# For developers: Extending emmeans

## Contents

This vignette explains how developers may incorporate emmeans support in their packages. If you are a user looking for a quick way to obtain results for an unsupported model, you are probably better off trying to use the qdrg() function.

Index of all vignette topics

## Introduction

Suppose you want to use emmeans for some type of model that it doesn’t (yet) support. Or, suppose you have developed a new package with a fancy model-fitting function, and you’d like it to work with emmeans. What can you do? Well, there is hope because emmeans is designed to be extended.

The first thing to do is to look at the help page for extending the package:

help("extending-emmeans", package="emmeans")

It gives details about the fact that you need to write two S3 methods, recover_data and emm_basis, for the class of object that your model-fitting function returns. The recover_data method is needed to recreate the dataset so that the reference grid can be identified. The emm_basis method then determines the linear functions needed to evaluate each point in the reference grid and to obtain associated information—such as the variance-covariance matrix—needed to do estimation and testing.

These methods must also be exported from your package so that they are available to users. See the section on exporting the methods for details and suggestions.

This vignette presents an example where suitable methods are developed, and discusses a few issues that arise.

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## Data example

The MASS package contains various functions that do robust or outlier-resistant model fitting. We will cobble together some emmeans support for these. But first, let’s create a suitable dataset (a simulated two-factor experiment) for testing.

fake = expand.grid(rep = 1:5, A = c("a1","a2"), B = c("b1","b2","b3"))
fake$y = c(11.46,12.93,11.87,11.01,11.92,17.80,13.41,13.96,14.27,15.82, 23.14,23.75,-2.09,28.43,23.01,24.11,25.51,24.11,23.95,30.37, 17.75,18.28,17.82,18.52,16.33,20.58,20.55,20.77,21.21,20.10) The y values were generated using predetermined means and Cauchy-distributed errors. There are some serious outliers in these data. ## Supporting rlm The MASS package provides an rlm function that fits robust-regression models using M estimation. We’ll fit a model using the default settings for all tuning parameters: library(MASS) fake.rlm = rlm(y ~ A * B, data = fake) library(emmeans) emmeans(fake.rlm, ~ B | A) ## A = a1: ## B emmean SE df asymp.LCL asymp.UCL ## b1 11.8 0.477 NA 10.9 12.8 ## b2 23.3 0.477 NA 22.4 24.2 ## b3 17.8 0.477 NA 16.9 18.7 ## ## A = a2: ## B emmean SE df asymp.LCL asymp.UCL ## b1 14.7 0.477 NA 13.7 15.6 ## b2 24.7 0.477 NA 23.8 25.6 ## b3 20.6 0.477 NA 19.7 21.6 ## ## Confidence level used: 0.95 The first lesson to learn about extending emmeans is that sometimes, it already works! It works here because rlm objects inherit from lm, which is supported by the emmeans package, and rlm objects aren’t enough different to create any problems. Back to Contents ## Supporting lqs objects The MASS resistant-regression functions lqs, lmsreg, and ltsreg are another story, however. They create lqs objects that are not extensions of any other class, and have other issues, including not even having a vcov method. So for these, we really do need to write new methods for lqs objects. First, let’s fit a model. fake.lts = ltsreg(y ~ A * B, data = fake) ### The recover_data method It is usually an easy matter to write a recover_data method. Look at the one for lm objects: emmeans:::recover_data.lm ## function (object, ...) ## { ## fcall = object$call
##     recover_data(fcall, delete.response(terms(object)), object$na.action, ## ...) ## } ## <bytecode: 0x000000001f978fc8> ## <environment: namespace:emmeans> Note that all it does is obtain the call component and call the method for class call, with additional arguments for its terms component and na.action. It happens that we can access these attributes in exactly the same way as for lm objects; so: recover_data.lqs = emmeans:::recover_data.lm Let’s test it: rec.fake = recover_data(fake.lts) head(rec.fake) ## A B ## 1 a1 b1 ## 2 a1 b1 ## 3 a1 b1 ## 4 a1 b1 ## 5 a1 b1 ## 6 a2 b1 Our recovered data excludes the response variable y (owing to the delete.response call), and this is fine. #### Special arguments By the way, there are two special arguments data and params that may be handed to recover_data via ref_grid or emmeans or a related function; and you may need to provide for if you don’t use the recover_data.call function. The data argument is needed to cover a desperate situation that occurs with certain kinds of models where the underlying data information is not saved with the object—e.g., models that are fitted by iteratively modifying the data. In those cases, the only way to recover the data is to for the user to give it explicitly, and recover_data just adds a few needed attributes to it. The params argument is needed when the model formula refers to variables besides predictors. For example, a model may include a spline term, and the knots are saved in the user’s environment as a vector and referred to in the call to fit the model. In trying to recover the data, we try to construct a data frame containing all the variables present on the right-hand side of the model, but if some of those are scalars or of different lengths than the number of observations, an error occurs. So you need to exclude any names in params when reconstructing the data. #### Error handling If you check for any error conditions in recover_data, simply have it return a character string with the desired message, rather than invoking stop. This provides a cleaner exit. The reason is that whenever recover_data throws an error, an informative message suggesting that data or params be provided is displayed. But a character return value is tested for and throws a different error with your string as the message. ### The emm_basis method The emm_basis method has four required arguments: args(emmeans:::emm_basis.lm) ## function (object, trms, xlev, grid, ...) ## NULL These are, respectively, the model object, its terms component (at least for the right-hand side of the model), a list of levels of the factors, and the grid of predictor combinations that specify the reference grid. The function must obtain six things and return them in a named list. They are the matrix X of linear functions for each point in the reference grid, the regression coefficients bhat; the variance-covariance matrix V; a matrix nbasis for non-estimable functions; a function dffun(k,dfargs) for computing degrees of freedom for the linear function sum(k*bhat); and a list dfargs of arguments to pass to dffun. To write your own emm_basis function, examining some of the existing methods can help; but the best resource is the predict method for the object in question, looking carefully to see what it does to predict values for a new set of predictors (e.g., newdata in predict.lm). Following this advice, let’s take a look at it: MASS:::predict.lqs ## function (object, newdata, na.action = na.pass, ...) ## { ## if (missing(newdata)) ## return(fitted(object)) ## Terms <- delete.response(terms(object)) ## m <- model.frame(Terms, newdata, na.action = na.action, xlev = object$xlevels)
##     if (!is.null(cl <- attr(Terms, "dataClasses")))
##         .checkMFClasses(cl, m)
##     X <- model.matrix(Terms, m, contrasts = object$contrasts) ## drop(X %*% object$coefficients)
## }
## <bytecode: 0x0000000025225b08>
## <environment: namespace:MASS>

Based on this, here is a listing of an emm_basis method for lqs objects:

emm_basis.lqs = function(object, trms, xlev, grid, ...) {
m = model.frame(trms, grid, na.action = na.pass, xlev = xlev)
X = model.matrix(trms, m, contrasts.arg = object$contrasts) bhat = coef(object) Xmat = model.matrix(trms, data=object$model)                      # 5
V = rev(object$scale)[1]^2 * solve(t(Xmat) %*% Xmat) nbasis = matrix(NA) dfargs = list(df = nrow(Xmat) - ncol(Xmat)) dffun = function(k, dfargs) dfargs$df
list(X = X, bhat = bhat, nbasis = nbasis, V = V,                  #10
dffun = dffun, dfargs = dfargs)
}

Before explaining it, let’s verify that it works:

emmeans(fake.lts, ~ B | A)
## A = a1:
##  B  emmean    SE df lower.CL upper.CL
##  b1   11.9 0.228 24     11.4     12.3
##  b2   23.1 0.228 24     22.6     23.6
##  b3   17.8 0.228 24     17.3     18.2
##
## A = a2:
##  B  emmean    SE df lower.CL upper.CL
##  b1   13.9 0.228 24     13.4     14.4
##  b2   24.1 0.228 24     23.6     24.5
##  b3   20.5 0.228 24     20.0     21.0
##
## Confidence level used: 0.95

Hooray! Note the results are comparable to those we had for fake.rlm, albeit the standard errors are quite a bit smaller. (In fact, the SEs could be misleading; a better method for estimating covariances should probably be implemented, but that is beyond the scope of this vignette.)

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### Dissecting emm_basis.lqs

Let’s go through the listing of this method, line-by-line:

• Lines 2–3: Construct the linear functions, X. This is a pretty standard two-step process: First obtain a model frame, m, for the grid of predictors, then pass it as data to model.matrix to create the associated design matrix. As promised, this code is essentially identical to what you find in predict.lqs.

• Line 4: Obtain the coefficients, bhat. Most model objects have a coef method.

• Lines 5–6: Obtain the covariance matrix, V, of bhat. In many models, this can be obtained using the object’s vcov method. But not in this case. Instead, I cobbled one together using the inverse of the X’X matrix as in ordinary regression, and the variance estimate found in the last element of the scale element of the object. This probably under-estimates the variances and distorts the covariances, because robust estimators have some efficiency loss.

• Line 7: Compute the basis for non-estimable functions. This applies only when there is a possibility of rank deficiency in the model. But lqs methods don’t allow rank deficiencies, so it we have fitted such a model, we can be sure that all linear functions are estimable; we signal that by setting nbasis equal to a 1 x 1 matrix of NA. If rank deficiency were possible, the estimability package (which is required by emmeans) provides a nonest.basis function that makes this fairly painless—I would have coded nbasis = estimability::nonest.basis(Xmat).

There some subtleties you need to know regarding estimability. Suppose the model is rank-deficient, so that the design matrix X has p columns but rank r < p. In that case, bhat should be of length p (not r), and there should be p - r elements equal to NA, corresponding to columns of X that were excluded from the fit. Also, X should have all p columns. In other words, do not alter or throw-out columns of X or their corresponding elements of bhat—even those with NA coefficients—as they are essential for assessing estimability. V should be r x r, however—the covariance matrix for the non-excluded predictors.

• Lines 8–9: Obtain dffun and dfargs. This is a little awkward because it is designed to allow support for mixed models, where approximate methods may be used to obtain degrees of freedom. The function dffun is expected to have two arguments: k, the vector of coefficients of bhat, and dfargs, a list containing any additional arguments. In this case (and in many other models), the degrees of freedom are the same regardless of k. We put the required degrees of freedom in dfargs and write dffun so that it simply returns that value. (Note: If asymptotic tests and CIs are desired, return Inf degrees of freedom.)

• Line 10: Return these results in a named list.

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## Communication between methods

If you need to pass information obtained in recover_data() to the emm_basis() method, simply incorporate it as attr(data, "misc") where data is the dataset returned by recover_data(). Subsequently, that attribute is available in emm_grid() by adding a misc argument.

## Hook functions

Most linear models supported by emmeans have straightforward structure: Regression coefficients, their covariance matrix, and a set of linear functions that define the reference grid. However, a few are more complex. An example is the clm class in the ordinal package, which allows a scale model in addition to the location model. When a scale model is used, the scale parameters are included in the model matrix, regression coefficients, and covariance matrix, and we can’t just use the usual matrix operations to obtain estimates and standard errors. To facilitate using custom routines for these tasks, the emm_basis.clm function function provided in emmeans includes, in its misc part, the names (as character constants) of two “hook” functions: misc$estHook has the name of the function to call when computing estimates, standard errors, and degrees of freedom (for the summary method); and misc$vcovHook has the name of the function to call to obtain the covariance matrix of the grid values (used by the vcov method). These functions are called in lieu of the usual built-in routines for these purposes, and return the appropriately sized matrices.

In addition, you may want to apply some form of special post-processing after the reference grid is constructed. To provide for this, give the name of your function to post-process the object in misc$postGridHook. Again, clm objects (as well as polr in the MASS package) serve as an example. They allow a mode specification that in two cases, calls for post-processing. The "cum.prob" mode uses the regrid function to transform the linear predictor to the cumulative-probability scale. And the "prob" mode performs this, as well as applying the contrasts necessary to convert the cumulative probabilities into the class probabilities. Back to Contents ## Exported methods from emmeans For package developers’ convenience, emmeans exports some of its S3 methods for recover_data and/or emm_basis—use methods("recover_data") and methods("emm_basis") to discover which ones. It may be that all you need is to invoke one of those methods and perhaps make some small changes—especially if your model-fitting algorithm makes heavy use of an existing model type supported by emmeans. For those methods that are not exported, use recover_data() and .emm_basis(), which run in emmeans’s namespace, thus providing access to all available methods.. A few additional functions are exported because they may be useful to developers. They are as follows: • emmeans::.all.vars(expr, retain) Some users of your package may include $ or [[]] operators in their model formulas. If you need to get the variable names, base::all.vars will probably not give you what you need. For example, if form = ~ data$x + data[[5]], then base::all.vars(form) returns the names "data" and "x", whereas emmeans::.all.vars(form) returns the names "data$x" and "data[[5]]". The retain argument may be used to specify regular expressions for patterns to retain as parts of variable names.

• emmeans::.diag(x, nrow, ncol) The base diag function has a booby trap whereby, for example, diag(57.6) returns a 57 x 57 identity matrix rather than a 1 x 1 matrix with 57.6 as its only element. But emmeans::.diag(57.6) will return the latter. The function works identically to diag except for its tail run around the identity-matrix trap.

• emmeans::.aovlist.dffun(k, dfargs) This function is exported because it is needed for computing degrees of freedom for models fitted using aov, but it may be useful for other cases where Satterthwaite degrees-of-freedom calculations are needed. It requires the dfargs slot to contain analogous contents.

• emmeans::.get.offset(terms, grid) If terms is a model formula containing an offset call, this is will compute that offset in the context of grid (a data.frame).

• emmeans::.my.vcov(object, ...) In a call to ref_grid, emmeans, etc., the user may use vcov. to specify an alternative function or matrix to use as the covariance matrix of the fixed-effects coefficients. This function supports that feature. Calling .my.vcov in place of the vcov method will substitute the user’s vcov. when it is specified.

• emmeans::.std.link.labels(fam, misc) This is useful in emm_basis methods for generalized linear models. Call it with fam equal to the family object for your model, and misc either an existing list, or just list() if none. It returns a new misc list containing the link function and, in some cases, extra features that are used for certain types of link functions (e.g., for a log link, the setups for returning ratio comparisons with type = "response").

• emmeans::.num.key(levs, key) Returns integer indices of elements of key in levs when key is a character vector; or just returns integer values if already integer. Also throws an error if levels are mismatched or indices exceed legal range. This is useful in custom contrast functions (.emmc functions).

• emmeans::.get.excl(levs, exclude, include) This is support for the exclude and include arguments of contrast functions. It checks legality and returns an integer vector of exclude indices in levs, given specified integer or character arguments exclude and include. In your .emmc function, exclude should default to integer(0) and include should have no default.

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## Existing support for rsm objects

As a nontrivial example of how an existing package supports emmeans, we show the support offered by the rsm package. Its rsm function returns an rsm object which is an extension of the lm class. Part of that extension has to do with coded.data structures whereby, as is typical in response-surface analysis, models are fitted to variables that have been linearly transformed (coded) so that the scope of each predictor is represented by plus or minus 1 on the coded scale.

Without any extra support in rsm, emmeans will work just fine with rsm objects; but if the data are coded, it becomes awkward to present results in terms of the original predictors on their original, uncoded scale. The emmeans-related methods in rsm provide a mode argument that may be used to specify whether we want to work with coded or uncoded data. The possible values for mode are "asis" (ignore any codings, if present), "coded" (use the coded scale), and "decoded" (use the decoded scale). The first two are actually the same in that no decoding is done; but it seems clearer to provide separate options because they represent two different situations.

### The recover_data method

Note that coding is a predictor transformation, not a response transformation (we could have that, too, as it’s already supported by the emmeans infrastructure). So, to handle the "decode" mode, we will need to actually decode the predictors used to construct he reference grid. That means we need to make recover_data a lot fancier! Here it is:

recover_data.rsm = function(object, data, mode = c("asis", "coded", "decoded"), ...) {
mode = match.arg(mode)
cod = rsm::codings(object)
fcall = object$call if(is.null(data)) # 5 data = emmeans::recover_data(fcall, delete.response(terms(object)), object$na.action, ...)
if (!is.null(cod) && (mode == "decoded")) {
pred = cpred = attr(data, "predictors")
trms = attr(data, "terms")                                    #10
data = rsm::decode.data(rsm::as.coded.data(data, formulas = cod))
for (form in cod) {
vn = all.vars(form)
if (!is.na(idx <- grep(vn[1], pred))) {
pred[idx] = vn[2]                                     #15
cpred = setdiff(cpred, vn[1])
}
}
attr(data, "predictors") = pred
new.trms = update(trms, reformulate(c("1", cpred)))           #20
attr(new.trms, "orig") = trms
attr(data, "terms") = new.trms
attr(data, "misc") = cod
}
data
}

Lines 2–7 ensure that mode is legal, retrieves the codings from the object, and obtain the results we would get from recover_data had it been an lm object. If mode is not "decoded", or if no codings were used, that’s all we need. Otherwise, we need to return the decoded data. However, it isn’t quite that simple, because the model equation is still defined on the coded scale. Rather than to try to translate the model coefficients and covariance matrix to the decoded scale, we elected to remember what we will need to do later to put things back on the coded scale. In lines 9–10, we retrieve the attributes of the recovered data that provide the predictor names and terms object on the coded scale. In line 11, we replace the recovered data with the decoded data.

By the way, the codings comprise a list of formulas with the coded name on the left and the original variable name on the right. It is possible that only some of the predictors are coded (for example, blocking factors will not be). In the for loop in lines 12–18, the coded predictor names are replaced with their decoded names. For technical reasons to be discussed later, we also remove these coded predictor names from a copy, cpred, of the list of all predictors in the coded model. In line 19, the "predictors" attribute of data is replaced with the modified version.

Now, there is a nasty technicality. The ref_grid function in emmeans has a few lines of code after recover_data is called that determine if any terms in the model convert covariates to factors or vice versa; and this code uses the model formula. That formula involves variables on the coded scale, and those variables are no longer present in the data, so an error will occur if it tries to access them. Luckily, if we simply take those terms out of the formula, it won’t hurt because those coded predictors would not have been converted in that way. So in line 20, we update trms with a simpler model with the coded variables excluded (the intercept is explicitly included to ensure there will be a right-hand side even is cpred is empty). We save that as the terms attribute, and the original terms as a new "orig" attribute to be retrieved later. The data object, modified or not, is returned. If data have been decoded, ref_grid will construct its grid using decoded variables.

In line 23, we save the codings as the "misc" attribute, to be accessed later by emm_basis().

### The emm_basis method

Now comes the emm_basis method that will be called after the grid is defined. It is listed below:

emm_basis.rsm = function(object, trms, xlev, grid,
mode = c("asis", "coded", "decoded"), misc, ...) {
mode = match.arg(mode)
cod = misc
if(!is.null(cod) && mode == "decoded") {                          # 5
grid = rsm::coded.data(grid, formulas = cod)
trms = attr(trms, "orig")
}

m = model.frame(trms, grid, na.action = na.pass, xlev = xlev)     #10
X = model.matrix(trms, m, contrasts.arg = object$contrasts) bhat = as.numeric(object$coefficients)
V = emmeans::.my.vcov(object, ...)

if (sum(is.na(bhat)) > 0)                                         #15
nbasis = estimability::nonest.basis(object$qr) else nbasis = estimability::all.estble dfargs = list(df = object$df.residual)
dffun = function(k, dfargs) dfargs$df #20 list(X = X, bhat = bhat, nbasis = nbasis, V = V, dffun = dffun, dfargs = dfargs, misc = list()) } This is much simpler. The coding formulas are obtained from misc (line 4) so that we don’t have to re-obtain them from the object. All we have to do is determine if decoding was done (line 5); and, if so, convert the grid back to the coded scale (line 6) and recover the original terms attribute (line 7). The rest is borrowed directly from the emm_basis.lm method in emmeans. Note that line 13 uses one of the exported functions we described in the preceding section. Lines 15–18 use functions from the estimability package to handle the possibility that the model is rank-deficient. ### A demonstration Here’s a demonstration of this rsm support. The standard example for rsm fits a second-order model CR.rs2 to a dataset organized in two blocks and with two coded predictors. library("rsm") example("rsm") ### (output is not shown) ### First, let’s look at some results on the coded scale—which are the same as for an ordinary lm object. emmeans(CR.rs2, ~ x1 * x2, mode = "coded", at = list(x1 = c(-1, 0, 1), x2 = c(-2, 2))) ## x1 x2 emmean SE df lower.CL upper.CL ## -1 -2 75.0 0.298 7 74.3 75.7 ## 0 -2 77.0 0.240 7 76.4 77.5 ## 1 -2 76.4 0.298 7 75.6 77.1 ## -1 2 76.8 0.298 7 76.1 77.5 ## 0 2 79.3 0.240 7 78.7 79.9 ## 1 2 79.2 0.298 7 78.5 79.9 ## ## Results are averaged over the levels of: Block ## Confidence level used: 0.95 Now, the coded variables x1 and x2 are derived from these coding formulas for predictors Time and Temp: codings(CR.rs1) ##$x1
## x1 ~ (Time - 85)/5
##
## \$x2
## x2 ~ (Temp - 175)/5

Thus, for example, a coded value of x1 = 1 corresponds to a time of 85 + 1 x 5 = 90. Here are some results working with decoded predictors. Note that the at list must now be given in terms of Time and Temp:

emmeans(CR.rs2, ~ Time * Temp, mode = "decoded",
at = list(Time = c(80, 85, 90), Temp = c(165, 185)))
##  Time Temp emmean    SE df lower.CL upper.CL
##    80  165   75.0 0.298  7     74.3     75.7
##    85  165   77.0 0.240  7     76.4     77.5
##    90  165   76.4 0.298  7     75.6     77.1
##    80  185   76.8 0.298  7     76.1     77.5
##    85  185   79.3 0.240  7     78.7     79.9
##    90  185   79.2 0.298  7     78.5     79.9
##
## Results are averaged over the levels of: Block
## Confidence level used: 0.95

Since the supplied settings are the same on the decoded scale as were used on the coded scale, the EMMs are identical to those in the previous output.

## Dispatching and restrictions

The emmeans package has internal support for a number of model classes. When recover_data() and emm_basis() are dispatched, a search is made for external methods for a given class; and if found, those methods are used instead of the internal ones. However, certain restrictions apply when you aim to override an existing internal method:

1. The class name being extended must appear in the first or second position in the results of class(object). That is, you may have a base class for which you provide recover_data() and emm_basis() methods, and those will also work for direct descendants thereof; but any class in third place or later in the inheritance is ignored.
2. Certain classes vital to the correct operation of the package, e.g., "lm", "glm", etc., may not be overridden.

If there are no existing internal methods for the class(es) you provide methods for, there are no restrictions on them.

## Exporting and registering your methods

To make the methods available to users of your package, the methods must be exported. R and CRAN are evolving in a way that having S3 methods in the registry is increasingly important; so it is a good idea to provide for that. The problem is not all of your package users will have emmeans installed.

Thus, registering the methods must be done conditionally. We provide a courtesy function .emm_register() to make this simple. Suppose that your package offers two model classes foo and bar, and it includes the corresponding functions recover_data.foo, recover_data.bar, emm_basis.foo, and emm_basis.bar. Then to register these methods, add or modify the .onLoad function in your package (traditionally saved in the source file zzz.R):

.onLoad <- function(libname, pkgname) {
if (requireNamespace("emmeans", quietly = TRUE))
emmeans::.emm_register(c("foo", "bar"), pkgname)
}


You should also add emmeans (>= 1.4) and estimability (which is required by emmeans) to the Suggests field of your DESCRIPTION file.

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## Conclusions

It is relatively simple to write appropriate methods that work with emmeans for model objects it does not support. I hope this vignette is helpful for understanding how. Furthermore, if you are the developer of a package that fits linear models, I encourage you to include recover_data and emm_basis methods for those classes of objects, so that users have access to emmeans support.

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Index of all vignette topics