Emmeans in r example

Emmeans in r example. 5, position = position_dodge(), stat="summary") Then using emmeans, I calculated the upper and lower confidence levels from the below model: These functions are provided in lsmeans because they have been renamed in emmeans Compact letter displays are often used to report results of all pairwise comparisons among treatment means in comparative experiments. It is very simple: emmeans auto-detects the transformation function (which is made inside the model specification) and automatically produces the back-transformation, when this is requested by using the ‘ type = "response" ’ argument (we can also use the argument ‘ regrid = "response" ’, with slight differences that I will discuss in a Here we show how to carry out Tukey-Kramer tests between all pairs of means. Estimated marginal means (EMMs, previously known as least-squares means in the context of traditional regression models) are derived by using a model to make predictions over a regular grid of predictor combinations (called a reference grid ). Mar 4, 2019 · 1. A named list of defaults for objects created by emmeans or emtrends. If you do, post the data (or some other dataset that leads to this error) here somehow, or email it to the maintainer of emmeans. Dec 12, 2022 · This step can be tricky; I use the showtext package which makes this a bit easier. Apr 12, 2019 at 12:32. Apr 20, 2019 · A two-way ANOVA was conducted to examine the effects of gender (male, female) and exercise regimen (none, light, intense) on weight loss (measure in lbs). From what I understand emmip uses ggplot under the hood. You only The emtrends function is useful when a fitted model involves a numerical predictor x interacting with another predictor a (typically a factor). The customization of plot. For Type III you will need to change the contrasts R uses to code dummy variables. . Estimability has to do with ambiguities arising from rank-deficient models. The emmeans package, unlike many (most) others such as multcomp, tests for estimability. 34 2 true ct 4. plot. Analogous to the emmeans setting, we construct a reference grid Oct 18, 2023 · emmeans: Estimated marginal means (Least-squares means) emmeans-package: Estimated marginal means (aka Least-squares means) emm_example: Run or list additional examples; emmGrid-class: The 'emmGrid' class; emmGrid-methods: Miscellaneous methods for 'emmGrid' objects; emmip: Interaction-style plots for estimated marginal means Simple interaction plot. plant genotype (categorical) and plant genotype height (continuous). 9. Such models specify that x has a different trend depending on a; thus, it may be of interest to estimate and compare those trends. The Anova function allows you to use Type II or Type III. Least-squares means are discussed, and the term "estimated marginal means" is suggested, in Searle, Speed, and Milliken (1980) Population marginal means in the linear model: An alternative to least squares means, The American Statistician Jan 14, 2021 · Thanks for the comment, I did not realize that my example code did not make it in. As an example, sometimes a fitted model has a treatment factor that comprises combinations of other factors. CLD function is active, but was not documented in the emmeans package. If you fit a model based on an underlying assumption of equal variances, and the design is balanced, then the SEs will be equal because the model assumes that to be true. The fun=mean option indicates that the mean for each group will be plotted. nb function in the MASS package. emmeans — Estimated Marginal Means, aka Least-Squares Means. Almost all results you need will be displayed together, including effect sizes (partial η 2 and Cohen's d) and their confidence Oct 18, 2023 · So, for example, one may have different symbols for each group by simply specifying dotarg = list(). This package allows you to formulate a wide variety Apr 10, 2019 · It depends on whether you want me to try to reproduce this condition on my own pc and to try to figure out what’s going wrong. The help page for ptukey states: Note. dv ~ gend * group + ISFregscores + age_dup + edu + empl + civ_dup + kids + known, data = data. Pipe-friendly wrapper arround the functions <code>emmans () + contrast ()</code> from the <code>emmeans</code> package, which need to be installed before using this function. In this Chapter, we will look at how to estimate and perform hypothesis tests for linear mixed-effects models. y=mean, geom="point") emmeans(m, c("f1","f3")) For example the mean for male in day1 is 0. emm <- emmeans (noise. For example, consider: noise. s12, s22: variance of sample 1 and sample 2, respectively. The B. Conceptually, this function is equivalent to interaction. emmGrid to recalculate confidence intervals, and (probably more importantly) also adjust for multiple hypothesis testing. (RG <- expand. Pairwise comparisons. call(rbind, contrast) -output. See Also. Statistical Details A2 = c (0, 1, 0, 0, 0) Similarly, to pull out the mean of B. 65 48 33. I will conduct an example multinomial logistic regression analysis use a dataset provided here. $\endgroup$ Oct 7, 2021 · One of its strengths is its versatility: it is compatible with a huge range of packages. Consider, for example, the warpbreaks data provided with R. m <- lm(Y ~ Type*Treatment) Anova(m, type = 3) How do I set up orthogonal contrasts in R? If I run. To change the color palette, specify the color scale (rather than the fill scale). – Russ Lenth. CLD is available. Note. ANCOVA example. Modeling is not the focus of emmeans, but this is an extremely important step If a matrix, each row of the matrix is used in turn, wrapping back to the first row as needed. lm()' in R. May 12, 2022 · One of the most common measurements of effect size is Cohen’s d, which is calculated as: Cohen’s d = (x1 – x2) / √(s12 + s22) / 2. Plots and other displays. 96" r The latter is just a front end for emmeans, and in fact, the lsmeans() function itself is part of emmeans. The options shown indicate which variables will used for the x -axis, trace variable, and response variable. 1. The first graph is just displaying the middle meadow. library ( estimatr) warp. For example: Oct 8, 2019 · emmeans use the Tukey method for the pairwise comparisons. Tukey’s HSD post hoc tests were carried out. Possibly you should do them with type = “response" so that the results are on a more interpretable scale. 5. Sep 20, 2018 · But the structure is the same, with one factor and one covariate as predictors. Features. A L 44. compSlopes() function in. The main workhorse for estimating linear mixed-effects models is the lme4 package ( Bates et al. Oct 1, 2018 · $\begingroup$ Look at vignette(“FAQs”). contrast(emm, list(con = c(0,0,0,0,-1,1,0,0,-1,0,0,0))) However, this is actually a linear function, not a contrast, because the coefficients do not sum to zero. (prior to v0. 2 Jan 14, 2020 · on the emmeans data don't work, it just gives the emmeans at different levels with confidence intervals, not for the contrasts. Examples Oct 18, 2023 · emm_example: Run or list additional examples; emmGrid-class: The 'emmGrid' class; emmGrid-methods: Miscellaneous methods for 'emmGrid' objects; emmip: Interaction-style plots for estimated marginal means; emm_list-object: The 'emm_list' class; emmobj: Construct an 'emmGrid' object from scratch; emm_options: Set or change emmeans options Dec 3, 2020 · emmeans output interpretation of a glmer fit with nesting. emm1 = emmeans (fit1, specs = ~ sub. The warpbreaks dataset provided in base R has the results of a two-factor experiment. In the first example below, there are two treatments ( D and C) each at two levels ( 1 and 2 ), and then there is a Control treatment. 7 the predict function has been implemented to obtain predictions for either fixed or random effects the way asreml does. About This is a read-only mirror of the CRAN R package repository. There are two answers to this (i. UPDATE: THE ANSWER I finally figured it out: confint (contrast (emmeans (fit1,~A*G*L),interaction=c ("pairwise"))) r. Note: emmeans::emmip() returns a ggplot object, which can be modified and saved with ggplot2 syntax. The Analysis of Covariance ( ANCOVA) is used to compare means of an outcome variable between two or more groups taking into account (or to correct for) variability of other variables, called covariates. ggplot(aes(x=f3,y=dep,colour=f1),data=data) + stat_summary(fun. reduce, or fac. Jan 28, 2021 · For this post, I'm using the default pigs dataset as a toy example to plot source by percentage. facetlab. The interaction. CL upper. Much of what you do with the emmeans package involves these three basic steps: Fit a good model to your data, and do reasonable checks to make sure it adequately explains the respons (es) and reasonably meets underlying statistical assumptions. plot function in the native stats package creates a simple interaction plot for two-way data. Note: The model is what accounts for the random effect. Perhaps gam already creates some variable for source:treatment that you may use as a by variable. emmGrid or pairs May 9, 2020 · R: problem using emmeans with lme4::glmer object with logit link. As an example, let's use Helmert contrasts (sometimes called 'reverse Helmert', but the R way of doing these suits my purpose) on a subset of the 'warpbreaks' data set. Otherwise, if object is an emmGrid object, its first element is Oct 18, 2023 · A method for multcomp::cld () is provided for users desiring to produce compact-letter displays (CLDs). But to put a very fine edge on it, the Tukey HSD method is really defined only for independent samples of Oct 30, 2021 · With rbind, instead of rbind. Such models specify that x x has a different trend depending on a a; thus, it may be of interest to estimate and compare those trends. Jul 9, 2021 · The emmeans package is one of several alternatives to facilitate post hoc methods application and contrast analysis. I am trying to fit a mixed-effects model using lme4, using logit link transformation. For the example at hand, the reference grid is. Nov 2, 2023 · Now I want to fit a mixed model with lme4::glmer on my counts data, and perform contrasts for each cell population, to see if they are significantly over-represented in the "Yes" treatment group over the "No" treatment group (probably using emmeans). Interactions are formed by the product of any two variables. adjust. 2023). 0) was used to statistically compare slopes for all pairs of groups in an indicator/dummy variable regression (I/DVR). emm, simple = "size") is the same as pairs emmeans provides method confint. Chapter 9. Jul 11, 2018 · C is the group variable, just like in the example above. A named list of defaults for objects created by contrast. Data = read. I have edited it and both are Tukey-adj p. In other words, ANCOVA allows to compare the adjusted means of two or more independent groups. The emmip function generates these automatically and provides therm via the labs attribute, but the user may override these if desired. 0) An alternative way to specify conditional contrasts or comparisons is through the use of the simple argument to contrast () or pairs (), which amounts to specifying which factors are not used as by variables. e. 2 group is on the fourth row in emm1. emmeans package, Version 1. emmeans. Those are the same critical values that are used in the Tukey HSD test. And we have to test to make sure that L_i + R_j < d_ij when the difference is significant, and >= d_ij when it Aug 11, 2021 · Calling emmeans (Model, simple = "each") will give you a straightforward table with each possible combination of your factors. contrast. 3 Example by Card and Krueger (1993) 26. I will name this output emm1. emmeans() summarizes am model, not its underlying data. Mar 22, 2023 · 1 Answer. This vignette gives a few examples of the use of the emmeans package to analyze other than the basic types of models provided by the stats package. 9 Staggered Dif-n-dif. Find centralized, trusted content and collaborate around the technologies you use most. packages("multcomp")} Multiple comparisons with emmeans . ctrl") compares the first level with everything that follows it (there are 7 factor levels in C, and I want to remove last 3 of them and compute the contrasts for the remaining 4). In sommer >= 3. – Apr 15, 2019 · Building custom contrasts. g. Mar 14, 2021 · This can be done pretty easily, but what you have to do is get the basic output and then plug in the right P values. The Anova function in the car package will be used for an analysis of deviance, and the nagelkerke function will be used to determine a p-value and pseudo R-squared value for the model. cld has been documented, but no similar documentation of plot. Analogous to the emmeans setting, we construct a reference grid of Jun 13, 2019 · For example, I want to report the mean and 95% confidence intervals, how would I do so? It feels wrong to just say, "the difference in relative humidity between city A and B is 3. 89 3 false mm 2. It takes a model and the classify argument to know which arguments to use for aggregating the hypertable and come up with the right standard errors. Sorted by: 1. I have recently discovered that emmeans is compatible with the brms package, but am having trouble getting it to work. 2 we’ll have a vector of 5 values with a 1 as the fourth value. There is also an xtable method that preserves the annotations. It is a very simple model, where the response f is a function of the fixed effect case and the random effect journal. Here's my plot: pigs_plot <- pigs %>% ggplot(aes(x=source, y=percent, fill=source)) + geom_bar(width = 0. Note: I may have mis-remembered the factor levels, and if so, the coefficients may need to be rearranged. This function is based on and extends (1) emmeans::joint_tests(), (2) emmeans::emmeans(), and (3) emmeans::contrast(). In fact, the output is not transformed at all. Package ‘emmeans’ January 24, 2024 Type Package Title Estimated Marginal Means, aka Least-Squares Means Version 1. The output table will say “ \(t\) ” but it is actually “ \(q\) ” as we describe in the book. This is typically used when some of the Jun 7, 2020 · Now, on to the question. Do think: Make sure you fit a model that really explains the responses. wool tension emmean SE df lower. This method uses the Piepho (2004) algorithm (as implemented in the multcompView package) to generate a compact letter display of all pairwise comparisons of estimated marginal means. Special behavior with log transformations. 0. Nov 17, 2022 · Collectives™ on Stack Overflow. Model: > mod = glm(log(strength) ~ machine + diameter, data = fiber) Comparing Multiple Means in R. Other contrasts. It’s all documented. exam scores) g: A vector that specifies the group names (e. The plot. This function is based on and extends (1) emmeans::joint_tests () , (2) emmeans::emmeans (), and (3) emmeans::contrast () . vs. b 1: the simple effect or slope of X, for a one unit change in X the predicted change in Y at W = 0. The yield of plant genotype is the dependent variable. Its response variable is fiber strength, the continuous predictor is the diameter, and the factor is the machine it was made on. Oct 2, 2023 · Interaction Plot (See Examples Below) You can save the returned object and use the emmeans::emmip() function to create an interaction plot (based on the fitted model and a formula). library(emmeans) lm &lt;- lm(breaks ~ wool Oct 23, 2018 · I use the emmeans package for post-hoc tests and ggplot2 to plot the results. In this sense, I would like to know what would be the Mar 14, 2020 · 1 Answer. It is intended for use with a wide variety of ANOVA models, including repeated measures and nested designs where the initial Oct 7, 2022 · I have made some changes in an upcoming version to emmeans and emmip_ggplot() in particular to increase flexibility with line types and shapes, as well as color, so that this sort of thing can be done more easily within the emmip() context. table(header=TRUE, stringsAsFactors=TRUE, text=" Speaker Likert Pooh 3 Pooh 5 A factorial experiment. Custom contrasts and linear functions. 1 Example by Doleac and Hansen (2020) 26. Be careful in jumping in with calling complex contrast without first visualizing your results; you might overlook crucial interaction impacts, potentially rendering your interpretation invalid. The function obtains (possibly adjusted) P values for all Prediction is not the central purpose of the emmeans package. A graph or two might help as well. ctrl", by = "R") The built-in contrast option ("trt. 7 Two-way Fixed-effects; 26. I have read that the interpretation of generalized linear mixed models (GLMM) at the response level is more complex because the back transformation is nonlinear and the random terms do not play a strictly additive role. As you don't provide sample data, here is an example using the warpbreaks data. Use an equally weighted average. Oct 18, 2023 · This could affect other objects as well. 3) For adjusted (marginal or least square) means, you can use the emmeans package. emm = emmeans(m, ~ V * N) emm. 6 One Difference; 26. However, the excellent. Use "label_value" to show just the factor levels, or "label_both" to show both the factor names and factor levels. The fact that the model is rank deficient is an important omission from what is shown in the question. For a reproducible example, I'm using warpbreaks data. We start by fitting a model. This vignette covers techniques for comparing EMMs at levels of a factor predictor, and other related analyses. Dec 12, 2023 · Beginner Guides. See Piepho (2004) and Piepho (2018) for more details and find a coding example below. They should correspond to the combinations Apr 25, 2018 · contrast(emmeans(my_lm, ~ C * R), "trt. Perform (1) simple-effect (and simple-simple-effect) analyses, including both simple main effects and simple interaction effects, and (2) post-hoc multiple comparisons (e. We will define a single factor and fit a non homogeneous-variance model: Oct 18, 2023 · emmeans: Estimated marginal means (Least-squares means) emmeans-package: Estimated marginal means (aka Least-squares means) emm_example: Run or list additional examples; emmGrid-class: The 'emmGrid' class; emmGrid-methods: Miscellaneous methods for 'emmGrid' objects; emmip: Interaction-style plots for estimated marginal means Contrasts can be used to make specific comparisons of treatments within a model. Even its name refers to the idea of obtaining marginal averages of fitted values; and it is a rare situation where one would want to make a prediction of the average of several observations. I'm not sure, but if you do emmeans::ref_grid (fit, at = list (percent = 9:18)), it will show you a summary of the reference grid obtained from the model you fitted, including the names of the variables you may legally use. We can certainly do that if it is truly desired, but almost always, predictions should be Oct 21, 2018 · I'm using emmeans and would like to learn how to customize plots. data. You only need to specify the model object, to-be-tested effect (s), and moderator (s). 4 Example by Butcher, McEwan, and Weerapana (2014) 26. Use as. do. Oct 18, 2023 · The reference grid, and definition of EMMs {#refgrid} Estimated marginal means are defined as marginal means of model predictions over the grid comprising all factor combinations -- called the reference grid . Apr 8, 2019 · Tukey-adjusted P values are computed using the ptukey() function in R (Studentized range distribution). Post-hoc analysis can be conducted with the emmeans package. However, the degrees of freedom for the means will still be considerably less than those for the comparisons. Nov 25, 2020 · 5. The raw data for the “Wood-wide web” example (Example 15. studying technique) The following code shows how to use this function for our example: Mar 6, 2018 · I'll consider adding a simple one-factor example somewhere in the documentation. , pairwise, sequential, polynomial), with p values adjusted for factors with >= 3 levels. 6 55. The ANCOVA model analyzes the influence of plant genotypes on genotype yield whilst controlling the effect of the covariate. Jan 8, 2018 · 2) By default, R uses Type I Sums of Squares. EDIT 2: And here's the exact code I ran on the simulated data: Description. plot where the summarization function is thought to return the EMMs. Formula interface. frame, there is a specific method for 'emmGrid' object and it can directly use the correct method by matching the class if we specify just rbind. Sep 29, 2018 · I have the following data structure (with example values): id var1 var2 value 1 true tr 1. Contents. In subsequent analysis, we may well want to break it down into the individual factors’ contributions. Here's an example with a dataset I created for the feature request I posted on metafor's GitHub site Oct 4, 2021 · 0. In the second graph, I put in the p-values from the results of the interaction from the Tukey post hoc. emmmeans. We provide real examples and useful tips to help you master this essential tool. This function is based on and extends (1) emmeans::joint_tests () , (2 The emtrends function is useful when a fitted model involves a numerical predictor x x interacting with another predictor a (typically a factor). 0141). 4) are not available, so we have used the circadian rhythm data to demonstrate the R method here instead. To illustrate, I'm going to show a different example where one factor has more than two levels. For example, if emmeans is called with a fitted model object, it calls ref_grid and this option will affect the resulting emmGrid object. A Legendre 16-point formula is used for the integral of ptukey. emmeans just summarizes results from a model; so if the model accounts properly for the random effect(s), you don't need to do anything extra in emmeans. 1 Assumptions; 26. The first step to building custom contrasts is to calculate the estimated marginal means so we have them to work with. rate) emm1. lm, ~ size * side * type) Then pairs (noise. Emphasis here is placed on accessing the optional capabilities that are typically not needed for the more basic models. Sep 16, 2018 · 1 Answer. 38 4 true tr 1. X and Y are the controls, with X being trial number and Y being sex. These predictions may possibly be averaged (typically with equal weights) over one or more If object is a fitted model, emmeans is called with an appropriate specification to obtain estimated marginal means for each combination of the factors present in formula (in addition, any arguments in that match at, trend, cov. A reviewer of my paper does not like Tukey method as she said: "Tukey’s HSD assumes all measures are independent from each other and is not appropriate for repeated measures. 573, but the emmean Sophisticated models in emmeans emmeans package, Version 1. Learn more about Collectives This is why the concept of reference grid () is so important for direct predictions. emmeans(m, ~Type*Treatment) it compares everything. CL. cld. 10. An example is provided in the official documentation to write a It is very simple: emmeans auto-detects the transformation function (which is made inside the model specification) and automatically produces the back-transformation, when this is requested by using the ‘ type = "response" ’ argument (we can also use the argument ‘ regrid = "response" ’, with slight differences that I will discuss in a 26. The cld function was brought forward in the emmeans package as CLD. emtrends() function in the. Chapter 9 Linear mixed-effects models. This example will use the glm. This example uses data set and model from the One-way Ordinal regression with CLM chapter. I am using the lm () function in R to analyze it and emmeans for post hoc tests. B2 = c (0, 0, 0, 1, 0) When building custom contrasts via vectors like this, the vectors will always be the same length as the number of rows in the emmeans () output. Y ^ = b 0 + b 1 X + b 2 W + b 3 X ∗ W. Interaction contrasts (in “interactions” vignette) if(!require(emmeans)){install. 28 Sep 28, 2020 · To perform Dunnett’s Test in R we can use the DunnettTest() function from the DescTools library which uses the following syntax: DunnettTest(x, g) where: x: A numeric vector of data values (e. I think in your paper you should show a table of the EMMs and SEs, and another table showing the comparisons among them and their Tukey-adjusted P values. emmeans, interaction. I'm finding some differences between the means calculated by ggplot and the means from emmeans. Learn how to install, load, and use the emmeans package in R with our beginner's guide. Using adjust = "tukey" means that critical values and adjusted P values are obtained from the Studentized range distribution qtukey () and ptukey () respectively. We give greater weight when d_ij is close to e_ij, because those are the cases where it is more critical that we get the lengths of the arrows right. , be careful what you wish for): Don’t think; just fit the first model that comes to mind and run emmeans (model, pairwise ~ treatment). Both f and case are binary values, while journal can have several integer Mar 15, 2017 · If you instead use the lme4 package and the lmer function to fit the model, lsmeans will use a Satterthwaite or Kendall-Roger method to obtain degrees of freedom, and those results might be somewhat larger. method = "bonferroni", detailed = TRUE) <p>Performs pairwise comparisons between groups using the estimated marginal means. grid (source = levels (pigs $ source), percent = unique (pigs $ percent))) Compute contrasts or linear functions of EMMs, trends, and comparisons of slopes. 2 Example from Princeton; 26. I am trying to plot predictions across levels of a couple of predictors. 8 Multiple periods and variation in treatment timing; 26. Linear mixed-effects models. 26. I have a data set consisting of several Types and two treatments (example below). package is a more general and strongly principaled function for this purpose. This is the fastest way; however, the results have a good chance of being invalid. December 12, 2023. Each coefficient is interpreted as: b 0: the intercept, or the predicted outcome when X = 0 and W = 0. When in doubt about what is being averaged (or how many), first call emmeans with weights = "show. levels". If a matrix, each row of the matrix is used in turn, wrapping back to the first row as needed. 0 Date 2024-01-23 Depends R (>= 4. *Means not sharing any letter are significantly different by the Tukey-test at the 5% level of significance. May 15, 2020 · The code in emmeans uses a weighted regression method to solve the above equations. where: x1 , x2: mean of sample 1 and sample 2, respectively. rlm <- lm_robust ( log (breaks) ~ wool * tension, data = warpbreaks) Typical use of emmeans () is to obtain predictions, or marginal means thereof, via a formula of the form The three basic steps. Using this formula, here is how we interpret Cohen’s d: Mar 11, 2019 · I've been trying to do this with the emmeans packages, and I followed the steps described in the emmeans package vignette, however, I find that the summary results for the estimated means are not at all similar to the untransformed data. Jul 17, 2023 · The qdrg() function in emmeans almost works out-of-the-box. Jul 3, 2018 · I'm using the emmeans package and the emmip function to plot predicted probabilities from an clmm object. I also added an example of producing a black-and-white plot, which is a common need. 5 Examples. FSA. reduce are passed to emmeans ). flabel <- c ('con1','con1','con1', 'con2','con2 May 16, 2022 · I'm trying to understand why the values under 'estimate' from an emmeans contrast function differ from those of the default 'Estimate' values from, say, 'summary. One common use is when a factorial design is used, but control or check treatments are used in addition to the factorial design. There was a statistically significant interaction between the effects of gender and exercise on weight loss (F (2, 54) = 4. These functions work on the contrasts data, but these do not show the 3-way interactions. The following is a short example in R. frame () and then whatever else you want to put it in the form you want. If weights is a string, it should partially match one of the following: "equal". The example is the emmeans::fiber dataset. Custom contrasts are based on the estimated marginal means output from emmeans (). See examples below for the usage. emmeans_test(len ~ dose, p. Apr 10, 2019 · The function cld was designed for glht -type data, which can be visualized using plot. Oct 29, 2018 · 4. This is one of the toughest distributions to compute, among those in common use. Labeller for facets (when by variables are in play). The following hypothetical example data consist of two independent variables viz. The only hitch is that rma models name the intercept intrcpt instead of (Intercept), and we have to fix that. It is a relatively recent replacement for the lsmeans package that some R users may be familiar with. , pairwise, sequential, polynomial), with p values adjusted for factors with &gt;= 3 levels. . 6 3. packages("emmeans")} if(!require(multcomp)){install. 615, p = 0. Marginal "means", obtained via estimate_means (), are an extension of such predictions, allowing to "average" (collapse) some of the predictors, to obtain the average response value at a specific predictors configuration. ky uy po fr kr sz ob zx lj hj