# mcPlots

##### Draw Linear Model Marginal and Conditional Plots in Parallel or Overlaid

the `mcPlot`

function draws two plots, or overlay the two graphs on one plot. For a response Y and a regressor X, the first plot is the *m*arginal plot of Y versus X with both variables centered, visualizing the conditional distribution of Y given X ignoring all other regressors. The second plot is an added-variable for X after all other regressors, visualizing the *c*onditional distribution of Y given X after adjusting for all other predictors. The added variable plot by default is drawn using the same xlim and ylim as the centered marginal plot to emphasize that conditioning removes variation in both the regressor and the response.The plot is primarily intended as a pedagogical tool for understanding coefficients in first-order models.

- Keywords
- hplot, regression

##### Usage

`mcPlots(model, terms=~., layout=NULL, ask, overlaid=TRUE, ...)`mcPlot(model, ...)

# S3 method for lm
mcPlot(model, variable,
id.method = list(abs(residuals(model, type="pearson")), "x"),
labels,
id.n = if(id.method[1]=="identify") Inf else 0,
id.cex=1, id.col=palette()[1], id.location="lr",
col.marginal="blue", col.conditional="red", col.arrows="gray",
pch = c(16, 1), lwd = 2, grid=TRUE, ###removed arg main
ellipse=FALSE, ellipse.args=list(levels=0.5),
overlaid=TRUE, new=TRUE, ...)

##### Arguments

- model
model object produced by

`lm`

.- terms
A one-sided formula that specifies a subset of the predictors. One added-variable plot is drawn for each numeric predictor and for each basis function used to define a factor. For example, the specification

`terms = ~ . - X3`

would plot against all terms except for`X3`

. If this argument is a quoted name of one of the terms, the added-variable plot is drawn for that term only.- variable
A quoted string giving the name of a numeric predictor in the model matrix for the horizontal axis. To plot against a factor, you need to specify the full name of one of the indicator variables that define the factor. For example, for a factor called

`type`

with levels`A`

,`B`

and C, using the usual drop-first level parameterization of the factor, the regressors for`type`

would be`typeB`

or`typeC`

.- layout
If set to a value like

`c(1, 2)`

or`c(6, 2)`

, the layout of the graph will have this many rows and columns. If not set, behavior depends on the value of the`overlaid`

argument; see the details- ask
If

`TRUE`

, ask the user before drawing the next plot; if`FALSE`

don't ask.- …
`mcPlots`

passes these arguments to`mcPlot`

.`mcPlot`

passes arguments to`plot`

.- id.method,labels,id.n,id.cex,id.col,id.location
Arguments for the labelling of points. The default is

`id.n=0`

for labeling no points. See`showLabels`

for details of these arguments.- overlaid
If TRUE, the default, overlay the marginal and conditional plots on the same graph; otherwise plot them side-by-side. See the details below

- col.marginal, col.conditional
colors for points, lines, ellipses in the marginal and conditional plots, respectively

- col.arrows
color for the arrows with

`overlaid=TRUE`

- pch
Plotting character for marginal and conditional plots, respectively.

- lwd
line width; default is

`2`

(see`par`

).- grid
If

`TRUE`

, the default, a light-gray background grid is put on the graph.- ellipse
If

`TRUE`

, plot a concentration ellipse; default is`FALSE`

.- ellipse.args
Arguments to pass to the

`dataEllipse`

function, in the form of a list with named elements; e.g.,`ellipse.args=list(robust=TRUE))`

will cause the ellipse to be plotted using a robust covariance-matrix.- new
if

`TRUE`

, the default, the plot window is reset when`overlaid=FALSE`

using`par{mfrow=c(1, 2)}`

. If`FALSE`

, the layout of the plot window is not reset. Users will ordinarily ignore this argument.

##### Details

With an `lm`

object, suppose the response is Y, X is a focal numeric predictor of interest, and Z is all the remaining predictors, possibly including interactions and factors. This function produces two graphs. The first graph is the marginal plot of Y versus X, with each variable centered around its mean. The second conditional plot is the added-variable plot of e(Y|Z) versus e(X|Z) where e(a|b) means the Pearson residuals from the regression of a on b. If `overlaid=TRUE`

, these two plots are overlaid in one graph, with the points in different colors. In addition, each point in the marginal plot is joined to its value in the conditional plot by an arrow. Least squares regression lines fit to the marginal and conditional graphs are also shown; data ellipsoids can also be added. If `overlaid=FALSE`

, then the two graphs are shown in side-by-side plots as long as the second argument to `layout`

is equal to `2`

, or `layout`

is set by the function. The arrows are omitted if the graphs are not overlaid.

These graphs are primarily for teaching, as the marginal plot shows the relationship between Y and X ignoring Z, while the conditional is the relationship between Y and X given X. By keeping the scales the same in both graphs the effect of conditioning on both X and Y can be visualized.

This function is intended for first-order models with numeric predictors only. If the focal predictor is a factor, then one (pair) of mcPlots will be produced for each of the basis variables that define the factor, and the resulting plots are not generally meaningful because they depend on parameterization. If the mean function includes interactions, then mcPlots for main effects may violate the hierarchy principle, and may also be of little interest. mcPlots for interactions of numerical predictors, however, can be useful.

These graphs are closely related to the ARES plots proposed by Cook and Weisberg (1989). This plot would benefit from animation.

##### Value

These functions are used for their side effect of producing plots.

##### References

Cook, R. D. and Weisberg, S. (1989)
*Regression diagnostics with dynamic graphics,* Technometrics, 31, 277.

Fox, J. (2016)
*Applied Regression Analysis and Generalized Linear Models*,
Third Edition. Sage.

Fox, J. and Weisberg, S. (2011)
*An R Companion to Applied Regression*, Second Edition, Sage.

Weisberg, S. (2014) *Applied Linear Regression*, Fourth Edition, Wiley.

##### See Also

##### Examples

```
# NOT RUN {
m1 <- lm(partic ~ tfr + menwage + womwage + debt + parttime, data = Bfox)
mcPlot(m1, "womwage")
mcPlot(m1, "womwage", overlaid=FALSE, ellipse=TRUE)
# }
```

*Documentation reproduced from package car, version 2.1-6, License: GPL (>= 2)*