ref.grid objectsUse these methods to summarize, print, plot, or examine objects of class "ref.grid". They also apply to the class "lsmobj", which is an extension of "ref.grid".
# S3 method for ref.grid
summary(object, infer, level, adjust, by, type, df,
null, delta, side, ...)# S3 method for ref.grid
predict(object, type, ...)
# S3 method for ref.grid
str(object, ...)
# S3 method for ref.grid
rbind(..., deparse.level = 1, adjust = "bonferroni")
# S3 method for ref.grid
[(x, i, adjust, drop.levels = TRUE, ...)
# S3 method for ref.grid
print(x, ...)
# S3 method for summary.ref.grid
print(x, ..., digits = NULL, quote = FALSE, right = TRUE)
# S3 method for ref.grid
xtable(x, caption = NULL, label = NULL, align = NULL,
digits = 4, display = NULL, auto = FALSE, ...)
# S3 method for summary.ref.grid
xtable(x, caption = NULL, label = NULL, align = NULL,
digits = 4, display = NULL, auto = FALSE, ...)
# S3 method for xtable.lsm
print(x, type = getOption("xtable.type", "latex"),
include.rownames = FALSE, sanitize.message.function = footnotesize,
...)
# S3 method for lsmobj
plot(x, y, type, intervals = TRUE, comparisons = FALSE,
alpha = 0.05, adjust = "tukey", int.adjust, ...)
# S3 method for summary.ref.grid
plot(x, y, horizontal = TRUE,
xlab, ylab, layout, ...)
# S3 method for ref.grid
vcov(object, ...)
regrid (object, transform = c("response", "mu", "unlink", "log", "none"),
inv.log.lbl = "response", predict.type)
# S3 method for ref.grid
as.mcmc(x, names = TRUE, sep.chains = TRUE, ...)
# S3 method for ref.grid
as.mcmc.list(x, names = TRUE, ...)
as.stanfit(object, names = TRUE, ...)
An object of class "ref.grid".
A vector of two logical values. The first determines whether confidence intervals are displayed, and the second determines whether t tests and P values are displayed. If only one value is provided, it is used for both.
Confidence level for confidence intervals, if infer[1] is TRUE.
Character value naming the method used to adjust \(p\) values or confidence limits; or to adjust comparison arrows in plot. See Details.
Character name(s) of variables to use for grouping. This affects the family of tests considered in adjusted P values. The printed display of the summary is grouped by the by variables.
Type of prediction desired (except in print.xtable). This only has an effect if there is a known transformation or link function. "response" specifies that the inverse transformation be applied. "mu" (or equivalently, "unlink" is usually the same as "response", but in the case where the model has both a link function and a response transformation, only the link part is back-transformed. Other valid values are "link", "lp", and "linear"; these are equivalent, and request that results be shown for the linear predictor, with no back-transformation. The default is "link", unless the "predict.type" option is in force; see lsm.options.
Note that type is also an argument for the print.xtable method; it is passed to print.xtableList in the xtable package.
If non-missing a constant number of degrees of freedom to use in constructing confidence intervals and P values (NA specifies asymptotic results).
Null hypothesis value(s) against which estimates are tested. May be a single value used for all, or a numeric vector of length equal to the number of tests in each family (i.e., by group in the displayed table).
Numeric value. If zero, ordinary tests of significance are performed. If positive, this specifies a threshold for testing equivalence (using the TOST or two-one-sided-test method), non-inferiority, or non-superiority, depending on side. See Details for how the test statistics are defined.
Numeric or character value specifying whether the test is left-tailed (-1, "-", code"<", "left", or "nonsuperiority"); right-tailed (1, "+", ">", "right", or "noninferiority"); or two-sided (0, 2, "!=", "two-sided", "both", "equivalence", or "=").
This argument is needed by the generic rbind method, but ignored by its ref.grid method.
Logical value to specify whether or not the levels slot should be recomputed based on a possibly reduced number of levels of factors in the grid.
The object to be subsetted, printed, plotted, or converted.
This argument is ignored.
Integer index(es) of which linear functions to extract.
Determines orientation of plotted confidence intervals.
If TRUE, confidence intervals are plotted for each estimate
If TRUE, “comparison arrows” are added to the plot, in such a way that the degree to which arrows overlap reflects as much as possible the significance of the comparison of the two estimates.
The alpha argument to use in constructing comparison arrows.
the multiplicity adjustment method for the plotted confidence intervals; if missing, it defaults to the object's internal adjust setting (see update). (Note: the adjust argument in plot sets the adjust method for the comparison arrows, not the confidence intervals.)
Character value. If "response" or "mu", the inverse transformation is applied to the estimates in the grid (but if there is both a link function and a response transformation, "mu" back-transforms only the link part); if "log", the results are formulated as if the response had been log-transformed; if "none", predictions thereof are on the same scale as in object, and any internal transformation information is preserved. For compatibility with past versions, transform may also be logical; TRUE is taken as "response", and FALSE as "none".
Character value. This applies only when transform = "log", and is used to label the predictions if subsequently summarized with type = "response".
Character value. If provided, the returned object is first updated with the given type, e.g., "response".
Logical scalar or vector specifying whether variable names are appended to levels in the column labels for the as.mcmc or as.mcmc.list result -- e.g., column names of treat A and treat B versus just A and B. When there is more than one variable involved, the elements of names are used cyclically.
Logical value. If TRUE, and there is more than one MCMC chain available, an mcmc.list object is returned by as.mcmc, with separate lsmeans posteriors in each chain.
For summaries, these are additional arguments passed to other methods including print.data.frame,
xtableList, print.xtableList,
update, or dotplot as appropriate. If not specified, appropriate defaults are used. For example, the default layout is one column of horizontal panels or one row of vertical panels.
The summary method for "ref.grid" objects returns an object of class "summary.ref.grid", which extends "data.frame". xtable returns an object of class "xtable.lsm", as explained in details. plot returns an object of class "trellis". vcov returns the covariance matrix of the product of the object's linfct and bhat slots. as.mcmc returns a coda mcmc object.
Defaults for summarization, etc.:
The misc slot in object contains default values for by, infer, level, adjust, type, null, side, and delta. These defaults vary depending on the code that created the object. The update method may be used to change these defaults. In addition, any options set using lsm.options(summary=...) will trump those stored in the object's misc slot.
Transformations and links:
With type="response", the transformation assumed can be found in object@misc$tran, and its label, for the summary is in object@misc$inv.lbl. Any \(t\) or \(z\) tests are still performed on the scale of the linear predictor, not the inverse-transformed one. Similarly, confidence intervals are computed on the linear-predictor scale, then inverse-transformed.
Confidence-limit and P-value adjustments:
The adjust argument specifies a multiplicity adjustment for tests or confidence intervals. This adjustment always is applied separately to each table or sub-table that you see in the printed output (see the details on rbind below for how to combine tables). The valid values of adjust are as follows:
"tukey"Uses the Studentized range distribution with the number of means in the family. (Available for two-sided cases only.)
"scheffe"Computes \(p\) values from the \(F\) distribution, according to the Scheffe critical value of \(\sqrt{kF(k,d)}\), where \(d\) is the error degrees of freedom and \(k\) is (family size minus 1) for contrasts, and (number of estimates) otherwise. (Available for two-sided cases only.)
"sidak"Makes adjustments as if the estimates were independent (a conservative adjustment in many cases).
"bonferroni"Multiplies \(p\) values, or divides significance levels by the number of estimates. This is a conservative adjustment.
"dunnettx"Uses an approximation to the Dunnett distribution for a family of estimates having pairwise correlations of \(0.5\) (as is true when comparing treatments with a control with equal sample sizes). The accuracy of the approximation improves with the number of simultaneous estimates, and is much faster than "mvt". (Available for two-sided cases only.)
"mvt"Uses the multivariate \(t\) distribution to assess the probability or critical value for the maximum of \(k\) estimates. This method produces the same \(p\) values and intervals as the default summary or confint methods to the results of as.glht. In the context of pairwise comparisons or comparisons with a control, this produces “exact” Tukey or Dunnett adjustments, respectively. However, the algorithm (from the mvtnorm package) uses a Monte Carlo method, so results are not exactly repeatable unless the random-number seed is used (see set.seed). As the family size increases, the required computation time will become noticeable or even intolerable, making the "tukey", "dunnettx", or others more attractive.
"none"Makes no adjustments to the \(p\) values.
For P-value adjustments only, the Bonferroni-inequality-based adjustment methods in p.adjust are also available (currently, these include "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", and "none"). If a p.adjust.methods method other than "bonferroni" or "none" is specified for confidence limits, the straight Bonferroni adjustment is used instead.
Also, if an adjustment method is not appropriate (e.g., using "tukey" with one-sided tests, or with results that are not pairwise comparisons), a more appropriate method (usually "sidak") is substituted.
In some cases, confidence and \(p\)-value adjustments are only approximate -- especially when the degrees of freedom or standard errors vary greatly within the family of tests. The "mvt" method is always the correct one-step adjustment, but it can be very slow. One may use as.glht with methods in the multcomp package to obtain non-conservative multi-step adjustments to tests.
Information:
The str method outputs a very brief summary of the object, whereas levels produces a data.frame containing the combinations of levels of predictor values that define the reference grid.
xtable-related methods:
The xtable methods actually use xtableList, because of the ability to display messages such as those for P-value adjustments. These methods return an object of class "xtable.lsm" -- an extension of "xtableList". Unlike other xtable methods, the number of digits defaults to 4; and degrees of freedom and t ratios are always formatted independently of digits. The print method uses print.xtableList, and any … arguments are passed there.
rbind and [ methods:
rbind can be used to combine two or more reference grids into one. The "[" method for ref.grids may be used to obtain a subset. The primary reason for doing this would be to redefine the family of tests to which a P-value adjustment method applies. In rbind, the variables defined in the objects' grids are merged into one grid, and the returned object has no “by” variables and the multiplicity adjustment method set to "mvt" (as this is likely the only appropriate one).
rbind throws an error if there are any mismatches among the dimensions, fixed-effect coefficients, or covariance matrices.
Non-estimable cases:
When the model is rank-deficient, each row x of object's linfct slot is each checked for estimability. If sum(x*bhat) is found to be non-estimable, then an NA is displayed for the estimate (as well as any associated statistics). This check is performed using the orthonormal basis N in the nbasis slot for the null space of the rows of the model matrix. Estimability fails when \(||Nx||^2 / ||x||^2\) exceeds tol, which by default is 1e-8. You may change it via lsm.options by setting estble.tol to the desired value.
More on tests:
When delta = 0, test statistics are of the usual form (estimate - null)/SE, or notationally, \(t = (Q - \theta_0)/SE\) where \(Q\) is our estimate of \(\theta\); then left, right, or two-sided \(p\) values are produced.
When delta is positive, the test statistic depends on side as follows.
Left-sided (nonsuperiority, \(H_0: \theta \ge \theta_0 + \delta\) versus \(H_1: \theta < \theta_0 + \delta\)): \(t = (Q - \theta_0 - \delta)/SE\). The \(p\) value is the lower-tail probability.
Right-sided (noninferiority): \(H_0: \theta \le \theta_0 - \delta\) versus \(H_1: \theta > \theta_0 - \delta\)): \(t = (Q - \theta_0 + \delta)/SE\). The \(p\) value is the upper-tail probability.
Two-sided (equivalence): \(H_0: |\theta - \theta_0| \ge \delta\) versus \(H_1: |\theta - \theta_0| < \delta\)): \(t = (|Q - \theta_0| - \delta)/SE\). The \(p\) value is the lower-tail probability.
Plots:
The plot method for "lsmobj" or "summary.ref.grid" objects (but not "ref.grid" objects themselves) produces a plot displaying confidence intervals for the estimates. If any by variables are in force, the plot is divided into separate panels. These functions use the dotplot function, and thus require that the lattice package be installed. For "summary.ref.grid" objects, the … arguments in plot are passed only to dotplot, whereas for "lsmobj" objects, the object is updated using … before summarizing and plotting.
In plots with comparisons = TRUE, the resulting arrows are only approximate, and in some cases may fail to accurately reflect the pairwise comparisons of the estimates -- especially when estimates having large and small standard errors are intermingled in just the wrong way.
Re-gridding:
The regrid function reparameterizes an existing ref.grid so that its linfct slot is the identity matrix and its bhat slot consists of the estimates at the grid points. If transform is TRUE, the inverse transform is applied to the estimates. Outwardly, the summary after applying regrid is identical to what it was before (using type="response" if transform is TRUE). But subsequent contrasts will be conducted on the transformed scale -- which is the reason this function exists. See the example below. In cases where the degrees of freedom depended on the linear function being estimated, the d.f. from the reference grid are saved, and a kind of “containment” method is substituted in the returned object whereby the calculated d.f. for a new linear function will be the minimum d.f. among those having nonzero coefficients. This is kind of an ad hoc method, and it can over-estimate the degrees of freedom in some cases.
MCMC samplers:
When the object's post.beta slot is non-trivial, as.mcmc will return an mcmc or mcmc.list object that can be summarized or plotted using methods in the coda package. Alternatively, as.stanfit will return a stanfit object that can be summarized or plotted using methods in the rstan package. You may use any of these functions regardless of what packages were originally used to implement the MCMC method.
In these functions, post.beta is transformed by post-multiplying it by t(linfct), creating a sample from the posterior distribution of LS means. In as.mcmc, if sep.chains is TRUE and there is in fact more than one chain, an mcmc.list is returned with each chain's results. The as.mcmc.list method is guaranteed to return an mcmc.list, even if it comprises just one chain. Note that stanfit objects are designed already for multiple chains.
Methods for the closely related "lsmobj" class can be found in contrast, cld, and glht. For more on Bonferroni-based P-value adjustments, see p.adjust. Also, test and confint are essentially front-ends for summary, so additional examples may be found there.
# NOT RUN {
require(lsmeans)
warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)
warp.rg <- ref.grid(warp.lm)
str(warp.rg)
levels(warp.rg)
summary(warp.rg)
summary(warp.rg, by = "wool",
infer = c(TRUE, FALSE), level = .90, adjust = "sidak")
# Do all pairwise comparisons within rows or within columns,
# all considered as one faily of tests:
w.t <- pairs(lsmeans(warp.rg, ~ wool | tension))
t.w <- pairs(lsmeans(warp.rg, ~ tension | wool))
rbind(w.t, t.w)
# Transformed response
sqwarp.rg <- ref.grid(update(warp.lm, sqrt(breaks) ~ .))
summary(sqwarp.rg)
# Back-transformed results - compare with summary of 'warp.rg'
summary(sqwarp.rg, type = "response")
# But differences of sqrts can't be back-transformed
summary(pairs(sqwarp.rg, by = "wool"), type = "response")
# We can do it via regrid
sqwarp.rg2 <- regrid(sqwarp.rg)
summary(sqwarp.rg2) # same as for sqwarp.rg with type = "response"
pairs(sqwarp.rg2, by = "wool")
# Logistic regression
# Reshape the Titanic data
Titan <- do.call("expand.grid", dimnames(Titanic)[-4])
Titan$Died <- matrix(Titanic, ncol=2)
Titan.glm <- glm(Died ~ (Class + Sex + Age)^2,
family = binomial, data = Titan)
Titan.lsm <- lsmeans(Titan.glm, ~ Class|Sex, at = list(Age="Adult"))
summary(Titan.lsm, type="response")
summary(pairs(Titan.lsm), type="response")
# Nonsuperiority test: Is any class no more likely to die than
# the 1st class passengers?
summary(contrast(Titan.lsm, "trt.vs.ctrl1"), delta = 1,
adjust = "none", side = "<")
# Plot 90% CIs on the response scale
plot(Titan.lsm, type = "response", level = .90,
xlab = "Predicted probability of drowning")
# }
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