[U] User's Guide

[ U ] 20.14 Obtaining marginal means, adjusted predictions, and predictive margins 28520.14 Obtaining marginal means, adjusted predictions, and predictivemarginspredict uses the current estimation results (the coefficients and the VCE) to estimate the value ofstatistics for observations in the data. lincom and nlcom use the current estimation results to estimatea specific linear or nonlinear expression of the coefficients. The margins command combines aspectsof both and estimates margins of responses.margins answers the question “What does my model have to say about such-and-such a group orsuch-and-such a person”, where such-and-such might be• my estimation sample or another sample• a sample with the values of some covariates fixed• a sample evaluated at each level of a treatment• a population represented by a complex survey sample• someone who looks like the fifth person in my sample• someone who looks like the mean of the covariates in my sample• someone who looks like the median of the covariates in my sample• someone who looks like the 25th percentile of the covariates in my sample• someone who looks like some other statistics of the covariates in my sample• a standardized population• a balanced experimental design• any combination of the above• any comparison of the aboveIt answers these questions either conditionally, based on fixed values of all covariates, or averagedover the observations in a sample. It answers these questions about almost any predictions or anyother response that you can calculate as a function of your estimated parameters—linear responses,probabilities, hazards, survival times, odds ratios, risk differences, etc. It answers these questions interms of the response given covariate levels, or in terms of the change in the response for a changein levels (also known as marginal effects). It answers these questions providing standard errors, teststatistics, and confidence intervals; and those statistics can take the covariates as given or adjust forsampling, also known as predictive margins and survey statistics.A margin is a statistic based on a response for a fitted model calculated over a dataset in whichsome of or all the covariates are fixed at values different from what they really are.Margins go by different names in different fields, and they can estimate many interesting statisticsrelated to a fitted model. We discuss some common uses below; see [R] margins for more applications.20.14.1 Obtaining expected marginal meansA classic application of margins is to estimate the expected marginal means from a linear estimatoras though the design for the covariates were balanced—assuming an equal number of observationsfor each unique combination of levels for the factor-variable covariates. These means have a longhistory in the study of ANOVA and MANOVA but are of limited use with nonexperimental data. For adiscussion, see Obtaining margins as though the data were balanced in [R] margins and example 4in [R] anova.Estimated marginal means are also called “least-squares means”.