# Models supported by emmeans" In emmeans: Estimated Marginal Means, aka Least-Squares Means

Here we document what model objects may be used with emmeans, and some special features of some of them that may be accessed by passing additional arguments through ref_grid or emmeans().

Certain objects are affected by optional arguments to functions that construct emmGrid objects, including ref_grid(), emmeans(), emtrends(), and emmip(). When "arguments" are mentioned in the subsequent quick reference and object-by-object documentation, we are talking about arguments in these constructors.

If a model type is not included here, users may be able to obtain usable results via the qdrg() function; see its help page. Package developers may support their models by writing appropriate recover_data and emm_basis methods. See the package documentation for extending-emmeans and vignette("xtending") for details.

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## Quick reference for supported objects and options {#quickref}

Here is an alphabetical list of model classes that are supported, and the arguments that apply. Detailed documentation follows, with objects grouped by the code in the "Group" column. Scroll down or follow the links to those groups for more information.

For mgcv::gamm objects, emmeans() results are based on the object$gam part. Unfortunately, that is missing its call component, so the user must supply it in the call argument (e.g., call = quote(gamm(y ~ s(x), data = dat))) or give the dataset in the data argument. Alternatively (and recommended), you may first set object$gam$call to the quoted call ahead of time. The what arguments are used to select which model formula to use: "location", "scale" apply to gaulss and gevlss families, "shape" applies only to gevlss, and "rate", "prob.gt.0" apply to ziplss. With gam::Gam objects, standard errors are estimated using a bootstrap method when there are any smoothers involved. Accordingly, there is an optional nboot argument that sets the number of bootstrap replications used to estimate the variances and covariances of the smoothing portions of the model. Generally, it is better to use models fitted via mgcv::gam() rather than gam::gam(). Back to quick reference ## Group H -- gamlss models {#H} The what argument has possible values of "mu" (default), "sigma", "nu", or "tau" depending on which part of the model you want results for. Currently, there is no support when the selected part of the model contains a smoothing method like pb(). ## Group I -- Multiple models (via imputation or averaging) {#I} These objects are the results of fitting several models with different predictor subsets or imputed values. The bhat and V slots are obtained via averaging and, in the case of multiple imputation, adding a multiple of the between-imputation covariance per Rubin's rules. Support for MuMIn::averaging objects may be somewhat dodgy, as it is not clear that all supported model classes will work. The object must have a "modelList" attribute (obtained by constructing the object explicitly from a model list or by including fit = TRUE in the call). And each model should be fitted with data as a named argument in the call; or else provide a data argument in the call to emmeans() or ref_grid(). Only full'' averaging is supported; conditional averaging can result in non-positive-definite covariance matrices, and so cannot be considered. No estimability checking is done at present (not clear what we even mean by it). ## Group K -- gls and lme models {#K} The sigmaAdjust argument is a logical value that defaults to TRUE. It is comparable to the adjustSigma option in nlme::summary.lme (the name-mangling is to avoid conflicts with the often-used adjust argument), and determines whether or not a degrees-of-freedom adjustment is performed with models fitted using the ML method. The optional mode argument affects the degrees of freedom. The mode = "satterthwaite" option determines degrees of freedom via the Satterthwaite method: If s^2 is the estimate of some variance, then its Satterthwaite d.f. is 2*s^4 / Var(s^2). In case our numerical methods for this fail, we also offer mode = "appx-satterthwaite" as a backup, by which quantities related to Var(s^2) are obtained by randomly perturbing the response values. Currently, only "appx-satterthwaite" is available for lme objects, and it is used if "satterthwaite" is requested. Because appx-satterthwaite is simulation-based, results may vary if the same analysis is repeated. An extra.iter argument may be added to request additional simulation runs (at [possibly considerable] cost of repeating the model-fitting that many more times). (Note: Previously, "appx-satterthwaite" was termed "boot-satterthwaite"; this is still supported for backward compatibility. The "boot" was abandoned because it is really an approximation method, not a bootstrap method in the sense as many statistical methods.) An alternative method is "df.error" (for gls) and "containment" (for lme). df.error is just the error degrees of freedom for the model, minus the number of extra random effects estimated; it generally over-estimates the degrees of freedom. The asymptotic mode simply sets the degrees of freedom to infinity. "containment"mode (forlmemodels) determines the degrees of freedom for the coarsest grouping involved in the contrast or linear function involved, so it tends to under-estimate the degrees of freedom. The default ismode = "auto", which uses Satterthwaite if there are estimated random effects and the non-Satterthwaite option otherwise. User reports indicate that models with special terms like poly() are not adequately supported by gls in that the needed basis is not recoverable from its terms component. This is not a problem with lme. The extra.iter argument is ignored unless the d.f. method is (or defaults to) appx-satterthwaite. Back to quick reference ## Group L -- lmerMod models {#L} There is an optional lmer.df argument that defaults to get_EMM_option("lmer.df") (which in turn defaults to "kenward-roger"). The possible values are "kenward-roger", "satterthwaite", and "asymptotic" (these are partially matched and case-insensitive). With "kenward-roger", d.f. are obtained using code from the pbkrtest package, if installed. With "satterthwaite", d.f. are obtained using code from the lmerTest package, if installed. With "asymptotic", or if the needed package is not installed, d.f. are set to Inf. (For backward compatibility, the user may specify mode in lieu of lmer.df.) A by-product of the Kenward-Roger method is that the covariance matrix is adjusted using pbkrtest::vcovAdj(). This can require considerable computation; so to avoid that overhead, the user should opt for the Satterthwaite or asymptotic method; or, for backward compatibility, may disable the use of pbkrtest via emm_options(disable.pbkrtest = TRUE) (this does not disable the pbkrtest package entirely, just its use in emmeans). The computation time required depends roughly on the number of observations, N, in the design matrix (because a major part of the computation involves inverting an N x N matrix). Thus, pbkrtest is automatically disabled if N exceeds the value of get_emm_option("pbkrtest.limit"), for which the factory default is 3000. (The user may also specify pbkrtest.limit or disable.pbkrtest as an argument in the call to emmeans() or ref_grid()) Similarly to the above, the disable.lmerTest and lmerTest.limit options or arguments affect whether Satterthwaite methods can be implemented. The df argument may be used to specify some other degrees of freedom. Note that if df and method = "kenward-roger" are both specified, the covariance matrix is adjusted but the K-R degrees of freedom are not used. Finally, note that a user-specified covariance matrix (via the vcov. argument) will also disable the Kenward-Roger method; in that case, the Satterthwaite method is used in place of Kenward-Roger. Back to quick reference ## Group M -- Multivariate models {#M} When there is a multivariate response, the different responses are treated as if they were levels of a factor -- named rep.meas by default. The mult.name argument may be used to change this name. The mult.levs argument may specify a named list of one or more sets of levels. If this has more than one element, then the multivariate levels are expressed as combinations of the named factor levels via the function base::expand.grid. ## N - Multinomial responses {#N} The reference grid includes a pseudo-factor with the same name and levels as the multinomial response. There is an optional mode argument which should match "prob" or "latent". With mode = "prob", the reference-grid predictions consist of the estimated multinomial probabilities. The "latent" mode returns the linear predictor, recentered so that it averages to zero over the levels of the response variable (similar to sum-to-zero contrasts). Thus each latent variable can be regarded as the log probability at that level minus the average log probability over all levels. There are two optional arguments: mode and rescale (which defaults to c(0, 1)). Please note that, because the probabilities sum to 1 (and the latent values sum to 0) over the multivariate-response levels, all sensible results from emmeans() must involve that response as one of the factors. For example, if resp is a response with k levels, emmeans(model, ~ resp | trt) will yield the estimated multinomial distribution for each trt; but emmeans(model, ~ trt) will just yield the average probability of 1/k for each trt. Back to quick reference ## Group O - Ordinal responses {#O} The reference grid for ordinal models will include all variables that appear in the main model as well as those in the scale or nominal models (if provided). There are two optional arguments: mode (a character string) and rescale (which defaults to c(0, 1)). mode should match one of "latent" (the default), "linear.predictor", "cum.prob", "exc.prob", "prob", "mean.class", or "scale" -- see the quick reference and note which are supported. With mode = "latent", the reference-grid predictions are made on the scale of the latent variable implied by the model. The scale and location of this latent variable are arbitrary, and may be altered via rescale. The predictions are multiplied by rescale[2], then added to rescale[1]. Keep in mind that the scaling is related to the link function used in the model; for example, changing from a probit link to a logistic link will inflate the latent values by around$\pi/\sqrt{3}$, all other things being equal. rescale has no effect for other values of mode. With mode = "linear.predictor", mode = "cum.prob", and mode = "exc.prob", the boundaries between categories (i.e., thresholds) in the ordinal response are included in the reference grid as a pseudo-factor named cut. The reference-grid predictions are then of the cumulative probabilities at each threshold (for mode = "cum.prob"), exceedance probabilities (one minus cumulative probabilities, for mode = "exc.prob"), or the link function thereof (for mode = "linear.predictor"). With mode = "prob", a pseudo-factor with the same name as the model's response variable is created, and the grid predictions are of the probabilities of each class of the ordinal response. With "mean.class", the returned results are means of the ordinal response, interpreted as a numeric value from 1 to the number of classes, using the "prob" results as the estimated probability distribution for each case. With mode = "scale", and the fitted object incorporates a scale model, EMMs are obtained for the factors in the scale model (with a log response) instead of the response model. The grid is constructed using only the factors in the scale model. Any grid point that is non-estimable by either the location or the scale model (if present) is set to NA, and any EMMs involving such a grid point will also be non-estimable. A consequence of this is that if there is a rank-deficient scale model, then all latent responses become non-estimable because the predictions are made using the average log-scale estimate. rms models have an additional mode. With mode = "middle" (this is the default), the middle intercept is used, comparable to the default for rms::Predict(). This is quite similar in concept to mode = "latent", where all intercepts are averaged together. Back to quick reference ## P -- Other packages {#P} Models in this group have their emmeans support provided by the package that implements the model-fitting procedure. Users should refer to the package documentation for details on emmeans support. In some cases, a package's models may have been supported here in emmeans; if so, the other package's support overrides it. ## Q -- Quantile regression {#Q} The argument tau should match (within a very small margin) one of the quantiles actually specified in fitting the model; otherwise an error results. In these models, the covariance matrix is obtained via the model's summary() method with covariance = TRUE. The user may specify one or more of the other arguments for summary or to be passed to, say, a bootstrap routine. If so, those optional arguments must be spelled-out completely (e.g., start will not be matched to startQR). ## S -- Sampling (MCMC) methods {#S} Models fitted using MCMC methods contain a sample from the posterior distribution of fixed-effect coefficients. In some cases (e.g., results of MCMCpack::MCMCregress() and MCMCpack::MCMCpoisson()), the object may include a "call" attribute that emmeans() can use to reconstruct the data and obtain a basis for the EMMs. If not, a formula and data argument are provided that may help produce the right results. In addition, the contrasts specifications are not necessarily recoverable from the object, so the system default must match what was actually used in fitting the model. The summary.emmGrid() method provides credibility intervals (HPD intervals) of the results, and ignores the frequentist-oriented arguments (infer, adjust, etc.) An as.mcmc() method is provided that creates an mcmc object that can be summarized or plotted using the coda package (or others that support those objects). It provides a posterior sample of EMMs, or contrasts thereof, for the given reference grid, based on the posterior sample of the fixed effects from the model object. In MCMCglmm objects, the data argument is required; however, if you save it as a member of the model object (e.g., object$data = quote(mydata)), that removes the necessity of specifying it in each call. The special keyword trait is used in some models. When the response is multivariate and numeric, trait is generated automatically as a factor in the reference grid, and the arguments mult.levels can be used to name its levels. In other models such as a multinomial model, use the mode argument to specify the type of model, and trait = <factor name> to specify the name of the data column that contains the levels of the factor response.

The brms package version 2.13 and later, has its own emmeans support. Refer to the documentation in that package.

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## Group V -- aovList objects (also used with afex_aov objects) {#V}

Support for these objects is limited. To avoid strong biases in the predictions, it is strongly recommended that when fitting the model, the contrasts attribute of all factors should be of a type that sums to zero -- for example, "contr.sum", "contr.poly", or "contr.helmert" but not "contr.treatment". If that is found not to be the case, the model is re-fitted using sum-to-zero contrasts (thus requiring additional computation). Doing so does not remove all bias in the EMMs unless the design is perfectly balanced, and an annotation is added to warn of that. This bias cancels out when doing comparisons and contrasts.

Only intra-block estimates of covariances are used. That is, if a factor appears in more than one error stratum, only the covariance structure from its lowest stratum is used in estimating standard errors. Degrees of freedom are obtained using the Satterthwaite method. In general, aovList support is best with balanced designs, with due caution in the use of contrasts. If a vcov. argument is supplied, it must yield a single covariance matrix for the unique fixed effects (not a set of them for each error stratum). In that case, the degrees of freedom are set to NA`.

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emmeans documentation built on June 22, 2022, 9:07 a.m.