Here we document what model objects may be used with lsmeans, and some special features of some of them. We start with those in the stats package; the other packages follow in alphabetical order.
Certain objects are affected by optional arguments to functions that construct ref.grid or lsmobj objects, including ref.grid, lsmeans, lstrends, and lsmip. When “arguments” are mentioned in the subsequent object-by-object documentation, we are talking about arguments in these constructors.
Additional models can be supported by writing appropriate recover.data and lsm.basis methods. See extending-lsmeans and vignette("extending") for details.
No extended features. Note that the lm support often extends to a number of model objects that inherit from it, such as rlm in the MASS package and rsm in the rsm package.
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 expand.grid.
Support for these objects is limited. To avoid strong biases in the predictions, 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". 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, and 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, and the degrees of freedom are set to NA.
Support for mixed objects has been removed. Version 0.14 and later of afex provides new object classes with their own lsmeans support.
The additional mode argument has possible values of "response", "link", "precision", "phi.link", "variance", and "quantile", which have the same meaning as the type argument in predict.betareg -- with the addition that "phi.link" is like "link", but for the precision portion of the model. When mode = "quantile" is specified, the additional argument quantile (a numeric scalar or vector) specifies which quantile(s) to compute; the default is 0.5 (the median). Also in "quantile" mode, an additional variable quantile is added to the reference grid, and its levels are the values supplied.
The user must supply (via the data argument) the dataset used in fitting the model. As with other MCMC-based objects, the summaries and such are frequentist, but the as.mcmc method provides a posterior sample of the desired quantities.
No additional options. Support for these models is experimental; may throw errors or incorrect results.
Currently, gam objects are not supported. Past versions of lsmeans appeared to support gam models owing to inheritance from lm, but the results were incorrect because spline features were ignored. We now explicitly trap gam objects to avoid these misleading analyses.
These models all have more than one covariance estimate available, and it may be selected by supplying a string as the vcov.method argument. It is partially matched with the available choices; thus, for example, vcov = "n" translates to vcov.method = "naive"
Available covariance estimates are specified in vcov.method as "robust" (the default) and "naive".
Available covariance estimates are specified in vcov.method as "vbeta" (the default), "vbeta.naiv", "vbeta.j1s", or "vbeta.fij". The aliases "robust" (for "vbeta") and "naive" (for "vbeta.naiv" are also accepted.
If a matrix or function is supplied as vcov.method, it is interpreted as a vcov. specification as described for ... in ref.grid.
No extended features.
There is an optional mode argument that defaults to get.lsm.option("lmer.df") (which in turn defaults to "satterthwaite"). The possible values are "satterthwaite", "kenward-roger", and "asymptotic" (these are partially matched and case-insensitive). With "satterthwaite", d.f. are obtained using code from the lmerTest package, if installed. With "kenward-roger", d.f. are obtained using code from the pbkrtest package, if installed. With "asymptotic", or if the needed package is not installed, d.f. are set to NA.
A by-product of the Kenward-Roger method is that the covariance matrix is adjusted using 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 lsm.options(disable.pbkrtest=TRUE) (this does not disable the pbkrtest package entirely, just its use in lsmeans). 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.lsm.option("pbkrtest.limit"). If desired, the user may use lsm.options to adjust this limit from the default of 3000.
The df argument may be used to specify some other degrees of freedom. Note that if df and method = "satterthwaite" are both specified, the covariance matrix is adjusted but the K-R degrees of freedom are not used.
No degrees of freedom are available for these objects, so tests and confidence intervals are asymptotic.
Only asymptotic results are available (no d.f.).
Supported by virtue of inheritance from lme in the nlme package.
Supported by virtue of inheritance from glm.
There are two optional arguments: mode and rescale (which defaults to c(0,1)). For details, see the documentation below regarding the support for the ordinal package, which produces comparable objects (but since polr does not support scale models, mode="scale" is not supported).
Tests and confidence intervals are asymptotic.
Supported by virtue of inheritance from lm.
Currently, I have found no way to reconstruct the data based on information in the object; thus, you must provide the dataset via the data argument. In addition, the contrasts specifications are not recoverable from the object, so the system default must match what was actually used in fitting the model. The usual summary, test, etc. methods provide frequentist analyses of the results based on the posterior means and covariances. However, an as.mcmc method is provided that creates an mcmc object that can be summarized or plotted using the coda package. It provides a posterior sample of lsmeans for the given reference grid, based on the posterior sample of the fixed effects from the MCMCglmm object.
Certain linear-model or mixed-model objects are of class mcmc, and contain a sample from the posterior distribution of fixed-effect coefficients. In some cases (e.g., results of MCMCregress and MCMCpoisson), the object may include a "call" attribute that lsmeans can use to reconstruct the data and obtain a basis for the least-squares means. If not, a formula and data argument are provided that may help produce the right results. In addition, the contrasts specifications are not recoverable from the object, so the system default must match what was actually used in fitting the model. As for other MCMC-based objects, the summaries and such are frequentist, but the as.mcmc method provides a posterior sample of the desired quantities.
No additional features. Degrees of freedom are computed using N - p in object$dims. This is consistent with nlme:::summary.gls but seems questionable.
Degrees of freedom are obtained using a containment method, i.e., the minimum of those elements of object$fixDF$X receiving nonzero weight (but with a correction to the lme object's intercept df). (This is similar to SAS's containment method, but I believe SAS does it incorrectly when the estimands are not contrasts.) The optional argument sigmaAdjust (defaults to TRUE) will adjust standard errors like in summary.lme when the model is fitted using the "ML" method. Note: sigmaAdjust is comparable to adjustSigma in summary.lme but it is renamed to avoid conflicting with adjust.
Support is provided for inferences on parameters named in the fixed part of the model. The user must specify param in the call and give the name of a parameter that appears in the right-hand side of a fixed formula. Degrees of freedom are obtained using the containment-like method described above for lme.
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.
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 lsmeans must involve that response as one of the factors. For example, if resp is a response with \(k\) levels, lsmeans(model, ~ resp | trt) will yield the estimated multinomial distribution for each trt; but lsmeans(model, ~ trt) will just yield the average probability of \(1/k\) for each trt.
The reference grid will include all variables that appear in the main model as well as those in the scale or nominal models. 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".
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 rescale[1] is added. 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, least-squares means are obtained for the factors in the scale model 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 LS-means involving such a grid point will also be non-estimable. A consequence of this is that if there is a rank-deficient scale model, and then all latent responses become non-estimable because the predictions are made using the average log-scale estimate.
Tests and confidence intervals are asymptotic.
Two optional arguments -- mode and lin.pred -- are provided. The mode argument has possible values "response" (the default), "count", "zero", or "prob0". lin.pred is logical and defaults to FALSE.
With lin.pred = FALSE, the results are comparable to those returned by predict(..., type = "response"), predict(..., type = "count"), predict(..., type = "zero"), or predict(..., type = "prob")[, 1]. See the documentation for predict.hurdle and predict.zeroinfl.
The option lin.pred = TRUE only applies to mode = "count" and mode = "zero". The results returned are on the linear-predictor scale, with the same transformation as the link function in that part of the model. The predictions for a reference grid with mode = "count", lin.pred = TRUE, and type = "response" will be the same as those obtained with lin.pred = FALSE and mode = "count"; however, any LS means derived from these grids will be different, because the averaging is done on the log-count scale and the actual count scale, respectively -- thereby producing geometric means versus arithmetic means of the predictions.
If the vcov. argument is used (see details in ref.grid), it must yield a matrix of the same size as would be obtained using vcov.hurdle or vcov.zeroinfl with its model argument set to ("full", "count", "zero") in respective correspondence with mode of ("mean", "count", "zero").
If vcov. is a function, it must support the model argument.
Both rms and lsmeans offer contrast methods, and whichever package is loaded later masks the other. Thus, you may need to call lsmeans::contrast or rms::contrast explicitly to access the one you want.
Standard support is provided. However, with models having more than one intercept (e.g. from orm), a mode argument is provided that works similarly to that for the ordinal package. The available modes are "middle" (the default), "latent", "linear.predictor", "cum.prob", "exc.prob", "prob", and "mean.class". All are as described for the ordinal package, except as noted below.
With mode = "middle" (this is the default), the middle intercept is used, comparable to the default for rms's Predict function. This is quite similar in concept to mode = "latent", where all intercepts are averaged together.
Results for mode = "linear.predictor" are reversed from those in the ordinal package, because orm models predict the link function of the upper-tail (exceedance) probabilities.
With mode = "prob", a pseudo-factor is created having the same name as the model response variable, but its levels are always integers 1, 2, ... regardless of the levels of the original response.
Support for models fitted using stan_xxx is similar to that for models fitted by xxx, where supported, except that posterior samples are also available. For example, stan_glm models are treated like stats::glm, and stan_polr results are similar to those for MASS::polr (including its available mode and rescale options). Models fitted using stan_biglm, stan_betareg, and stan_gamm4 are currently not supported. The user may use
as.mcmc, as.mcmc.list, or as.stanfit on the ref.grid or lsmobj produced to obtain posterior samples of LS means, contrasts, etc.
No extended features.