var_2"). That's fixed.
- Confidence intervals for merMod objects were not respecting the user-requested confidence level and that has been fixed.
- Confidence intervals for merMod objects were throwing a spurious warning on R 3.4.2.
- interact_plot was mis-ordering secondary moderators. That has been fixed.
- export_summs had a major performance problem when providing extra arguments which may have also caused it to wrongly ignore some arguments. That has been fixed and it is much faster.

Enhancements:

- interact_plot now gives more informative labels for secondary moderators when the user has defined the values but not the labels.
- confidence intervals are now properly supported with export_summs
- changes made to export_summs for compatibility with huxtable 1.0.0 changes

Important bugfix:

- When standardize was set to TRUE using summ, the model was not mean-centered as the output stated. This has been fixed. I truly regret the error---double-check any analyses you may have run with this feature.

New function: `export_summs`

.

This function outputs regression models supported by summ in table formats useful for RMarkdown output as well as specific options for exporting to Microsoft Word files. This is particularly helpful for those wanting an efficient way to export regressions that are standardized and/or use robust standard errors.

The documentation for j_summ has been reorganized such that each supported
model type has its own, separate documentation. `?j_summ`

will now just give you
links to each supported model type.

More importantly, j_summ will from now on be referred to as, simply, summ. Your old code is fine; j_summ will now be an alias for summ and will run the same underlying code. Documentation will refer to the summ function, though. That includes the updated vignette.

One new feature for summ.lm:

- With the
`part.corr = TRUE`

argument for a linear model, partial and semipartial correlations for each variable are reported.

More tweaks to summ.merMod:

- Default behavior with regard to p values depends on model type (lmer vs.
glmer/nlmer) and, in the case of linear models, whether the
`pbkrtest`

package is installed. If it is, p values are calculated based on the Kenward-Roger degrees of freedom calculation and printed. Otherwise, p values are not shown by default with lmer models. P values are shown with glmer models, since that is also the default behavior of`lme4`

. - There is an
`r.squared`

option, which for now is FALSE by default. It adds runtime since it must fit a null model for comparison and sometimes this also causes convergence issues.

Returning to CRAN!

A very strange bug on CRAN's servers was causing jtools updates to silently fail when I submitted updates; I'd get a confirmation that it passed all tests, but a LaTeX error related to an Indian journal I cited was torpedoing it before it reached CRAN servers.

The only change from 0.7.0 is fixing that problem, but if you're a CRAN user you will want to flip through the past several releases as well to see what you've missed.

New features:

- j_summ can now provide cluster-robust standard errors for lm models.
- j_summ output now gives info about missing observations for supported models.
- At long last, j_summ/scale_lm/center_lm can standardize/center models with logged terms and other functions applied.
- interact_plot and effect_plot will now also support predictors that have functions applied to them.
- j_summ now supports confidence intervals at user-specified widths.
- j_summ now allows users to not display p-values if requested.
- I've added a warning to j_summ output with merMod objects, since it provides p-values calculated on the basis of the estimated t-values. These are not to be interpreted in the same way that OLS and GLM p-values are, since with smaller samples mixed model t-values will give inflated Type I error rates.
- By default, j_summ will not show p-values for merMod objects.

Bug fix:

- scale_lm did not have its center argument implemented and did not explain the option well in its documentation.
- johnson_neyman got confused when a factor variable was given as a predictor

Bug fix release:

- wgttest acted in a way that might be unexpected when providing a weights variable name but no data argument. Now it should work as expected by getting the data frame from the model call.
- gscale had a few situations in which it choked on missing data, especially when weights were used. This in turn affected j_summ, scale_lm, and center_lm, which each rely on gscale for standardization and mean-centering. That's fixed now.
- gscale wasn't playing nicely with binary factors in survey designs, rendering the scaling incorrect. If you saw a warning, re-check your outputs after this update.

A lot of changes!

New functions:

- effect_plot: If you like the visualization of moderation effects from interact_plot, then you should enjoy effect_plot. It is a clone of interact_plot, but shows a single regression line rather than several. It supports GLMs and lme4 models and can plot original, observed data points.
- pf_sv_test: Another tool for survey researchers to test whether it's okay to run unweighted regressions. Named after Pfefferman and Svervchkov, who devised the test.
- weights_tests: Like probe_interaction does for the interaction functions, weights_tests will run the new pf_sv_test as well as wgttest simultaneously with a common set of arguments.

Enhancements:

- Set a default number of digits to print for all jtools functions with the option "jtools-digits".
- wgttest now accepts and tests GLMs and may work for other regression models.

Bug fixes:

- j_summ would print significance stars based on the rounded p value, sometimes resulting in misleading output. Now significance stars are based on the non-rounded p values.
- probe_interaction did not pass an "alpha" argument to sim_slopes, possibly confusing users of johnson_neyman. The argument sim_slopes is looking for is called "jnalpha". Now probe_interaction will pass "alpha" arguments as "jn_alpha".
- interact_plot would stop on an error when the model included a two-level factor not involved in the interaction and not centered. Now those factors in that situation are treated like other factors.
- interact_plot sometimes gave misleading output when users manually defined moderator labels. It is now more consistent with the ordering the labels and values and will not wrongly label them when the values are provided in an odd order.
- wgttest now functions properly when a vector of weights is provided to the weights argument rather than a column name.
- gscale now works properly on tibbles, which requires a different style of column indexing than data frames.
- Related to the prior point, j_summ/standardize_lm/center_lm now work properly on models that were originally fit with tibbles in the data argument.
- sim_slopes would fail for certain weighted lm objects depending on the way the weights were specified in the function call. It should now work for all weighted lm objects.

More goodies for users of interact_plot:

- Added support for models with a weights parameter in interact_plot. It would work previously, but didn't use a weighted mean or SD in calculating values of the moderator(s) and for mean-centering other predictors. Now it does.
- Added support for two-level factor predictors in interact_plot. Previously, factor variables had to be a moderator.
- When predictor in interact_plot has only two unique values (e.g., dummy variables that have numeric class), by default only those two values have tick marks on the x-axis. Users may use the pred.labels argument to specify labels for those ticks.
- Offsets are now supported (especially useful for Poisson GLMs), but only if specified via the offset argument rather than included in the model formula. You can (and should) specify the offset used for the plot using the set.offset argument. By default it is 1 so that the y-axis represents a proportion.

Other feature changes:

- sim_slopes now supports weights (from the weights argument rather than a svyglm model). Previously it used unweighted mean and standard deviation for non-survey models with weights.
- Improved printing features of wgttest

Bug fixes:

- R 3.4 introduced a change that caused warning messages when return objects are created in a certain way. This was first addressed in jtools 0.4.5, but a few instances slipped through the cracks. Thanks to Kim Henry for pointing out one such instance.
- When sim_slopes called johnson_neyman while the robust argument was set to TRUE, the robust.type argument was not being passed (causing the default of "HC3" to be used). Now it is passing that argument correctly.

- Added better support for plotting nonlinear interactions with interact_plot, providing an option to plot on original (nonlinear) scale.
- interact_plot can now plot fixed effects interactions from merMod objects
- Fixed warning messages when using j_summ with R 3.4.x
- Added preliminary merMod support for j_summ. Still needs convergence warnings, some other items.

- Under the hood changes to j_summ
- Cleaned up examples
- Added wgttest function, which runs a test to assess need for sampling weights in linear regression

- No matter what you do, there's nothing like seeing your package on CRAN to open your eyes to all the typos, etc. you've put into your package.

- This is the first CRAN release. Compared to 0.4.1, the prior Github release, dependencies have been removed and several functions optimized for speed.