lm.design: lm and aov methods for class design objects
In DoE.base: Full Factorials, Orthogonal Arrays and Base Utilities for DoE Packages
lm and aov method for class design objects R Documentation
lm and aov methods for class design objects
Description
Methods for automatic linear models for data frames of class design
Usage
lm(formula, ...)
## Default S3 method:
lm(formula, data, subset, weights, na.action, method = "qr",
model = TRUE, x = FALSE, y = FALSE, qr = TRUE, singular.ok = TRUE,
contrasts = NULL, offset, ...)
## S3 method for class 'design'
lm(formula, ..., response=NULL, degree=NULL, FUN=mean,
use.center=NULL, use.star=NULL, use.dummies=FALSE)
aov(formula, ...)
## Default S3 method:
aov(formula, data = NULL, projections = FALSE, qr = TRUE,
contrasts = NULL, ...)
## S3 method for class 'design'
aov(formula, ..., response=NULL, degree=NULL, FUN=mean,
use.center=FALSE)
## S3 method for class 'lm.design'
print(x, ...)
## S3 method for class 'lm.design'
summary(object, ...)
## S3 method for class 'lm.design'
coef(object, ...)
## S3 method for class 'summary.lm.design'
print(x, ...)
## S3 method for class 'aov.design'
print(x, ...)
## S3 method for class 'aov.design'
summary(object, ...)
## S3 method for class 'summary.aov.design'
print(x, ...)
lm.design
summary.lm.design
aov.design
summary.aov.design
Arguments
formula
for the default method, cf. documentation for lm
in package stats;cr
for the class design method, a data frame of S3 class
design
...
further arguments to functions lm,
print.lm or print.summary.lm
response
character string giving the name of the response variable
(must be among the responses of x;
for wide format repeated measurement or parameter designs,
response can also be among the column names of the responselist
element of the design.info attribute)
OR
integer number giving the position of the response in element
response.names of attribute design.info
For the default NULL, the first available response variable
is used; for wide format designs, this is an aggregation of the variables
given in first column from the responselist
element of the design.info attribute of x.
degree
degree for the formula; if NULL,
the default for the formula method is used
FUN
function for the aggregate.design method;
this must be an unquoted function name;
This option is relevant for repeated measurement designs
and parameter designs in long format only
use.center
NULL or logical indicating whether center points are to be used +
in the analysis;
if NULL, the default is FALSE for pb and FrF2 designs with
center points and TRUE for ccd designs; the option is irrelevant
for all other design types.
FALSE allows usage of simple analysis functions from package
FrF2-package (e.g. function IAPlot)
use.star
NULL or logical indicating whether the star portion of a CCD design
is to be used in the analysis (ignored for all other types of designs).
The default TRUE analyses the complete design. Specifying FALSE permits interim analyses of
the cube portion of a central composite design.
use.dummies
logical indicating whether the error dummies of a Plackett Burman design
are to be used in the formula (ignored for all other types of designs).
projections
logical indicating whether the projections should be returned;
for orthogonal arrays, these are helpful, as they provide the estimated
deviation from the overall average attributed to each particular factor;
it is not recommended to use them with unbalanced designs
x
object of class lm or summary.lm,
for lm.default like in lm
object
object of class lm.design created by function lm.design
lm.design
a class that is identical in content to class lm;
its purpose is to call a specific print method that provides slightly more
detail than the standard printout for linear models
summary.lm.design
a class that is identical in content to class summary.lm;
its purpose is to call a specific print method that provides slightly more
detail than the standard summary for linear models
data
like in lm
subset
like in lm
weights
like in lm
na.action
like in lm
method
like in lm
model
like in lm
y
like in lm
qr
like in lm
singular.ok
like in lm
contrasts
like in lm
offset
like in lm
Details
The aov and lm methods for class design
conduct a default linear model analysis for data frames of
class design that do contain at least one response.
The intention for providing default analyses is to support convenient quick inspections.
In many cases, there will be good reasons to customize the analysis, for example by including
some but not all effects of a certain degree. Also, it may be statistically more wise
to work with mixed models for some types of design. The default analyses must not
be taken as a statistical recommendation!
The choice of default analyses
has been governed by simplicity: It uses fixed effects only and does either
main effects models (degree=1, default for pb and oa designs),
models with main effects and 2-factor interactions (degree=2,
default for most designs) or second order models (that contain
quadratic effects in addition to the 2-factor interactions, unchangeable default
for designs with quantitative variables). The degree parameter can be used
to modify the degree of interactions. If blocks are
present, the block main effect is always entered as a fixed effect without interactions.
Designs with center points are per default analysed without the center points; the main
reason for this is convenient usage of functions DanielPlot,
MEPlot and IAPlot from package FrF2.
With the use.center option, this default can be changed; in this case, significance
of the center point indicator implies that there are one or more quadratic effect(s)
in the model.
Designs with repeated measurements (repeat.only=TRUE) and parameter
designs of long format are treated by aggregate.design
with aggregation function FUN (default: means are calculated)
before applying a linear model.
For designs with repeated measurements (repeat.only=TRUE) and parameter
designs of wide format, the default is to use the first aggregated response,
if the design has been aggregated already. For a so far unaggregated design,
the default is to treat the design by aggregate.design,
using the function FUN (default: mean) and then use the first response.
The defaults can be overridden by specifying response: Here,
response can not only be one of the current responses but also a column name
of the responselist element of the design.info attribute of the
design (i.e. a response name from the long version of the design).
The implementation of the formulae is not done in functions lm.design or
aov.design themselves
but based on the method for function formula (formula.design).
The print methods prepend the formula and the number of experimental runs
underlying the analysis to the default printout.
The purpose of this is meaningful output in case a call from
inside function lm.design or aov.design
(methods for functions lm and aov )
does not reveal enough information, and another pointer that center points have been
omitted or repeated measurements aggregated over. The coef method for objects
of class lm.design suppresses NA coefficients, i.e.
returns valid coefficients only. For aov objects, this is the default
anyway.
Value
The value for the lm functions is a linear model object,
exactly like for function lm,
except for the added class lm.design in case of the method for class design,
and an added list element WholePlotEffects for split plot designs.
The value for the aov functions is an aov object,
exactly like for function aov,
and an added list element WholePlotEffects for split plot designs.
The value of the summary functions for class lm.design and
aov.design respectively
is a linear model or aov summary, exactly like documented in summary.lm
or summary.aov,
except for the added classes summary.lm.design or summary.aov.design,
and an added list element WholePlotEffects (for summary.lm.design)
or attribute (for summary.aov.design) for split plot designs.
The print functions return NULL; they are used for their side effects only.
Warning
The generics for lm and aov replace the functions
from package stats. For normal use, this is not an issue, because their
default methods are exactly the functions from package stats.
However, when programming on the language (or when using a package that relies on
such constructs), you may see unexpected results.
For example, match.call(lm) returns a different result, depending on
whether or not package DoE.base is loaded. This can be avoided by
explicitly requesting e.g. match.call(stats::lm), which always works
in the same way.
Please report any additional issues that you may experience.
Note
The package is currently subject to intensive development; most key functionality is now included.
Some changes to input and output structures may still occur.
Author(s)
Ulrike Groemping
See Also
See also the information on class design
and its formula method formula.design
Examples
oa12 <- oa.design(nlevels=c(2,2,6))
## add a few variables to oa12
responses <- cbind(y=rexp(12),z=runif(12))
oa12 <- add.response(oa12, responses)
## want treatment contrasts rather than the default
## polynomial contrasts for the factors
oa12 <- change.contr(oa12, "contr.treatment")
linmod.y <- lm(oa12)
linmod.z <- lm(oa12, response="z")
linmod.y
linmod.z
summary(linmod.y)
summary(linmod.z)
## examples with aggregation
plan <- oa.design(nlevels=c(2,6,2), replications=2, repeat.only=TRUE)
y <- rnorm(24)
z <- rexp(24)
plan <- add.response(plan, cbind(y=y,z=z))
lm(plan)
lm(plan, response="z")
lm(plan, FUN=sd)
## wide format
plan <- reptowide(plan)
plan
design.info(plan)$responselist
## default: aggregate variables for first column of responselist
lm(plan)
## request z variables instead (z is the column name of response list)
lm(plan, response="z")
## force analysis of first z measurement only
lm(plan, response="z.1")
## use almost all options
## (option use.center can only be used with center point designs
## from package FrF2)
summary(lm(plan, response="z", degree=2, FUN=sd))
DoE.base documentation built on Nov. 15, 2023, 1:06 a.m.
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| lm and aov method for class design objects | R Documentation |
lm and aov methods for class design objects
Description
Methods for automatic linear models for data frames of class design
Usage
lm(formula, ...)
## Default S3 method:
lm(formula, data, subset, weights, na.action, method = "qr",
model = TRUE, x = FALSE, y = FALSE, qr = TRUE, singular.ok = TRUE,
contrasts = NULL, offset, ...)
## S3 method for class 'design'
lm(formula, ..., response=NULL, degree=NULL, FUN=mean,
use.center=NULL, use.star=NULL, use.dummies=FALSE)
aov(formula, ...)
## Default S3 method:
aov(formula, data = NULL, projections = FALSE, qr = TRUE,
contrasts = NULL, ...)
## S3 method for class 'design'
aov(formula, ..., response=NULL, degree=NULL, FUN=mean,
use.center=FALSE)
## S3 method for class 'lm.design'
print(x, ...)
## S3 method for class 'lm.design'
summary(object, ...)
## S3 method for class 'lm.design'
coef(object, ...)
## S3 method for class 'summary.lm.design'
print(x, ...)
## S3 method for class 'aov.design'
print(x, ...)
## S3 method for class 'aov.design'
summary(object, ...)
## S3 method for class 'summary.aov.design'
print(x, ...)
lm.design
summary.lm.design
aov.design
summary.aov.design
Arguments
formula |
for the default method, cf. documentation for |
... |
further arguments to functions |
response |
character string giving the name of the response variable
(must be among the responses of For the default |
degree |
degree for the formula; if |
FUN |
function for the |
use.center |
|
use.star |
|
use.dummies |
logical indicating whether the error dummies of a Plackett Burman design are to be used in the formula (ignored for all other types of designs). |
projections |
logical indicating whether the projections should be returned; for orthogonal arrays, these are helpful, as they provide the estimated deviation from the overall average attributed to each particular factor; it is not recommended to use them with unbalanced designs |
x |
object of class |
object |
object of class |
lm.design |
a class that is identical in content to class |
summary.lm.design |
a class that is identical in content to class |
data |
like in |
subset |
like in |
weights |
like in |
na.action |
like in |
method |
like in |
model |
like in |
y |
like in |
qr |
like in |
singular.ok |
like in |
contrasts |
like in |
offset |
like in |
Details
The aov and lm methods for class design
conduct a default linear model analysis for data frames of
class design that do contain at least one response.
The intention for providing default analyses is to support convenient quick inspections. In many cases, there will be good reasons to customize the analysis, for example by including some but not all effects of a certain degree. Also, it may be statistically more wise to work with mixed models for some types of design. The default analyses must not be taken as a statistical recommendation!
The choice of default analyses
has been governed by simplicity: It uses fixed effects only and does either
main effects models (degree=1, default for pb and oa designs),
models with main effects and 2-factor interactions (degree=2,
default for most designs) or second order models (that contain
quadratic effects in addition to the 2-factor interactions, unchangeable default
for designs with quantitative variables). The degree parameter can be used
to modify the degree of interactions. If blocks are
present, the block main effect is always entered as a fixed effect without interactions.
Designs with center points are per default analysed without the center points; the main
reason for this is convenient usage of functions DanielPlot,
MEPlot and IAPlot from package FrF2.
With the use.center option, this default can be changed; in this case, significance
of the center point indicator implies that there are one or more quadratic effect(s)
in the model.
Designs with repeated measurements (repeat.only=TRUE) and parameter
designs of long format are treated by aggregate.design
with aggregation function FUN (default: means are calculated)
before applying a linear model.
For designs with repeated measurements (repeat.only=TRUE) and parameter
designs of wide format, the default is to use the first aggregated response,
if the design has been aggregated already. For a so far unaggregated design,
the default is to treat the design by aggregate.design,
using the function FUN (default: mean) and then use the first response.
The defaults can be overridden by specifying response: Here,
response can not only be one of the current responses but also a column name
of the responselist element of the design.info attribute of the
design (i.e. a response name from the long version of the design).
The implementation of the formulae is not done in functions lm.design or
aov.design themselves
but based on the method for function formula (formula.design).
The print methods prepend the formula and the number of experimental runs
underlying the analysis to the default printout.
The purpose of this is meaningful output in case a call from
inside function lm.design or aov.design
(methods for functions lm and aov )
does not reveal enough information, and another pointer that center points have been
omitted or repeated measurements aggregated over. The coef method for objects
of class lm.design suppresses NA coefficients, i.e.
returns valid coefficients only. For aov objects, this is the default
anyway.
Value
The value for the lm functions is a linear model object,
exactly like for function lm,
except for the added class lm.design in case of the method for class design,
and an added list element WholePlotEffects for split plot designs.
The value for the aov functions is an aov object,
exactly like for function aov,
and an added list element WholePlotEffects for split plot designs.
The value of the summary functions for class lm.design and
aov.design respectively
is a linear model or aov summary, exactly like documented in summary.lm
or summary.aov,
except for the added classes summary.lm.design or summary.aov.design,
and an added list element WholePlotEffects (for summary.lm.design)
or attribute (for summary.aov.design) for split plot designs.
The print functions return NULL; they are used for their side effects only.
Warning
The generics for lm and aov replace the functions
from package stats. For normal use, this is not an issue, because their
default methods are exactly the functions from package stats.
However, when programming on the language (or when using a package that relies on
such constructs), you may see unexpected results.
For example, match.call(lm) returns a different result, depending on
whether or not package DoE.base is loaded. This can be avoided by
explicitly requesting e.g. match.call(stats::lm), which always works
in the same way.
Please report any additional issues that you may experience.
Note
The package is currently subject to intensive development; most key functionality is now included. Some changes to input and output structures may still occur.
Author(s)
Ulrike Groemping
See Also
See also the information on class design
and its formula method formula.design
Examples
oa12 <- oa.design(nlevels=c(2,2,6))
## add a few variables to oa12
responses <- cbind(y=rexp(12),z=runif(12))
oa12 <- add.response(oa12, responses)
## want treatment contrasts rather than the default
## polynomial contrasts for the factors
oa12 <- change.contr(oa12, "contr.treatment")
linmod.y <- lm(oa12)
linmod.z <- lm(oa12, response="z")
linmod.y
linmod.z
summary(linmod.y)
summary(linmod.z)
## examples with aggregation
plan <- oa.design(nlevels=c(2,6,2), replications=2, repeat.only=TRUE)
y <- rnorm(24)
z <- rexp(24)
plan <- add.response(plan, cbind(y=y,z=z))
lm(plan)
lm(plan, response="z")
lm(plan, FUN=sd)
## wide format
plan <- reptowide(plan)
plan
design.info(plan)$responselist
## default: aggregate variables for first column of responselist
lm(plan)
## request z variables instead (z is the column name of response list)
lm(plan, response="z")
## force analysis of first z measurement only
lm(plan, response="z.1")
## use almost all options
## (option use.center can only be used with center point designs
## from package FrF2)
summary(lm(plan, response="z", degree=2, FUN=sd))
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