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Index of vignette topics"
In emmeans: Estimated Marginal Means, aka Least-Squares Means
### Jump to: [A](#a) [B](#b) [C](#c) [D](#d) [E](#e) [F](#f) [G](#g) [H](#h) [I](#i) [J](#j) [K](#k) [L](#l) [M](#m) [N](#n) [O](#o) [P](#p) [Q](#q) [R](#r) [S](#s) [T](#t) [U](#u) [V](#v) [W](#w) [X](#x) [Z](#z) {#topnav}
### A {#a}
* [`add_grouping()`](utilities.html#groups)
* [`addl.vars`](sophisticated.html#random-slopes)
* `adjust`
* [in *comparisons: pairwise*](comparisons.html#pairwise)
* [in *confidence-intervals: adjust*](confidence-intervals.html#adjust)
* [vs. `cross.adjust`](confidence-intervals.html#cross-adjust)
* [Adjusted means](basics.html#RG)
* [Adjusted R-squared](basics.html#pigs)
* [`afex_aov` objects](models.html#V)
* [Alias matrix](xplanations.html#submodels)
* [Analysis of subsets of data](FAQs.html#model)
* Analysis of variance
* [versus *post hoc* comparisons](FAQs.html#anova)
* [Type III](confidence-intervals.html#joint_tests)
* [`aovList` objects](models.html#V)
* [`appx-satterthwaite` method](models.html#K)
* Arguments
* [`...`](basics.html#arguments)
* [Passed to `ref_grid()`](basics.html#arguments)
* `as.mcmc()`
* [in *models: S*](models.html#S)
* [in *sophisticated: bayesxtra*](sophisticated.html#bayesxtra)
* [ASA Statement on *P* values](basics.html#pvalues)
* [Asymptotic tests](sophisticated.html#dfoptions)
* [ATOM](basics.html#pvalues)
* [`averaging` models](models.html#I)
[Back to top](#topnav)
### B {#b}
* [Back-transforming](basics.html#transf)
* [Balanced allocation](basics.html#exper)
* [Bayes factor](sophisticated.html#bayesxtra)
* Bayesian models
* [in *models: S*](models.html#S)
* [in *sophisticated: mcmc*](sophisticated.html#mcmc)
* [**bayesplot** package](sophisticated.html#bayesxtra)
* [**bayestestR** package](sophisticated.html#bayesxtra)
* [Beta regression](models.html#B)
* [`betareg` models](models.html#B)
* Bias adjustment
* [For link functions vs. response transformations](transformations.html#link-bias)
* [in Bayesian models](sophisticated.html#bias-adj-mcmc)
* [In GLMMs and GEE models](transformations.html#cbpp)
* [When back-transforming](transformations.html#bias-adj)
* [When *not* to use](transformations.html#insects)
* [with random slopes](sophisticated.html#random-slopes)
* [Bonferroni adjustment](confidence-intervals.html#adjmore)
* [`boot-satterthwaite` method](models.html#K)
* [Brackets (`[ ]` and `[[ ]]` operators)](utilities.html#brackets)
* [`brmsfit` objects](models.html#S)
* [`by` groups](confidence-intervals.html#byvars)
* [Adjusting across groups](confidence-intervals.html#cross-adjust)
* [Identical comparisons](FAQs.html#additive)
[Back to top](#topnav)
### C {#c}
* [Causal inference](messy-data.html#counterfact)
* [`cld()`](comparisons.html#CLD)
* CLDs
* [Alternative](re-engineering-clds.html#alt-CLDs)
* [For equivalence sets](re-engineering-clds.html#equiv-CLDs)
* [For significance sets](re-engineering-clds.html#signif-CLDs)
* [**multcompView** package](re-engineering-clds.html#CLDs)
* [Principles](re-engineering-clds.html#CLDs)
* [Re-engineered](re-engineering-clds.html#alt-CLDs)
* [References](re-engineering-clds.html#refs)
* [Relation to underlining](re-engineering-clds.html#underlining)
* [Simulated example](re-engineering-clds.html#CLD-example)
* [`clm` models](models.html#O)
* [**coda** package](sophisticated.html#bayesxtra)
* [`coef()`](comparisons.html#contrasts)
* [Cohen's *d*](comparisons.html#pwpm)
* [Compact letter displays](comparisons.html#CLD)
* [Compact letter displays (CLDs)](re-engineering-clds.html)
* Comparison arrows
* [Derivation](xplanations.html#arrows)
* Comparisons
* [Back-transforming](comparisons.html#logs)
* [Displaying as groups](comparisons.html#CLD)
* [Displaying *P* values](comparisons.html#pwpp)
* [Graphical](comparisons.html#graphical)
* [How arrows are determined](xplanations.html#arrows)
* [with logs](comparisons.html#logs)
* [Obtaining differences rather than ratios](FAQs.html#ratios)
* [with overlapping CIs](FAQs.html#CIerror)
* [Comparisons result in `(nothing)`](FAQs.html#nopairs)
* [Confidence intervals](confidence-intervals.html#summary)
* [Overlapping](FAQs.html#CIerror)
* [`confint()`](confidence-intervals.html#summary)
* [Confounded effects](xplanations.html#joint_tests)
* [Confounding](basics.html#emms)
* [`consec` contrasts](comparisons.html#contrasts)
* [Constrained marginal means](xplanations.html#submodels)
* [Consultants](basics.html#recs3)
* [Containment d.f.](models.html#K)
* [`contrast()`](comparisons.html#contrasts)
* [`adjust`](comparisons.html#linfcns)
* [Changing defaults](utilities.html#defaults)
* [`combine`](interactions.html#simple)
* [`interaction`](interactions.html#contrasts)
* [Linear functions](comparisons.html#linfct)
* `simple`
* [in *confidence-intervals: simple*](confidence-intervals.html#simple)
* [in *interactions: simple*](interactions.html#simple)
* Contrasts
* [of other contrasts](interactions.html#contrasts)
* [Custom](comparisons.html#linfcns)
* [Formula](comparisons.html#formulas)
* [Multivariate](interactions.html#multiv)
* [Pairwise](comparisons.html#pairwise)
* [Polynomial](comparisons.html#contrasts)
* Tests of
* [with transformations](comparisons.html#logs)
* [Controlled experiments](basics.html#exper)
* [Count regression](models.html#C)
* [Counterfactuals](messy-data.html#counterfact)
* [`cov.reduce`](messy-data.html#med.covred)
* Covariates
* [Adjusted](messy-data.html#adjcov)
* [`cov.keep`](FAQs.html#numeric)
* [`cov.reduce`](FAQs.html#numeric)
* [Derived](basics.html#depcovs)
* [`emmeans()` doesn't work](FAQs.html#numeric)
* [Interacting with factors](FAQs.html#trends)
* [Mediating](messy-data.html#mediators)
* [cross-group comparisons](confidence-intervals.html#cross-adjust)
* [`cross.adjust`](confidence-intervals.html#cross-adjust)
[Back to top](#topnav)
### D {#d}
* [Degrees of freedom](sophisticated.html#dfoptions)
* [Infinite](FAQs.html#asymp)
* Digits
* [Displaying more digits](utilities.html#data)
* [Digits, optimizing](utilities.html#digits)
* [Dunnett method](comparisons.html#contrasts)
[Back to top](#topnav)
### E {#e}
* [`eff` contrasts](comparisons.html#contrasts)
* [`eff_size()`](comparisons.html#pwpm)
* [Effect size](comparisons.html#pwpm)
* [`emm_basis()`](xtending.html#intro)
* [Arguments and returned value](xtending.html#ebreqs)
* [Communicating with `recover_data()`](xtending.html#communic)
* [Dispatching](xtending.html#dispatch)
* [Hook functions](xtending.html#hooks)
* [for `lqs` objects](xtending.html#eblqs)
* [for `rsm` objects](xtending.html#ebrsm)
* [`emm_list` object](comparisons.html#formulas)
* [`emm_options()`](utilities.html#defaults)
* [`.emmc` functions](comparisons.html#linfcns)
* **emmeans** package
* [Exporting extensions to](xtending.html#exporting)
* [Quick-start guide](AQuickStart.html)
* [`emmeans()`](basics.html#emms)
* [And the underlying model](FAQs.html#nowelch)
* [Arguments passed to `ref_grid()`](basics.html#arguments)
* [Changing defaults](utilities.html#defaults)
* [Fastest way to get wrong answers](FAQs.html#fastest)
* [Surprising results from](FAQs.html#transformations)
* `weights`
* [in *basics: weights*](basics.html#weights)
* [in *messy-data: weights*](messy-data.html#weights)
* [With transformations](transformations.html#regrid)
* [`emmGrid` objects](basics.html#emmobj)
* [Accessing data](utilities.html#data)
* [Combining and subsetting](utilities.html#rbind)
* [Modifying](utilities.html#update)
* [Setting defaults for](utilities.html#defaults)
* `emmip()`
* [in *basics: emmip*](basics.html#emmip)
* [in *basics: plots*](basics.html#plots)
* [in *interactions: factors*](interactions.html#factors)
* [nested factors](messy-data.html#cows)
* EMMs
* [Projecting to a submodel](xplanations.html#submodels)
* [What are they?](FAQs.html#what)
* `emtrends()`
* [in *interactions: covariates*](interactions.html#covariates)
* [in *interactions: oranges*](interactions.html#oranges)
* [Equivalence sets (with CLDs)](re-engineering-clds.html#equiv-CLDs)
* [`estHook`](xtending.html#hooks)
* [Estimability](messy-data.html#nonestex)
* [Estimability issues](FAQs.html#NAs)
* [Estimable functions](xplanations.html#joint_tests)
* Estimated marginal means
* [Definition of](basics.html#refgrid)
* [Demonstrated](basics.html#emms)
* [Manually computed](basics.html#refgrid)
* [Reference grid](basics.html#emms)
* [vs. ordinary marginal means](basics.html#emms)
* Examples
* [`auto.noise`](interactions.html#factors)
* [Bayesian model](sophisticated.html#mcmc)
* `cbpp`
* [in *sophisticated: mcmc*](sophisticated.html#mcmc)
* [in *transformations: cbpp*](transformations.html#cbpp)
* [`ChickWeight`](sophisticated.html#random-slopes)
* [CLDs (simulated)](re-engineering-clds.html#CLD-example)
* [`cows`](messy-data.html#cows)
* [`feedlot`](predictions.html#feedlot)
* `fiber`
* [in *interactions: covariates*](interactions.html#covariates)
* [in *transformations: stdize*](transformations.html#stdize)
* [`framing`](messy-data.html#mediators)
* [Gamma regression](transformations.html#tranlink)
* [`InsectSprays`](transformations.html#insects)
* [`Insurance`](xplanations.html#offsets)
* [Insurance claims (SAS)](sophisticated.html#offsets)
* [Logistic regression](transformations.html#links)
* [`lqs` objects](xtending.html#lqs)
* [`MOats`](basics.html#multiv)
* `mtcars`
* [in *basics: depcovs*](basics.html#depcovs)
* [in *messy-data: nuis.example*](messy-data.html#nuis.example)
* [Multivariate](basics.html#multiv)
* [Nested fixed effects](messy-data.html#cows)
* `neuralgia`
* [`counterfactuals`](messy-data.html#neuralgia)
* [in *transformations: links*](transformations.html#links)
* [in *transformations: trangraph*](transformations.html#trangraph)
* [`nutrition`](messy-data.html#nutrex)
* [`submodel`](messy-data.html#submodels)
* [`weights`](messy-data.html#weights)
* [`Oats`](sophisticated.html#lmer)
* `oranges`
* [in *comparisons: formulas*](comparisons.html#formulas)
* [in *interactions: oranges*](interactions.html#oranges)
* [Ordinal model](sophisticated.html#ordinal)
* `pigs`
* [in *basics: pigs*](basics.html#pigs)
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [in *transformations: altscale*](transformations.html#altscale)
* [in *transformations: overview*](transformations.html#overview)
* [in *transformations: pigs-biasadj*](transformations.html#pigs-biasadj)
* [`rlm` objects](xtending.html#rlm)
* [Robust regression](xtending.html#rlm)
* [Split-plot experiment](sophisticated.html#lmer)
* [Unbalanced data](basics.html#pigs)
* `warpbreaks`
* [in *confidence-intervals: cross-adjust*](confidence-intervals.html#cross-adjust)
* [in *transformations: tranlink*](transformations.html#tranlink)
* [in *utilities: relevel*](utilities.html#relevel)
* [Welch's *t* comparisons](utilities.html#relevel)
* [`wine`](sophisticated.html#ordinal)
* Expected marginal means
* [Foundations of](basics.html#found)
* [Reliance on a model](basics.html#models)
* [Experimental versus observational data](basics.html#exper)
* [Exporting output](basics.html#formatting)
* Extending **emmeans**
* [Exports useful to developers](xtending.html#exported)
* [Restrictions](xtending.html#dispatch)
[Back to top](#topnav)
### F {#f}
* *F* test
* [vs. pairwise comparisons](FAQs.html#anova)
* [Role in *post hoc* tests](basics.html#recs1)
* Factors
* [Mediating](messy-data.html#weights)
* [Formatting results](basics.html#formatting)
* [Foundations of EMMs](basics.html#found)
* [Frequently asked questions](FAQs.html)
[Back to top](#topnav)
### G {#g}
* [G-Computation](messy-data.html#counterfact)
* [`gam` models](models.html#G)
* [`gamlss` models](models.html#H)
* [GEE models](models.html#E)
* [Generalized additive models](models.html#G)
* [Generalized linear models](models.html#G)
* [Geometric means](transformations.html#bias-adj)
* [Get the model right first](FAQs.html#nowelch)
* [`get_emm_option()`](utilities.html#options)
* **ggplot2** package
* [in *basics: ggplot*](basics.html#ggplot)
* [in *messy-data: cows*](messy-data.html#cows)
* [GIGO (garbage in, garbage out)](basics.html#models)
* [`glm`*xxx* models](models.html#G)
* [`gls` models](models.html#K)
* [Graphical displays](basics.html#plots)
* [Grouping factors](utilities.html#groups)
* [Grouping into separate sets](confidence-intervals.html#byvars)
[Back to top](#topnav)
### H {#h}
* [Hook functions](xtending.html#hooks)
* [Hotelling's $T^2$](interactions.html#multiv)
* [`hpd.summary()`](sophisticated.html#mcmc)
* [`hurdle` models](models.html#C)
[Back to top](#topnav)
### I {#i}
* [Indicator variables](basics.html#RG)
* [Infinite degrees of freedom](FAQs.html#asymp)
* [Interaction-style plots](basics.html#emmip)
* Interactions
* [Analysis](interactions.html)
* [Contrasts](interactions.html#contrasts)
* [Covariate with factors](interactions.html#covariates)
* [Implied](interactions.html#oranges)
* [Plotting](interactions.html#factors)
* [Possible inappropriateness of marginal means](interactions.html#factors)
* [`inverse()`](basics.html#pigs)
[Back to top](#topnav)
### J {#j}
* [`joint`](confidence-intervals.html#joint)
* `joint_tests()`
* [in *confidence-intervals: joint_tests*](confidence-intervals.html#joint_tests)
* [Confounded effects](xplanations.html#joint_tests)
* [in *interactions: contrasts*](interactions.html#contrasts)
* [with `submodel = "type2"`](messy-data.html#type2submodel)
[Back to top](#topnav)
### K {#k}
* [`kable`](basics.html#formatting)
* [Kenward-Roger d.f.](models.html#L)
[Back to top](#topnav)
### L {#l}
* Labels
* [Changing](utilities.html#relevel)
* [Large models](messy-data.html#nuisance)
* [Latin squares](basics.html#exper)
* [Least-squares means](FAQs.html#what)
* Levels
* [Changing](utilities.html#relevel)
* [Linear functions](comparisons.html#linfct)
* [Link functions](transformations.html#links)
* [`lme` models](models.html#K)
* `lmerMod` models
* [in *models: L*](models.html#L)
* [in *sophisticated: lmer*](sophisticated.html#lmer)
* [System options for](sophisticated.html#lmerOpts)
* Logistic-like regression
* [Non-logit links](transformations.html#not-logit)
* Logistic regression
* [Odds ratios](transformations.html#oddsrats)
* [Risk ratios](transformations.html#riskrats)
* [Surprising results](FAQs.html#transformations)
* LSD
* [protected](basics.html#recs2)
[Back to top](#topnav)
### M {#m}
* [`make.tran()`](transformations.html#special)
* [`mcmc` objects](models.html#S)
* Means
* [Generalized](transformations.html#bias-adj)
* [Weighted](basics.html#weights)
* [Mediating covariates](messy-data.html#mediators)
* [Memory usage](messy-data.html#nuisance)
* [Limiting](messy-data.html#rg.limit)
* [`mira` models](models.html#I)
* [`misc` attribute and argument](xtending.html#communic)
* [Missing cells](xplanations.html#joint_tests)
* [`mlm` models](models.html#N)
* [`mmer` models](models.html#G)
* Model
* [Get it right first](basics.html#recs2)
* Importance of
* [in *basics: models*](basics.html#models)
* [in *FAQs: fastest*](FAQs.html#fastest)
* [Importance of getting it right](FAQs.html#nowelch)
* [Model averaging](models.html#I)
* Modeling
* [`pigs` example](basics.html#pigs)
* [Response transformation](basics.html#pigs)
* [Modelling](basics.html#models)
* Models
* [Constrained](messy-data.html#submodels)
* [Large](messy-data.html#nuisance)
* [Quick reference](models.html#quickref)
* [Unsupported](FAQs.html#qdrg)
* [Multi-factor studies](FAQs.html#interactions)
* [Multinomial models](models.html#N)
* [Multiple imputation](models.html#I)
* [Multiplicity adjustments](confidence-intervals.html#adjust)
* [Multivariate contrasts](interactions.html#multiv)
* Multivariate models
* [in *basics: multiv*](basics.html#multiv)
* [in *interactions: oranges*](interactions.html#oranges)
* [in *models: M*](models.html#M)
* [with `submodel`](xplanations.html#mult.submodel)
* [Multivariate *t* (`"mvt"`) adjustment](confidence-intervals.html#adjmore)
* [`mvcontrast()`](interactions.html#multiv)
* [**mvtnorm** package](confidence-intervals.html#adjmore)
[Back to top](#topnav)
### N {#n}
* [`NA`s in the output](FAQs.html#NAs)
* [Nesting](messy-data.html#nesting)
* [Auto-detection](messy-data.html#nest-trap)
* Nesting factors
* [Creating](utilities.html#groups)
* [Non-estimability](messy-data.html#nonestex)
* [`non.nuisance`](messy-data.html#nuisance)
* [`NonEst` values](FAQs.html#NAs)
* [`(nothing)` in output](FAQs.html#nopairs)
* [`nuisance`](messy-data.html#nuisance)
* [Nuisance factors](messy-data.html#nuisance)
[Back to top](#topnav)
### O {#o}
* Observational data
* [in *basics: weights*](basics.html#weights)
* [in *messy-data: issues*](messy-data.html#issues)
* [Observational versus experimental data](basics.html#exper)
* [Odds ratios](transformations.html#oddsrats)
* [but I wanted differences](FAQs.html#ratios)
* Offsets
* [Models with offsets](sophisticated.html#offsets)
* [`offset()` term vs. `offset` argument in model](xplanations.html#offsets)
* [Only one mean](AQuickStart.html#covar)
* [`opt.digits` option](utilities.html#digits)
* [Options](utilities.html#options)
* [Startup](utilities.html#startup)
* Ordinal models
* [Latent scale](sophisticated.html#ordinal)
* [Linear-predictor scale](sophisticated.html#ordlp)
* [in *models: O*](models.html#O)
* [`prob` and `mean.class`](sophisticated.html#ordprob)
* [in *sophisticated: ordinal*](sophisticated.html#ordinal)
[Back to top](#topnav)
### P {#p}
* *P* values
* [Adjusted](basics.html#recs1)
* [Adjustment is ignored](FAQs.html#noadjust)
* [Interpreting](basics.html#pvalues)
* [`pairs()`](comparisons.html#pairwise)
* `pairwise ~ factors`
* [Why you should avoid this](AQuickStart.html#pairwise)
* [Pairwise comparisons](comparisons.html#pairwise)
* [Matrix displays](comparisons.html#pwpm)
* [`pairwise` contrasts](comparisons.html#contrasts)
* [Pairwise *P*-value plots](comparisons.html#pwpp)
* [`params`](basics.html#params)
* [Percentage differences](transformations.html#altscale)
* [`plot()`](basics.html#plots)
* [nested factors](messy-data.html#cows)
* [`plot.emmGrid()`](basics.html#plot.emmGrid)
* Plots
* [of confidence intervals](basics.html#plot.emmGrid)
* [of EMMs](basics.html#plots)
* [Enhancing with **ggplot2** functions](basics.html#ggplot)
* [Interaction-style](basics.html#plots)
* [`+` operator](utilities.html#rbind)
* Poisson regression
* [Surprising results](FAQs.html#transformations)
* [`polreg` models](models.html#O)
* [Polynomial regression](basics.html#depcovs)
* Pooled *t*
* [Instead of Welch's *t*](FAQs.html#nowelch)
* [`postGridHook`](xtending.html#hooks)
* [Practices, recommended](basics.html#recs1)
* Precision
* [Displaying results with more digits](utilities.html#data)
* Predictions
* Bayesian models
* [in *predictions: bayes*](predictions.html#bayes)
* [in *sophisticated: predict-mcmc*](sophisticated.html#predict-mcmc)
* [Error SD](predictions.html#sd-estimate)
* [graphics](predictions.html#feedlot)
* [on Particular strata](predictions.html#strata)
* [Posterior predictive distribution](sophisticated.html#predict-mcmc)
* [Reference grid](predictions.html#ref-grid)
* [Total SD](predictions.html#feedlot)
* [`print.summary_emm()`](basics.html#emmobj)
* Probit regression
* [Odds or risk ratios](transformations.html#not-logit)
* [`pwpm()`](comparisons.html#pwpm)
* [`pwpp()`](comparisons.html#pwpp)
[Back to top](#topnav)
### Q {#q}
* [`qdrg()`](FAQs.html#qdrg)
* [Quadratic terms](basics.html#depcovs)
* [Quick-start guide](AQuickStart.html)
[Back to top](#topnav)
### R {#r}
* [R-squared](basics.html#pigs)
* Random predictors
* [Accessing levels](sophisticated.html#random-slopes)
* Random slopes
* [Bias adjustment](sophisticated.html#random-slopes)
* [Rank deficiency](xplanations.html#joint_tests)
* Ratios
* [but I wanted differences](FAQs.html#ratios)
* [`rbind()`](utilities.html#rbind)
* [Re-labeling](utilities.html#relevel)
* [Recommended practices](basics.html#recs1)
* [`recover_data()`](xtending.html#intro)
* [Communicating with `emm_basis()`](xtending.html#communic)
* [`data` and `params` arguments](xtending.html#rdargs)
* [Dispatching](xtending.html#dispatch)
* [Error handling](xtending.html#rderrs)
* [for `lqs` objects](xtending.html#rd.lqs)
* [for `rsm` objects](xtending.html#rdrsm)
* `recover_data.call()`
* [`frame` argument](xtending.html#rdargs)
* [`ref_grid()`](basics.html#RG)
* [`at`](basics.html#RG)
* `cov.reduce`
* [in *basics: plot.emmGrid*](basics.html#plot.emmGrid)
* [in *basics: RG*](basics.html#RG)
* [`mult.name`](basics.html#multiv)
* [`nesting`](messy-data.html#nest-trap)
* [`offset`](sophisticated.html#offsets)
* [`regrid` argument](transformations.html#regrid2)
* [Reference grid](basics.html#emms)
* [Covariates](basics.html#RG)
* [Defined](basics.html#RG)
* [Indicator variables](basics.html#RG)
* [Predictions on](basics.html#refgrid)
* Reference grids
* [Prediction on](predictions.html#ref-grid)
* [Region of practical equivalence](sophisticated.html#bayesxtra)
* [Registering `recover_data` and `emm_basis` methods](xtending.html#exporting)
* [`regrid` argument](transformations.html#stdize)
* [`regrid()`](transformations.html#regrid)
* [probit or other lon-logit models](transformations.html#not-logit)
* [`regrid` vs. `type`](transformations.html#regrid2)
* [to obtain risk ratios](transformations.html#riskrats)
* [`transform = "log"`](transformations.html#logs)
* [Residual plots](basics.html#pigs)
* [Response scale](confidence-intervals.html#tran)
* [Response transformations](basics.html#transf)
* [`revpairwise` contrasts](comparisons.html#contrasts)
* [`rg.limit` option](messy-data.html#rg.limit)
* [Risk ratios](transformations.html#riskrats)
* [RMarkdown](basics.html#formatting)
* [ROPE](sophisticated.html#bayesxtra)
* [**rsm** package](xtending.html#rsm)
* [`rstanarm`](sophisticated.html#mcmc)
[Back to top](#topnav)
### S {#s}
* [Sample size, displaying](confidence-intervals.html#summary)
* [Sandwich estimators](messy-data.html#neuralgia)
* Satterthwaite d.f.
* [in *models: K*](models.html#K)
* [in *models: L*](models.html#L)
* [`"scale"` type](transformations.html#trangraph)
* [`scale()`](transformations.html#stdize)
* [Selecting results](utilities.html#brackets)
* [Sidak adjustment](confidence-intervals.html#adjust)
* Significance
* [Assessing](basics.html#pvalues)
* [Significance sets (with CLDs)](re-engineering-clds.html#signif-CLDs)
* [`simple = "each"`](confidence-intervals.html#simple)
* Simple comparisons
* [in *confidence-intervals: simple*](confidence-intervals.html#simple)
* [in *FAQs: interactions*](FAQs.html#interactions)
* [in *interactions: simple*](interactions.html#simple)
* [Simpson's paradox](basics.html#emms)
* `specs`
* [Formula](comparisons.html#formulas)
* [Standardized response](transformations.html#stdize)
* [`stanreg` objects](models.html#S)
* [* gazing (star gazing)](interactions.html#factors)
* [Startup options](utilities.html#startup)
* [Statistical consultants](basics.html#recs3)
* [Statistics is hard](basics.html#recs3)
* [`str()`](basics.html#emmobj)
* `submodel`
* [`"minimal"` and `"type2"`](messy-data.html#type2submodel)
* [in a multivariate model](xplanations.html#mult.submodel)
* [in *messy-data: submodels*](messy-data.html#submodels)
* [in *xplanations: submodels*](xplanations.html#submodels)
* [Subsets of data](FAQs.html#model)
* `summary()`
* [`adjust`](comparisons.html#pairwise)
* [in *basics: emmobj*](basics.html#emmobj)
* Bayesian models
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [in *models: S*](models.html#S)
* [Calculated columns](confidence-intervals.html#summary)
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [HPD intervals](sophisticated.html#mcmc)
* [`hpd.summary()`](confidence-intervals.html#summary)
* `infer`
* [in *comparisons: pairwise*](comparisons.html#pairwise)
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [Show sample size](confidence-intervals.html#summary)
* [`type = "unlink"`](transformations.html#tranlink)
* [`summary_emm` object](basics.html#emmobj)
* [As a data frame](utilities.html#data)
[Back to top](#topnav)
### T {#t}
* [*t* tests vs. *z* tests](FAQs.html#asymp)
* [`test()`](confidence-intervals.html#summary)
* [`delta`](confidence-intervals.html#equiv)
* [`joint = TRUE`](confidence-intervals.html#joint)
* Tests
* [Equivalence](confidence-intervals.html#equiv)
* [Noninferiority](confidence-intervals.html#equiv)
* [Nonzero null](confidence-intervals.html#summary)
* [One- and two-sided](confidence-intervals.html#summary)
* [Too few means](AQuickStart.html#covar)
* [Transformations](basics.html#transf)
* [Adding after the fact](transformations.html#after)
* [Auto-detected](transformations.html#auto)
* [Back-transforming](confidence-intervals.html#tran)
* [Bias adjustment](transformations.html#bias-adj)
* [Custom](transformations.html#special)
* [faking](transformations.html#faking)
* [Faking a log transformation](transformations.html#logs)
* [Graphical display](transformations.html#trangraph)
* [with link function](transformations.html#tranlink)
* [Log](comparisons.html#logs)
* [Overview](transformations.html#overview)
* [Percent difference](transformations.html#altscale)
* [Re-gridding](transformations.html#regrid)
* [Response versus link functions](transformations.html#link-bias)
* [`scale()`](transformations.html#stdize)
* [Standardizing](transformations.html#stdize)
* [Timing is everything](transformations.html#timing)
* Trends
* [Estimating and comparing](interactions.html#oranges)
* [`trt.vs.ctrl` contrasts](comparisons.html#contrasts)
* [Tukey adjustment](confidence-intervals.html#adjust)
* [Ignored or changed](FAQs.html#notukey)
* [`type`](confidence-intervals.html#tran)
* [`type = "response"`](basics.html#transf)
* [`type = "scale"`](transformations.html#trangraph)
* [Type II analysis](messy-data.html#type2submodel)
* Type III tests
* [in *confidence-intervals: joint*](confidence-intervals.html#joint)
* [in *confidence-intervals: joint_tests*](confidence-intervals.html#joint_tests)
[Back to top](#topnav)
### U {#u}
* [Unadjusted tests](confidence-intervals.html#adjmore)
* [Underlining, grouping by](re-engineering-clds.html#underlining)
* [`update()`](utilities.html#update)
* [`tran`](transformations.html#after)
* [Using results](utilities.html#data)
[Back to top](#topnav)
### V {#v}
* [Variables that are not predictors](basics.html#params)
* [`vcov.`](messy-data.html#neuralgia)
* [`vcovHook`](xtending.html#hooks)
* Vignettes
* [Comparisons](comparisons.html)
* [Confidence intervals and tests](confidence-intervals.html)
* [Explanations supplement](xplanations.html)
* [Extending **emmeans**](xtending.html)
* [FAQS](FAQs.html)
* [Interactions](interactions.html)
* [Messy data](messy-data.html)
* [Models](models.html)
* [Predictions](predictions.html)
* [Re-engineering CLDs](re-engineering-clds.html)
* [Sophisticated models](sophisticated.html)
* [Transformations and link functions](transformations.html)
* [Utilities and options](utilities.html)
[Back to top](#topnav)
### W {#w}
* Weighting
* [Equal weights](basics.html#exper)
* [`weights`](messy-data.html#weights)
* [Welch's *t* comparisons](FAQs.html#nowelch)
* [Example](utilities.html#relevel)
* [`wt.nuis`](messy-data.html#nuisance)
[Back to top](#topnav)
### X {#x}
* [`xtable` method](basics.html#formatting)
[Back to top](#topnav)
### Z {#z}
* [*z* tests](sophisticated.html#dfoptions)
* [vs. *t* tests](FAQs.html#asymp)
* [`zeroinfl` models](models.html#C)
[Back to top](#topnav)
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### Jump to: [A](#a) [B](#b) [C](#c) [D](#d) [E](#e) [F](#f) [G](#g) [H](#h) [I](#i) [J](#j) [K](#k) [L](#l) [M](#m) [N](#n) [O](#o) [P](#p) [Q](#q) [R](#r) [S](#s) [T](#t) [U](#u) [V](#v) [W](#w) [X](#x) [Z](#z) {#topnav}
### A {#a}
* [`add_grouping()`](utilities.html#groups)
* [`addl.vars`](sophisticated.html#random-slopes)
* `adjust`
* [in *comparisons: pairwise*](comparisons.html#pairwise)
* [in *confidence-intervals: adjust*](confidence-intervals.html#adjust)
* [vs. `cross.adjust`](confidence-intervals.html#cross-adjust)
* [Adjusted means](basics.html#RG)
* [Adjusted R-squared](basics.html#pigs)
* [`afex_aov` objects](models.html#V)
* [Alias matrix](xplanations.html#submodels)
* [Analysis of subsets of data](FAQs.html#model)
* Analysis of variance
* [versus *post hoc* comparisons](FAQs.html#anova)
* [Type III](confidence-intervals.html#joint_tests)
* [`aovList` objects](models.html#V)
* [`appx-satterthwaite` method](models.html#K)
* Arguments
* [`...`](basics.html#arguments)
* [Passed to `ref_grid()`](basics.html#arguments)
* `as.mcmc()`
* [in *models: S*](models.html#S)
* [in *sophisticated: bayesxtra*](sophisticated.html#bayesxtra)
* [ASA Statement on *P* values](basics.html#pvalues)
* [Asymptotic tests](sophisticated.html#dfoptions)
* [ATOM](basics.html#pvalues)
* [`averaging` models](models.html#I)
[Back to top](#topnav)
### B {#b}
* [Back-transforming](basics.html#transf)
* [Balanced allocation](basics.html#exper)
* [Bayes factor](sophisticated.html#bayesxtra)
* Bayesian models
* [in *models: S*](models.html#S)
* [in *sophisticated: mcmc*](sophisticated.html#mcmc)
* [**bayesplot** package](sophisticated.html#bayesxtra)
* [**bayestestR** package](sophisticated.html#bayesxtra)
* [Beta regression](models.html#B)
* [`betareg` models](models.html#B)
* Bias adjustment
* [For link functions vs. response transformations](transformations.html#link-bias)
* [in Bayesian models](sophisticated.html#bias-adj-mcmc)
* [In GLMMs and GEE models](transformations.html#cbpp)
* [When back-transforming](transformations.html#bias-adj)
* [When *not* to use](transformations.html#insects)
* [with random slopes](sophisticated.html#random-slopes)
* [Bonferroni adjustment](confidence-intervals.html#adjmore)
* [`boot-satterthwaite` method](models.html#K)
* [Brackets (`[ ]` and `[[ ]]` operators)](utilities.html#brackets)
* [`brmsfit` objects](models.html#S)
* [`by` groups](confidence-intervals.html#byvars)
* [Adjusting across groups](confidence-intervals.html#cross-adjust)
* [Identical comparisons](FAQs.html#additive)
[Back to top](#topnav)
### C {#c}
* [Causal inference](messy-data.html#counterfact)
* [`cld()`](comparisons.html#CLD)
* CLDs
* [Alternative](re-engineering-clds.html#alt-CLDs)
* [For equivalence sets](re-engineering-clds.html#equiv-CLDs)
* [For significance sets](re-engineering-clds.html#signif-CLDs)
* [**multcompView** package](re-engineering-clds.html#CLDs)
* [Principles](re-engineering-clds.html#CLDs)
* [Re-engineered](re-engineering-clds.html#alt-CLDs)
* [References](re-engineering-clds.html#refs)
* [Relation to underlining](re-engineering-clds.html#underlining)
* [Simulated example](re-engineering-clds.html#CLD-example)
* [`clm` models](models.html#O)
* [**coda** package](sophisticated.html#bayesxtra)
* [`coef()`](comparisons.html#contrasts)
* [Cohen's *d*](comparisons.html#pwpm)
* [Compact letter displays](comparisons.html#CLD)
* [Compact letter displays (CLDs)](re-engineering-clds.html)
* Comparison arrows
* [Derivation](xplanations.html#arrows)
* Comparisons
* [Back-transforming](comparisons.html#logs)
* [Displaying as groups](comparisons.html#CLD)
* [Displaying *P* values](comparisons.html#pwpp)
* [Graphical](comparisons.html#graphical)
* [How arrows are determined](xplanations.html#arrows)
* [with logs](comparisons.html#logs)
* [Obtaining differences rather than ratios](FAQs.html#ratios)
* [with overlapping CIs](FAQs.html#CIerror)
* [Comparisons result in `(nothing)`](FAQs.html#nopairs)
* [Confidence intervals](confidence-intervals.html#summary)
* [Overlapping](FAQs.html#CIerror)
* [`confint()`](confidence-intervals.html#summary)
* [Confounded effects](xplanations.html#joint_tests)
* [Confounding](basics.html#emms)
* [`consec` contrasts](comparisons.html#contrasts)
* [Constrained marginal means](xplanations.html#submodels)
* [Consultants](basics.html#recs3)
* [Containment d.f.](models.html#K)
* [`contrast()`](comparisons.html#contrasts)
* [`adjust`](comparisons.html#linfcns)
* [Changing defaults](utilities.html#defaults)
* [`combine`](interactions.html#simple)
* [`interaction`](interactions.html#contrasts)
* [Linear functions](comparisons.html#linfct)
* `simple`
* [in *confidence-intervals: simple*](confidence-intervals.html#simple)
* [in *interactions: simple*](interactions.html#simple)
* Contrasts
* [of other contrasts](interactions.html#contrasts)
* [Custom](comparisons.html#linfcns)
* [Formula](comparisons.html#formulas)
* [Multivariate](interactions.html#multiv)
* [Pairwise](comparisons.html#pairwise)
* [Polynomial](comparisons.html#contrasts)
* Tests of
* [with transformations](comparisons.html#logs)
* [Controlled experiments](basics.html#exper)
* [Count regression](models.html#C)
* [Counterfactuals](messy-data.html#counterfact)
* [`cov.reduce`](messy-data.html#med.covred)
* Covariates
* [Adjusted](messy-data.html#adjcov)
* [`cov.keep`](FAQs.html#numeric)
* [`cov.reduce`](FAQs.html#numeric)
* [Derived](basics.html#depcovs)
* [`emmeans()` doesn't work](FAQs.html#numeric)
* [Interacting with factors](FAQs.html#trends)
* [Mediating](messy-data.html#mediators)
* [cross-group comparisons](confidence-intervals.html#cross-adjust)
* [`cross.adjust`](confidence-intervals.html#cross-adjust)
[Back to top](#topnav)
### D {#d}
* [Degrees of freedom](sophisticated.html#dfoptions)
* [Infinite](FAQs.html#asymp)
* Digits
* [Displaying more digits](utilities.html#data)
* [Digits, optimizing](utilities.html#digits)
* [Dunnett method](comparisons.html#contrasts)
[Back to top](#topnav)
### E {#e}
* [`eff` contrasts](comparisons.html#contrasts)
* [`eff_size()`](comparisons.html#pwpm)
* [Effect size](comparisons.html#pwpm)
* [`emm_basis()`](xtending.html#intro)
* [Arguments and returned value](xtending.html#ebreqs)
* [Communicating with `recover_data()`](xtending.html#communic)
* [Dispatching](xtending.html#dispatch)
* [Hook functions](xtending.html#hooks)
* [for `lqs` objects](xtending.html#eblqs)
* [for `rsm` objects](xtending.html#ebrsm)
* [`emm_list` object](comparisons.html#formulas)
* [`emm_options()`](utilities.html#defaults)
* [`.emmc` functions](comparisons.html#linfcns)
* **emmeans** package
* [Exporting extensions to](xtending.html#exporting)
* [Quick-start guide](AQuickStart.html)
* [`emmeans()`](basics.html#emms)
* [And the underlying model](FAQs.html#nowelch)
* [Arguments passed to `ref_grid()`](basics.html#arguments)
* [Changing defaults](utilities.html#defaults)
* [Fastest way to get wrong answers](FAQs.html#fastest)
* [Surprising results from](FAQs.html#transformations)
* `weights`
* [in *basics: weights*](basics.html#weights)
* [in *messy-data: weights*](messy-data.html#weights)
* [With transformations](transformations.html#regrid)
* [`emmGrid` objects](basics.html#emmobj)
* [Accessing data](utilities.html#data)
* [Combining and subsetting](utilities.html#rbind)
* [Modifying](utilities.html#update)
* [Setting defaults for](utilities.html#defaults)
* `emmip()`
* [in *basics: emmip*](basics.html#emmip)
* [in *basics: plots*](basics.html#plots)
* [in *interactions: factors*](interactions.html#factors)
* [nested factors](messy-data.html#cows)
* EMMs
* [Projecting to a submodel](xplanations.html#submodels)
* [What are they?](FAQs.html#what)
* `emtrends()`
* [in *interactions: covariates*](interactions.html#covariates)
* [in *interactions: oranges*](interactions.html#oranges)
* [Equivalence sets (with CLDs)](re-engineering-clds.html#equiv-CLDs)
* [`estHook`](xtending.html#hooks)
* [Estimability](messy-data.html#nonestex)
* [Estimability issues](FAQs.html#NAs)
* [Estimable functions](xplanations.html#joint_tests)
* Estimated marginal means
* [Definition of](basics.html#refgrid)
* [Demonstrated](basics.html#emms)
* [Manually computed](basics.html#refgrid)
* [Reference grid](basics.html#emms)
* [vs. ordinary marginal means](basics.html#emms)
* Examples
* [`auto.noise`](interactions.html#factors)
* [Bayesian model](sophisticated.html#mcmc)
* `cbpp`
* [in *sophisticated: mcmc*](sophisticated.html#mcmc)
* [in *transformations: cbpp*](transformations.html#cbpp)
* [`ChickWeight`](sophisticated.html#random-slopes)
* [CLDs (simulated)](re-engineering-clds.html#CLD-example)
* [`cows`](messy-data.html#cows)
* [`feedlot`](predictions.html#feedlot)
* `fiber`
* [in *interactions: covariates*](interactions.html#covariates)
* [in *transformations: stdize*](transformations.html#stdize)
* [`framing`](messy-data.html#mediators)
* [Gamma regression](transformations.html#tranlink)
* [`InsectSprays`](transformations.html#insects)
* [`Insurance`](xplanations.html#offsets)
* [Insurance claims (SAS)](sophisticated.html#offsets)
* [Logistic regression](transformations.html#links)
* [`lqs` objects](xtending.html#lqs)
* [`MOats`](basics.html#multiv)
* `mtcars`
* [in *basics: depcovs*](basics.html#depcovs)
* [in *messy-data: nuis.example*](messy-data.html#nuis.example)
* [Multivariate](basics.html#multiv)
* [Nested fixed effects](messy-data.html#cows)
* `neuralgia`
* [`counterfactuals`](messy-data.html#neuralgia)
* [in *transformations: links*](transformations.html#links)
* [in *transformations: trangraph*](transformations.html#trangraph)
* [`nutrition`](messy-data.html#nutrex)
* [`submodel`](messy-data.html#submodels)
* [`weights`](messy-data.html#weights)
* [`Oats`](sophisticated.html#lmer)
* `oranges`
* [in *comparisons: formulas*](comparisons.html#formulas)
* [in *interactions: oranges*](interactions.html#oranges)
* [Ordinal model](sophisticated.html#ordinal)
* `pigs`
* [in *basics: pigs*](basics.html#pigs)
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [in *transformations: altscale*](transformations.html#altscale)
* [in *transformations: overview*](transformations.html#overview)
* [in *transformations: pigs-biasadj*](transformations.html#pigs-biasadj)
* [`rlm` objects](xtending.html#rlm)
* [Robust regression](xtending.html#rlm)
* [Split-plot experiment](sophisticated.html#lmer)
* [Unbalanced data](basics.html#pigs)
* `warpbreaks`
* [in *confidence-intervals: cross-adjust*](confidence-intervals.html#cross-adjust)
* [in *transformations: tranlink*](transformations.html#tranlink)
* [in *utilities: relevel*](utilities.html#relevel)
* [Welch's *t* comparisons](utilities.html#relevel)
* [`wine`](sophisticated.html#ordinal)
* Expected marginal means
* [Foundations of](basics.html#found)
* [Reliance on a model](basics.html#models)
* [Experimental versus observational data](basics.html#exper)
* [Exporting output](basics.html#formatting)
* Extending **emmeans**
* [Exports useful to developers](xtending.html#exported)
* [Restrictions](xtending.html#dispatch)
[Back to top](#topnav)
### F {#f}
* *F* test
* [vs. pairwise comparisons](FAQs.html#anova)
* [Role in *post hoc* tests](basics.html#recs1)
* Factors
* [Mediating](messy-data.html#weights)
* [Formatting results](basics.html#formatting)
* [Foundations of EMMs](basics.html#found)
* [Frequently asked questions](FAQs.html)
[Back to top](#topnav)
### G {#g}
* [G-Computation](messy-data.html#counterfact)
* [`gam` models](models.html#G)
* [`gamlss` models](models.html#H)
* [GEE models](models.html#E)
* [Generalized additive models](models.html#G)
* [Generalized linear models](models.html#G)
* [Geometric means](transformations.html#bias-adj)
* [Get the model right first](FAQs.html#nowelch)
* [`get_emm_option()`](utilities.html#options)
* **ggplot2** package
* [in *basics: ggplot*](basics.html#ggplot)
* [in *messy-data: cows*](messy-data.html#cows)
* [GIGO (garbage in, garbage out)](basics.html#models)
* [`glm`*xxx* models](models.html#G)
* [`gls` models](models.html#K)
* [Graphical displays](basics.html#plots)
* [Grouping factors](utilities.html#groups)
* [Grouping into separate sets](confidence-intervals.html#byvars)
[Back to top](#topnav)
### H {#h}
* [Hook functions](xtending.html#hooks)
* [Hotelling's $T^2$](interactions.html#multiv)
* [`hpd.summary()`](sophisticated.html#mcmc)
* [`hurdle` models](models.html#C)
[Back to top](#topnav)
### I {#i}
* [Indicator variables](basics.html#RG)
* [Infinite degrees of freedom](FAQs.html#asymp)
* [Interaction-style plots](basics.html#emmip)
* Interactions
* [Analysis](interactions.html)
* [Contrasts](interactions.html#contrasts)
* [Covariate with factors](interactions.html#covariates)
* [Implied](interactions.html#oranges)
* [Plotting](interactions.html#factors)
* [Possible inappropriateness of marginal means](interactions.html#factors)
* [`inverse()`](basics.html#pigs)
[Back to top](#topnav)
### J {#j}
* [`joint`](confidence-intervals.html#joint)
* `joint_tests()`
* [in *confidence-intervals: joint_tests*](confidence-intervals.html#joint_tests)
* [Confounded effects](xplanations.html#joint_tests)
* [in *interactions: contrasts*](interactions.html#contrasts)
* [with `submodel = "type2"`](messy-data.html#type2submodel)
[Back to top](#topnav)
### K {#k}
* [`kable`](basics.html#formatting)
* [Kenward-Roger d.f.](models.html#L)
[Back to top](#topnav)
### L {#l}
* Labels
* [Changing](utilities.html#relevel)
* [Large models](messy-data.html#nuisance)
* [Latin squares](basics.html#exper)
* [Least-squares means](FAQs.html#what)
* Levels
* [Changing](utilities.html#relevel)
* [Linear functions](comparisons.html#linfct)
* [Link functions](transformations.html#links)
* [`lme` models](models.html#K)
* `lmerMod` models
* [in *models: L*](models.html#L)
* [in *sophisticated: lmer*](sophisticated.html#lmer)
* [System options for](sophisticated.html#lmerOpts)
* Logistic-like regression
* [Non-logit links](transformations.html#not-logit)
* Logistic regression
* [Odds ratios](transformations.html#oddsrats)
* [Risk ratios](transformations.html#riskrats)
* [Surprising results](FAQs.html#transformations)
* LSD
* [protected](basics.html#recs2)
[Back to top](#topnav)
### M {#m}
* [`make.tran()`](transformations.html#special)
* [`mcmc` objects](models.html#S)
* Means
* [Generalized](transformations.html#bias-adj)
* [Weighted](basics.html#weights)
* [Mediating covariates](messy-data.html#mediators)
* [Memory usage](messy-data.html#nuisance)
* [Limiting](messy-data.html#rg.limit)
* [`mira` models](models.html#I)
* [`misc` attribute and argument](xtending.html#communic)
* [Missing cells](xplanations.html#joint_tests)
* [`mlm` models](models.html#N)
* [`mmer` models](models.html#G)
* Model
* [Get it right first](basics.html#recs2)
* Importance of
* [in *basics: models*](basics.html#models)
* [in *FAQs: fastest*](FAQs.html#fastest)
* [Importance of getting it right](FAQs.html#nowelch)
* [Model averaging](models.html#I)
* Modeling
* [`pigs` example](basics.html#pigs)
* [Response transformation](basics.html#pigs)
* [Modelling](basics.html#models)
* Models
* [Constrained](messy-data.html#submodels)
* [Large](messy-data.html#nuisance)
* [Quick reference](models.html#quickref)
* [Unsupported](FAQs.html#qdrg)
* [Multi-factor studies](FAQs.html#interactions)
* [Multinomial models](models.html#N)
* [Multiple imputation](models.html#I)
* [Multiplicity adjustments](confidence-intervals.html#adjust)
* [Multivariate contrasts](interactions.html#multiv)
* Multivariate models
* [in *basics: multiv*](basics.html#multiv)
* [in *interactions: oranges*](interactions.html#oranges)
* [in *models: M*](models.html#M)
* [with `submodel`](xplanations.html#mult.submodel)
* [Multivariate *t* (`"mvt"`) adjustment](confidence-intervals.html#adjmore)
* [`mvcontrast()`](interactions.html#multiv)
* [**mvtnorm** package](confidence-intervals.html#adjmore)
[Back to top](#topnav)
### N {#n}
* [`NA`s in the output](FAQs.html#NAs)
* [Nesting](messy-data.html#nesting)
* [Auto-detection](messy-data.html#nest-trap)
* Nesting factors
* [Creating](utilities.html#groups)
* [Non-estimability](messy-data.html#nonestex)
* [`non.nuisance`](messy-data.html#nuisance)
* [`NonEst` values](FAQs.html#NAs)
* [`(nothing)` in output](FAQs.html#nopairs)
* [`nuisance`](messy-data.html#nuisance)
* [Nuisance factors](messy-data.html#nuisance)
[Back to top](#topnav)
### O {#o}
* Observational data
* [in *basics: weights*](basics.html#weights)
* [in *messy-data: issues*](messy-data.html#issues)
* [Observational versus experimental data](basics.html#exper)
* [Odds ratios](transformations.html#oddsrats)
* [but I wanted differences](FAQs.html#ratios)
* Offsets
* [Models with offsets](sophisticated.html#offsets)
* [`offset()` term vs. `offset` argument in model](xplanations.html#offsets)
* [Only one mean](AQuickStart.html#covar)
* [`opt.digits` option](utilities.html#digits)
* [Options](utilities.html#options)
* [Startup](utilities.html#startup)
* Ordinal models
* [Latent scale](sophisticated.html#ordinal)
* [Linear-predictor scale](sophisticated.html#ordlp)
* [in *models: O*](models.html#O)
* [`prob` and `mean.class`](sophisticated.html#ordprob)
* [in *sophisticated: ordinal*](sophisticated.html#ordinal)
[Back to top](#topnav)
### P {#p}
* *P* values
* [Adjusted](basics.html#recs1)
* [Adjustment is ignored](FAQs.html#noadjust)
* [Interpreting](basics.html#pvalues)
* [`pairs()`](comparisons.html#pairwise)
* `pairwise ~ factors`
* [Why you should avoid this](AQuickStart.html#pairwise)
* [Pairwise comparisons](comparisons.html#pairwise)
* [Matrix displays](comparisons.html#pwpm)
* [`pairwise` contrasts](comparisons.html#contrasts)
* [Pairwise *P*-value plots](comparisons.html#pwpp)
* [`params`](basics.html#params)
* [Percentage differences](transformations.html#altscale)
* [`plot()`](basics.html#plots)
* [nested factors](messy-data.html#cows)
* [`plot.emmGrid()`](basics.html#plot.emmGrid)
* Plots
* [of confidence intervals](basics.html#plot.emmGrid)
* [of EMMs](basics.html#plots)
* [Enhancing with **ggplot2** functions](basics.html#ggplot)
* [Interaction-style](basics.html#plots)
* [`+` operator](utilities.html#rbind)
* Poisson regression
* [Surprising results](FAQs.html#transformations)
* [`polreg` models](models.html#O)
* [Polynomial regression](basics.html#depcovs)
* Pooled *t*
* [Instead of Welch's *t*](FAQs.html#nowelch)
* [`postGridHook`](xtending.html#hooks)
* [Practices, recommended](basics.html#recs1)
* Precision
* [Displaying results with more digits](utilities.html#data)
* Predictions
* Bayesian models
* [in *predictions: bayes*](predictions.html#bayes)
* [in *sophisticated: predict-mcmc*](sophisticated.html#predict-mcmc)
* [Error SD](predictions.html#sd-estimate)
* [graphics](predictions.html#feedlot)
* [on Particular strata](predictions.html#strata)
* [Posterior predictive distribution](sophisticated.html#predict-mcmc)
* [Reference grid](predictions.html#ref-grid)
* [Total SD](predictions.html#feedlot)
* [`print.summary_emm()`](basics.html#emmobj)
* Probit regression
* [Odds or risk ratios](transformations.html#not-logit)
* [`pwpm()`](comparisons.html#pwpm)
* [`pwpp()`](comparisons.html#pwpp)
[Back to top](#topnav)
### Q {#q}
* [`qdrg()`](FAQs.html#qdrg)
* [Quadratic terms](basics.html#depcovs)
* [Quick-start guide](AQuickStart.html)
[Back to top](#topnav)
### R {#r}
* [R-squared](basics.html#pigs)
* Random predictors
* [Accessing levels](sophisticated.html#random-slopes)
* Random slopes
* [Bias adjustment](sophisticated.html#random-slopes)
* [Rank deficiency](xplanations.html#joint_tests)
* Ratios
* [but I wanted differences](FAQs.html#ratios)
* [`rbind()`](utilities.html#rbind)
* [Re-labeling](utilities.html#relevel)
* [Recommended practices](basics.html#recs1)
* [`recover_data()`](xtending.html#intro)
* [Communicating with `emm_basis()`](xtending.html#communic)
* [`data` and `params` arguments](xtending.html#rdargs)
* [Dispatching](xtending.html#dispatch)
* [Error handling](xtending.html#rderrs)
* [for `lqs` objects](xtending.html#rd.lqs)
* [for `rsm` objects](xtending.html#rdrsm)
* `recover_data.call()`
* [`frame` argument](xtending.html#rdargs)
* [`ref_grid()`](basics.html#RG)
* [`at`](basics.html#RG)
* `cov.reduce`
* [in *basics: plot.emmGrid*](basics.html#plot.emmGrid)
* [in *basics: RG*](basics.html#RG)
* [`mult.name`](basics.html#multiv)
* [`nesting`](messy-data.html#nest-trap)
* [`offset`](sophisticated.html#offsets)
* [`regrid` argument](transformations.html#regrid2)
* [Reference grid](basics.html#emms)
* [Covariates](basics.html#RG)
* [Defined](basics.html#RG)
* [Indicator variables](basics.html#RG)
* [Predictions on](basics.html#refgrid)
* Reference grids
* [Prediction on](predictions.html#ref-grid)
* [Region of practical equivalence](sophisticated.html#bayesxtra)
* [Registering `recover_data` and `emm_basis` methods](xtending.html#exporting)
* [`regrid` argument](transformations.html#stdize)
* [`regrid()`](transformations.html#regrid)
* [probit or other lon-logit models](transformations.html#not-logit)
* [`regrid` vs. `type`](transformations.html#regrid2)
* [to obtain risk ratios](transformations.html#riskrats)
* [`transform = "log"`](transformations.html#logs)
* [Residual plots](basics.html#pigs)
* [Response scale](confidence-intervals.html#tran)
* [Response transformations](basics.html#transf)
* [`revpairwise` contrasts](comparisons.html#contrasts)
* [`rg.limit` option](messy-data.html#rg.limit)
* [Risk ratios](transformations.html#riskrats)
* [RMarkdown](basics.html#formatting)
* [ROPE](sophisticated.html#bayesxtra)
* [**rsm** package](xtending.html#rsm)
* [`rstanarm`](sophisticated.html#mcmc)
[Back to top](#topnav)
### S {#s}
* [Sample size, displaying](confidence-intervals.html#summary)
* [Sandwich estimators](messy-data.html#neuralgia)
* Satterthwaite d.f.
* [in *models: K*](models.html#K)
* [in *models: L*](models.html#L)
* [`"scale"` type](transformations.html#trangraph)
* [`scale()`](transformations.html#stdize)
* [Selecting results](utilities.html#brackets)
* [Sidak adjustment](confidence-intervals.html#adjust)
* Significance
* [Assessing](basics.html#pvalues)
* [Significance sets (with CLDs)](re-engineering-clds.html#signif-CLDs)
* [`simple = "each"`](confidence-intervals.html#simple)
* Simple comparisons
* [in *confidence-intervals: simple*](confidence-intervals.html#simple)
* [in *FAQs: interactions*](FAQs.html#interactions)
* [in *interactions: simple*](interactions.html#simple)
* [Simpson's paradox](basics.html#emms)
* `specs`
* [Formula](comparisons.html#formulas)
* [Standardized response](transformations.html#stdize)
* [`stanreg` objects](models.html#S)
* [* gazing (star gazing)](interactions.html#factors)
* [Startup options](utilities.html#startup)
* [Statistical consultants](basics.html#recs3)
* [Statistics is hard](basics.html#recs3)
* [`str()`](basics.html#emmobj)
* `submodel`
* [`"minimal"` and `"type2"`](messy-data.html#type2submodel)
* [in a multivariate model](xplanations.html#mult.submodel)
* [in *messy-data: submodels*](messy-data.html#submodels)
* [in *xplanations: submodels*](xplanations.html#submodels)
* [Subsets of data](FAQs.html#model)
* `summary()`
* [`adjust`](comparisons.html#pairwise)
* [in *basics: emmobj*](basics.html#emmobj)
* Bayesian models
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [in *models: S*](models.html#S)
* [Calculated columns](confidence-intervals.html#summary)
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [HPD intervals](sophisticated.html#mcmc)
* [`hpd.summary()`](confidence-intervals.html#summary)
* `infer`
* [in *comparisons: pairwise*](comparisons.html#pairwise)
* [in *confidence-intervals: summary*](confidence-intervals.html#summary)
* [Show sample size](confidence-intervals.html#summary)
* [`type = "unlink"`](transformations.html#tranlink)
* [`summary_emm` object](basics.html#emmobj)
* [As a data frame](utilities.html#data)
[Back to top](#topnav)
### T {#t}
* [*t* tests vs. *z* tests](FAQs.html#asymp)
* [`test()`](confidence-intervals.html#summary)
* [`delta`](confidence-intervals.html#equiv)
* [`joint = TRUE`](confidence-intervals.html#joint)
* Tests
* [Equivalence](confidence-intervals.html#equiv)
* [Noninferiority](confidence-intervals.html#equiv)
* [Nonzero null](confidence-intervals.html#summary)
* [One- and two-sided](confidence-intervals.html#summary)
* [Too few means](AQuickStart.html#covar)
* [Transformations](basics.html#transf)
* [Adding after the fact](transformations.html#after)
* [Auto-detected](transformations.html#auto)
* [Back-transforming](confidence-intervals.html#tran)
* [Bias adjustment](transformations.html#bias-adj)
* [Custom](transformations.html#special)
* [faking](transformations.html#faking)
* [Faking a log transformation](transformations.html#logs)
* [Graphical display](transformations.html#trangraph)
* [with link function](transformations.html#tranlink)
* [Log](comparisons.html#logs)
* [Overview](transformations.html#overview)
* [Percent difference](transformations.html#altscale)
* [Re-gridding](transformations.html#regrid)
* [Response versus link functions](transformations.html#link-bias)
* [`scale()`](transformations.html#stdize)
* [Standardizing](transformations.html#stdize)
* [Timing is everything](transformations.html#timing)
* Trends
* [Estimating and comparing](interactions.html#oranges)
* [`trt.vs.ctrl` contrasts](comparisons.html#contrasts)
* [Tukey adjustment](confidence-intervals.html#adjust)
* [Ignored or changed](FAQs.html#notukey)
* [`type`](confidence-intervals.html#tran)
* [`type = "response"`](basics.html#transf)
* [`type = "scale"`](transformations.html#trangraph)
* [Type II analysis](messy-data.html#type2submodel)
* Type III tests
* [in *confidence-intervals: joint*](confidence-intervals.html#joint)
* [in *confidence-intervals: joint_tests*](confidence-intervals.html#joint_tests)
[Back to top](#topnav)
### U {#u}
* [Unadjusted tests](confidence-intervals.html#adjmore)
* [Underlining, grouping by](re-engineering-clds.html#underlining)
* [`update()`](utilities.html#update)
* [`tran`](transformations.html#after)
* [Using results](utilities.html#data)
[Back to top](#topnav)
### V {#v}
* [Variables that are not predictors](basics.html#params)
* [`vcov.`](messy-data.html#neuralgia)
* [`vcovHook`](xtending.html#hooks)
* Vignettes
* [Comparisons](comparisons.html)
* [Confidence intervals and tests](confidence-intervals.html)
* [Explanations supplement](xplanations.html)
* [Extending **emmeans**](xtending.html)
* [FAQS](FAQs.html)
* [Interactions](interactions.html)
* [Messy data](messy-data.html)
* [Models](models.html)
* [Predictions](predictions.html)
* [Re-engineering CLDs](re-engineering-clds.html)
* [Sophisticated models](sophisticated.html)
* [Transformations and link functions](transformations.html)
* [Utilities and options](utilities.html)
[Back to top](#topnav)
### W {#w}
* Weighting
* [Equal weights](basics.html#exper)
* [`weights`](messy-data.html#weights)
* [Welch's *t* comparisons](FAQs.html#nowelch)
* [Example](utilities.html#relevel)
* [`wt.nuis`](messy-data.html#nuisance)
[Back to top](#topnav)
### X {#x}
* [`xtable` method](basics.html#formatting)
[Back to top](#topnav)
### Z {#z}
* [*z* tests](sophisticated.html#dfoptions)
* [vs. *t* tests](FAQs.html#asymp)
* [`zeroinfl` models](models.html#C)
[Back to top](#topnav)
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