Contents | Foundations | Emphasis on experimental data | Emphasis on models | Illustration: pigs experiment | Estimated marginal means | The reference grid, and definition of EMMs | More on the reference grid | Other topics | Passing arguments | Transformations | Derived covariates | Non-predictor variables | Graphical displays | Formatting results | Using weights | Multivariate responses | Objects, structures, and methods | P values, "significance", and recommendations | A set of comparisons or well-chosen contrasts is more useful and interpretable than an omnibus F test | Use adjusted P values | It is not necessary to have a significant F test as a prerequisite to doing comparisons or contrasts | Get the model right first | Consider seeking the advice of a statistical consultant | Summary of main points | References | Further reading

A complete example

Contents | Linear mixed models (lmer) | System options for lmerMod models | Bias adjustment with random slopes | Adding variables not in fixed model | Models with offsets | Ordinal models | Models fitted using MCMC methods | Bias-adjusted incidence probabilities | Bayesian prediction

Contents | The three basic steps | One-factor model | Two factors, no interaction | Two interacting factors | Diagonal comparisons | Interaction contrasts | Three or more factors | Additional options | What you see versus what you get | Common things that can go wrong | Only one mean is obtained -- or fewer than expected | Having trouble with follow-up analyses, and the pairwise ~ ... recipe | Further reading

Contents | Introduction | Data example | Supporting rlm | Quick and dirty support | Supporting lqs objects | The recover_data method | Special arguments | Error handling | The emm_basis method | Dissecting emm_basis.lqs | Communication between methods | Hook functions | Re-gridded basis | Exported methods from emmeans | Existing support for rsm objects | The recover_data method | The emm_basis method | A demonstration | Dispatching and restrictions | Exporting and registering your methods | Conclusions

Contents | Focus on reference grids | Need for an SD estimate | Feedlot example | Predictions on particular strata | Predictions with Bayesian models

Contents | Introduction | Grouping by underlining | Grouping using letters or symbols | Simulated example | Default CLD | Alternative CLDs | Equivalence sets | Significance sets | Conclusions | References

Jump to: A B C D E F G H I J K L M N O P Q R S T U V W X Z | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Z

Contents | Issues with observational data | Mediating covariates | Mediating factors and weights | Nuisance factors | Limiting the size of the reference grid | Counterfactuals and G-Computation | Sub-models | Nested fixed effects | Graphs with nesting | Auto-identification of nested factors -- avoid being trapped!

Contents | Pairwise comparisons | Matrix displays | Effect size | Graphical comparisons | Pairwise P-value plots | Compact letter displays (CLDs) | Other contrasts | Normalized contrasts | Formula interface | Custom contrasts and linear functions | Special properties of log (and logit) transformations

Contents | What are EMMs/lsmeans? | What is the fastest way to obtain EMMs and pairwise comparisons? | I wanted comparisons, but all I get is (nothing) | The model I fitted is not supported by emmeans | I have three (or two or four) factors that interact | I have covariate(s) that interact(s) with factor(s) | I have covariate(s) and am fitting a polynomial model | I have transformed covariate(s) | Some "significant" comparisons have overlapping confidence intervals | All my pairwise comparisons have the same P value | emmeans() doesn't work as expected | All or some of the results are NA | If I analyze subsets of the data separately, I get different results | My lsmeans/EMMs are way off from what I expected | Why do I get Inf for the degrees of freedom? | I get exactly the same comparisons for each "by" group | My ANOVA F is significant, but no pairwise comparisons are | I wanted differences, but instead I got ratios (or odds ratios) | I asked for Tukey adjustments, but that's not what I got | emmeans() completely ignores my P-value adjustments | emmeans() gives me pooled t tests, but I expected Welch's t | I want to see more digits | I want to reproduce results from Stata's margins command

Contents | summary(), confint(), and test() | Back-transforming | Multiplicity adjustments | "By" variables | Adjustments across by groups | Simple comparisons | Joint tests | Testing equivalence, noninferiority, and nonsuperiority | Graphics

Quick reference for supported objects and options | Group A -- "Standard" or minimally supported models | Group B -- Beta regression | Group C -- Count models | Group E -- GEE models | Group G -- Generalized linear models and relatives | Group H -- gamlss models | Group I -- Multiple models (via imputation or averaging) | Group K -- gls and lme models | Group L -- lmerMod models | Group M -- Multivariate models | N - Multinomial responses | Group O - Ordinal responses | Group P -- Other packages | Group Q -- Quantile regression | Group S -- Sampling (MCMC) methods | Group V -- aovList objects (also used with afex_aov objects)

Contents | Overview | Timing is everything | The model is our best guide | Re-gridding | Implied regridding with certain modes | Link functions | Graphing transformations and links | Models having both a response transformation and a link function | Special transformations | Specifying a transformation after the fact | Auto-detected response transformations | Faking a log transformation | Faking other transformations | Revisiting the neuralgia example | Alternative scale | Standardized response | What to do if auto-detection fails | Reverse-engineering a standardized response | Bias adjustment | Pigs example revisited | Response transformations vs. link functions | InsectSprays example | CBPP example

Abstract | The scenario | Initial experiment | But hold on a minute... First, assess the strategy | First-order design capability | Looking further ahead | OK, now we can collect some data | Explore the path of steepest-ascent | Relocated experiment | Foldover experiment | Augmenting further to estimate a second-order response surface | Ridge analysis (second-order steepest ascent) | Second-order design at the new location | Summary

Abstract | Introduction | Coding of data | Generating a design | Fitting a response-surface model | Displaying a response surface | Direction for further experimentation | Stationary and rising-ridge situations | Technical details | Discussion | References

Abstract | Introduction | Models with two predictors | Three or more predictors | Annotations and hooks | Saving graphs | More on perspective plots | Adding contours | Doing it your own way | References

Introduction | Estimating effects | Graphical analyses | Statistics | Other features

Contents | Sub-models | A note on multivariate models | Comparison arrows | Examples and tests | Related reading on comparisons | Confounded effects in joint tests | Intricacies of offsets

Contents | Interacting factors | Simple contrasts | Interaction contrasts | Multivariate contrasts | Interactions with covariates | Summary

Contents | Updating an emmGrid object | Setting options | Setting and viewing defaults | Optimal digits to display | Startup options | Combining and subsetting emmGrid objects | Accessing results to use elsewhere | Adding grouping factors | Re-labeling or re-leveling an emmGrid