# IAPlot: Main Effects and Interaction Plots In FrF2: Fractional Factorial Designs with 2-Level Factors

 IAPlot R Documentation

## Main Effects and Interaction Plots

### Description

Main effects plots and interaction plots are produced. The other documented functions are not intended for users.

### Usage

```MEPlot(obj, ...)
## S3 method for class 'design'
MEPlot(obj, ..., response = NULL)
## Default S3 method:
MEPlot(obj, main = paste("Main effects plot for", respnam),
pch = 15, cex.xax = par("cex.axis"), cex.yax = cex.xax, mgp.ylab = 4,
cex.title = 1.5, cex.main = par("cex.main"),
lwd = par("lwd"), abbrev = 3, select = NULL, ...)

IAPlot(obj, ...)
## S3 method for class 'design'
IAPlot(obj, ..., response = NULL)
## Default S3 method:
IAPlot(obj, main = paste("Interaction plot matrix for", respnam),
pch = c(15, 17), cex.lab = par("cex.lab"), cex = par("cex"),
cex.xax = par("cex.axis"), cex.yax = cex.xax, cex.title = 1.5,
lwd = par("lwd"), abbrev = 4, select = NULL, show.alias = FALSE, ...)

intfind(i, j, mat)

check(obj)

remodel(obj)

```

### Arguments

 `obj` an experimental design of class `design` with the `type` element of the `design.info` attribute containing “FrF2” or “pb” OR a linear model object with 2-level factors or numerical 2-level variables; the structure must be such that effects are either fully aliased or orthogonal, like in a regular fractional factorial 2-level design; note that `IAPlot` currently requires the response in `obj` to be a pre-defined variable and not a calculated quantity `...` further arguments to be passed to the default function; ... in the default method are not used, they have been added because of formal requirements only `response` character string that specifies response variable to be used, must be an element of `response.names(obj)`; if NULL, the first response from `response.names(obj)` is used `main` overall title for the plot assembly `pch` Plot symbol number `MEPlot`, or vector of two plot symbol numbers for the lower and higher level of the trace factor `iap` `cex.xax` size of x-axis annotation, defaults to `cex.axis`-parameter `cex.yax` size of y-axis annotation, defaults to cex.xax `mgp.ylab` horizontal placement of label of vertical axis in `MEPlot` `cex.title` multiplier for size of overall title (cex.main is multiplied with this factor) `cex.main` size of individual plot titles in `MEPlot` `cex.lab` Size of variable names in diagonal panels of interaction plots produced by `IAPlot`. `cex` size of plot symbols in interaction plots `lwd` line width for plot lines and axes `abbrev` number of characters shown for factor levels `select` vector with position numbers of the main effects to be displayed; default: all main effects; the default implies the full interaction plot matrix for `IAPlot`. For `IAPlot`, the full interaction plot matrix for the selected factors is displayed. Of course, at least two factors must be selected. Furthermore, the linear model `obj` must at least contain one interaction term among the selected variables. For interactions that do not occur in the linear model, not plot is shown. An interaction plot matrix of data means can be obtained by specifying the model with all possible 2-factor interactions (e.g. formula `y~(.)^2` for a regular 2-level fractional factorial, for which `y` is the only response and all other variables are 2-level factors). `show.alias` if TRUE, the interaction plot shows the number of the list entry from aliases(obj)\\$aliases (cf. `aliases`) in order to support immediate diagnosis of which depicted interaction may be due to other than the shown effect because of aliasing; CAUTION: if the `select` option is used, the model is reduced to the selected factors, i.e. aliases with unselected factors are not shown! `i` integer, for internal use only `j` integer, for internal use only `mat` matrix, for internal use only

### Details

For functions `MEPlot` or `IAPlot`, if `obj` is a design with at least one response variable rather than a linear model fit, the `lm`-method for class `design` is applied to it with the required degree (1 or 2), and the default method for the respective function is afterwards applied to the resulting linear model.
If the design contains a block factor, the plot functions show non-block effects only.

MEPlot

produces plots of all treatment main effects in the model, or selected ones if `select` is specified

IAPlot

produces plots of all treatment interaction effects in the model, or selected ones if `select` is specified

intfind

is an internal function not directly useful for users

check

is an internal function for checking whether the model complies with assumptions (fractional factorial of 2-level factors with full or no aliasing, not partial aliasing; this implies that Plackett-Burman designs with partial aliasing of 2-factor interactions give an OK (=TRUE) in `check` for pure main effects models only.)

remodel

is an internal function that redoes factor values into -1 and 1 coding, regardless of the contrasts that have been used for the original factors; numerical data are transformed by subtracting the mean and dividing by half the range (max-min), which also transforms them to -1 and 1 coding in the 2-level case (and leads to an error otherwise)

### Value

`MEPlot` and `IAPlot` invisibly return the plotted effects (two-row matrix or four-row matrix, respectively). If `show.alias=TRUE`, the matrix returned by IAPlot has as the attribute `aliasgroups`, which contains all alias groups (list element number corresponds to number in the graphics tableau).

The internal function `check` is used within other functions for checking whether the model is a fractional factorial with 2-level factors and no partial aliasing, as requested for the package to work. It is applied to remodeled objects only and returns a logical. If the returned value is FALSE, the calling function fails.

The internal function `intfind` returns an integer (length 1 or 0). It is not useful for users.

The internal function `remodel` is applied to a linear model object and returns a list of two components:

 `model ` is the redone model with x-variables recoded to numeric -1 and 1 notation and aov objects made into “pure” lm objects `labs ` is a list preserving the level information from original factors (levels are minus and plus for numerical variables)

Ulrike Groemping

### References

Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005) Statistics for Experimenters, 2nd edition. New York: Wiley.

`FrF2-package` for examples