# pairs.mlm: Pairwise HE Plots In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

## Description

The function (in the form of an `mlm` method for the generic `pairs` function) constructs a “matrix” of pairwise HE plots (see heplot) for a multivariate linear model.

## Usage

 ```1 2 3 4 5``` ```## S3 method for class 'mlm' pairs(x, variables, var.labels, var.cex=2, type = c("II", "III", "2", "3"), idata=NULL, idesign=NULL, icontrasts=NULL, imatrix=NULL, iterm=NULL, manova, offset.axes = 0.05, digits = getOption("digits") - 1, fill=FALSE, fill.alpha=0.3, ...) ```

## Arguments

 `x` an object of class `mlm`. `variables` indices or names of the three of more response variables to be plotted; defaults to all of the responses. `var.labels` labels for the variables plotted in the diagonal panels; defaults to names of the response variables. `var.cex` character expansion for the variable labels. `type` “type” of sum-of-squares-and-products matrices to compute; one of `"II"`, `"III"`, `"2"`, or `"3"`, where `"II"` is the default (and `"2"` is a synonym). `idata` an optional data frame giving a factor or factors defining the intra-subject model for multivariate repeated-measures data. See Details of `Anova` for an explanation of the intra-subject design and for further explanation of the other arguments relating to intra-subject factors. `idesign` a one-sided model formula using the “data” in idata and specifying the intra-subject design for repeated measure models. `icontrasts` names of contrast-generating functions to be applied by default to factors and ordered factors, respectively, in the within-subject “data”; the contrasts must produce an intra-subject model matrix in which different terms are orthogonal. The default is c("contr.sum", "contr.poly"). `imatrix` In lieu of `idata` and `idesign`, you can specify the intra-subject design matrix directly via `imatrix`, in the form of list of named elements. Each element gives the columns of the within-subject model matrix for an intra-subject term to be tested, and must have as many rows as there are responses; the columns of the within-subject model matrix for different terms must be mutually orthogonal. This functionality requires `car` version 2.0 or later. `iterm` For repeated measures designs, you must specify one intra-subject term (a character string) to select the SSPE (E) matrix used in the HE plot. Hypothesis terms plotted include the `iterm` effect as well as all interactions of `iterm` with `terms`. `manova` optional `Anova.mlm` object for the model; if absent a MANOVA is computed. Specifying the argument can therefore save computation in repeated calls. `offset.axes` proportion to extend the axes in each direction; defaults to 0.05. `digits` number of significant digits in axis end-labels; taken from the `"digits"` option. `fill` A logical vector indicating whether each ellipse should be filled or not. The first value is used for the error ellipse, the rest — possibly recycled — for the hypothesis ellipses; a single fill value can be given. Defaults to FALSE for backward compatibility. See Details of `heplot` `fill.alpha` Alpha transparency for filled ellipses, a numeric scalar or vector of values within `[0,1]`, where 0 means fully transparent and 1 means fully opaque. Defaults to 0.3. `...` arguments to pass down to `heplot`, which is used to draw each panel of the display.

Michael Friendly

## References

Friendly, M. (2006). Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples Journal of Statistical Software, 17(6), 1-42. https://www.jstatsoft.org/v17/i06/

Friendly, M. (2007). HE plots for Multivariate General Linear Models. Journal of Computational and Graphical Statistics, 16(2) 421-444. http://datavis.ca/papers/jcgs-heplots.pdf

`heplot`, `heplot3d`
 ```1 2 3 4 5``` ```# ANCOVA, assuming equal slopes rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ SES + n + s + ns + na + ss, data=Rohwer) # View all pairs, with ellipse for all 5 regressors pairs(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss"))) ```