wald: General Linear Hypothesis for the 'fixed' portion of a model...
In gmonette/spida15: Collection of miscellaneous functions for mixed models etc. prepared for SPIDA 2009+ (development version)
Description
Usage
Arguments
Details
Value
See Also
Examples
Description
Tests a general linear hypothesis for the linear fixed portion of a model. The hypothesis
can be specified in a variety of ways such as a hypothesis matrix or a pattern that is used as
a regular expression to be matched with the names of coefficients of the model.
A number of tools are available to facilitate the generation of hypothesis matrices.
Usage
1
2
Arguments
fit
a model for which a getFix method exists.
Llist
a hypothesis matrix or a pattern to be matched or a list of these
clevel
level for confidence intervals
data
used for 'data' attribute of value returned
debug
maxrows
maximum number of rows of hypothesis matrix for which a full variance-covariance matrix is returned
full
if TRUE, the hypothesis matrix is the model matrix for fit such that
the estimated coefficients are the predicted values for the fixed portion of the model. This is designed
to allow the calculation of standard errors for models for which the predict method does not provide them.
fixed
if Llist is a character to be used a regular expression, if fixed is TRUE
Llist is interpreted literally, i.e. characters that have a special meaning in regular expressions
are interpreted literally.
invert
if Llist is a character to be used a regular expression, invert == TRUE
causes the matches to be inverted so that coefficients that do not match will be selected.
method
'svd' (current default) or 'qr' is the method used to find the full rank version of the hypothesis matrix.
'svd' has correctly identified the rank of a large hypothesis matrix where 'qr' has failed.
help
obsolete
Details
General Linear Hypothesis with Wald test
for lm, glm, lme, nlme and lmer objects.
Can be extended to other objects (e.g.) 'glm' by writing 'getFix.glm'
Usage:
wald ( fit, L ) where L is a hypothesis matrix
wald ( fit, 'pat' ) where 'pat' a regular expression (see ?regex)
used to match names of coefficients of fixed effects.
e.g. wald( fit, ':.*:') tests all 2nd and higher order interactions.
wald ( fit, c(2,5,6)) to test 2nd, 5th and 6th coefficients.
wald ( fit, list( hyp1= c(2,5,6), H2 = 'pat')) for more than one hypothesis
matrix
There are number of functions to help construct hypothesis matrices:
Lform ( fit, list(expr1, expr2, ..., exprk), data = dframe)
creates an L matrix by evaluating expr1, expr2, ..., exprk in the dframe
environment to generate the k columns of the L matrix. 'dframe' is
model.frame(fit) by default. See the example below to estimate a derivative.
Creates an L matrix using formulas evaluated in 'data' for
each column of the L matrix
Example:
library(car)
fit <- lm( income ~ (education + I(education^2) )* type, Prestige)
summary(fit)
. . .
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 891.3 23889.1 0.037 0.97032
education 210.0 5638.8 0.037 0.97037
I(education^2) 38.3 328.3 0.117 0.90740
typeprof 191523.2 63022.0 3.039 0.00312 **
typewc 25692.3 73888.0 0.348 0.72887
education:typeprof -28133.0 10236.0 -2.748 0.00725 **
education:typewc -4485.4 14007.9 -0.320 0.74956
I(education^2):typeprof 1017.5 451.8 2.252 0.02679 *
I(education^2):typewc 170.9 671.6 0.255 0.79967
. . .
# estimate the marginal value of education for each
# occupation in the data set
L <- list( 'marginal value of education' =Lform( fit,
form = list(0, 1, 2 * education, 0, 0,
type == 'prof',
type == 'wc',
2 * education * (type == 'prof'),
2 * education * (type == 'wc')),
data = Prestige))
wald( fit, L )
chat <- coef( wald( fit, L ), se = 2)
xyplot( coef +coefp+coefm ~ education | type, cbind(Prestige,chat)[order(Prestige$education),],
type = 'l')
xyplot( chat~ education | type, Prestige)
# This approach can be used to predict responses with a fitting method that has a
# 'model.matrix' method but does not have a 'predict' method or does not return
# estimated standard errors with its 'predict' method.
datafit <- model.frame(fit) # or just the data frame used for the fit
ww <- wald(fit, model.matrix(fit))
datafit <- cbind(datafit, coef(ww, se =2))
# ...etc as above
# To extend the 'wald' function to a new class of objects, one needs to write a 'getFix'
# method to extract estimated coefficients, their estimated covariance matrix, and the
# denominator degrees of freedom for each estimated coefficient. The getFix method for
# glm objects is:
getFix.glm <- function(fit,...) {
ss <- summary(fit)
ret <- list()
ret$fixed <- coef(fit)
ret$vcov <- vcov(fit)
ret$df <- rep(ss$df.residual, length(ret$fixed))
ret
}
# and for 'mipo' objects in the packages 'mice':
getFix.mipo <- function( fit, ...){
#
# pooled multiple imputation object in mice
# 'wald' will use the minimal df for components with non-zero weights
# -- this is probably too conservative and should be improved
#
ret <- list()
ret$fixed <- fit$qbar
ret$vcov <- fit$t
ret$df <- fit$df
ret
}
Value
An object of class wald, with the following components
See Also
Lform,
xlevels,
dlevels,
Lall,Lc,Lequal,
Ldiff,Lmu,Lmat,Lrm,
Leff,
as.data.frame.wald. To extend to
new models see getFix. To generate
hypothesis matrices for general splines see gsp and sc.
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
##---- Should be DIRECTLY executable !! ----
##-- ==> Define data, use random,
##-- or do help(data=index) for the standard data sets.
# The derivative with respect
# to ses could be evaluated at each point in the following:
data(hs)
require( nlme )
fit <- lme( mathach ~ (ses + I(ses^2)) * Sex, hs, random = ~ 1 + ses | school)
wald( fit, 'Sex') # sig. overall effect of Sex
wald( fit, ':Sex') # but no evidence of interaction with ses
wald( fit, '\\^2') # nor of curvature
# but we continue for the sake of illustration
L <- Lform( fit, list( 0, 1, 2*ses, 0, Sex == 'Male', (Sex == 'Male')*2*ses), hs)
L
(ww <- wald ( fit, L ))
wald.dd <- as.data.frame(ww, se = 2)
head( wald.dd )
require(lattice)
xyplot( coef + U2 + L2 ~ ses | Sex, wald.dd,
main= 'Increase in predicted mathach per unit increase in ses')
gmonette/spida15 documentation built on May 17, 2019, 7:26 a.m.
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Description Usage Arguments Details Value See Also Examples
Description
Tests a general linear hypothesis for the linear fixed portion of a model. The hypothesis can be specified in a variety of ways such as a hypothesis matrix or a pattern that is used as a regular expression to be matched with the names of coefficients of the model. A number of tools are available to facilitate the generation of hypothesis matrices.
Usage
1 2 |
Arguments
fit |
a model for which a |
Llist |
a hypothesis matrix or a pattern to be matched or a list of these |
clevel |
level for confidence intervals |
data |
used for 'data' attribute of value returned |
debug |
|
maxrows |
maximum number of rows of hypothesis matrix for which a full variance-covariance matrix is returned |
full |
if TRUE, the hypothesis matrix is the model matrix for |
fixed |
if |
invert |
if |
method |
'svd' (current default) or 'qr' is the method used to find the full rank version of the hypothesis matrix. 'svd' has correctly identified the rank of a large hypothesis matrix where 'qr' has failed. |
help |
obsolete |
Details
General Linear Hypothesis with Wald test
for lm, glm, lme, nlme and lmer objects.
Can be extended to other objects (e.g.) 'glm' by writing 'getFix.glm'
Usage:
wald ( fit, L ) where L is a hypothesis matrix
wald ( fit, 'pat' ) where 'pat' a regular expression (see ?regex)
used to match names of coefficients of fixed effects.
e.g. wald( fit, ':.*:') tests all 2nd and higher order interactions.
wald ( fit, c(2,5,6)) to test 2nd, 5th and 6th coefficients.
wald ( fit, list( hyp1= c(2,5,6), H2 = 'pat')) for more than one hypothesis
matrix
There are number of functions to help construct hypothesis matrices:
Lform ( fit, list(expr1, expr2, ..., exprk), data = dframe)
creates an L matrix by evaluating expr1, expr2, ..., exprk in the dframe
environment to generate the k columns of the L matrix. 'dframe' is
model.frame(fit) by default. See the example below to estimate a derivative.
Creates an L matrix using formulas evaluated in 'data' for
each column of the L matrix
Example:
library(car)
fit <- lm( income ~ (education + I(education^2) )* type, Prestige)
summary(fit)
. . .
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 891.3 23889.1 0.037 0.97032
education 210.0 5638.8 0.037 0.97037
I(education^2) 38.3 328.3 0.117 0.90740
typeprof 191523.2 63022.0 3.039 0.00312 **
typewc 25692.3 73888.0 0.348 0.72887
education:typeprof -28133.0 10236.0 -2.748 0.00725 **
education:typewc -4485.4 14007.9 -0.320 0.74956
I(education^2):typeprof 1017.5 451.8 2.252 0.02679 *
I(education^2):typewc 170.9 671.6 0.255 0.79967
. . .
# estimate the marginal value of education for each
# occupation in the data set
L <- list( 'marginal value of education' =Lform( fit,
form = list(0, 1, 2 * education, 0, 0,
type == 'prof',
type == 'wc',
2 * education * (type == 'prof'),
2 * education * (type == 'wc')),
data = Prestige))
wald( fit, L )
chat <- coef( wald( fit, L ), se = 2)
xyplot( coef +coefp+coefm ~ education | type, cbind(Prestige,chat)[order(Prestige$education),],
type = 'l')
xyplot( chat~ education | type, Prestige)
# This approach can be used to predict responses with a fitting method that has a
# 'model.matrix' method but does not have a 'predict' method or does not return
# estimated standard errors with its 'predict' method.
datafit <- model.frame(fit) # or just the data frame used for the fit
ww <- wald(fit, model.matrix(fit))
datafit <- cbind(datafit, coef(ww, se =2))
# ...etc as above
# To extend the 'wald' function to a new class of objects, one needs to write a 'getFix'
# method to extract estimated coefficients, their estimated covariance matrix, and the
# denominator degrees of freedom for each estimated coefficient. The getFix method for
# glm objects is:
getFix.glm <- function(fit,...) {
ss <- summary(fit)
ret <- list()
ret$fixed <- coef(fit)
ret$vcov <- vcov(fit)
ret$df <- rep(ss$df.residual, length(ret$fixed))
ret
}
# and for 'mipo' objects in the packages 'mice':
getFix.mipo <- function( fit, ...){
#
# pooled multiple imputation object in mice
# 'wald' will use the minimal df for components with non-zero weights
# -- this is probably too conservative and should be improved
#
ret <- list()
ret$fixed <- fit$qbar
ret$vcov <- fit$t
ret$df <- fit$df
ret
}
Value
An object of class wald, with the following components
See Also
Lform,
xlevels,
dlevels,
Lall,Lc,Lequal,
Ldiff,Lmu,Lmat,Lrm,
Leff,
as.data.frame.wald. To extend to
new models see getFix. To generate
hypothesis matrices for general splines see gsp and sc.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ##---- Should be DIRECTLY executable !! ----
##-- ==> Define data, use random,
##-- or do help(data=index) for the standard data sets.
# The derivative with respect
# to ses could be evaluated at each point in the following:
data(hs)
require( nlme )
fit <- lme( mathach ~ (ses + I(ses^2)) * Sex, hs, random = ~ 1 + ses | school)
wald( fit, 'Sex') # sig. overall effect of Sex
wald( fit, ':Sex') # but no evidence of interaction with ses
wald( fit, '\\^2') # nor of curvature
# but we continue for the sake of illustration
L <- Lform( fit, list( 0, 1, 2*ses, 0, Sex == 'Male', (Sex == 'Male')*2*ses), hs)
L
(ww <- wald ( fit, L ))
wald.dd <- as.data.frame(ww, se = 2)
head( wald.dd )
require(lattice)
xyplot( coef + U2 + L2 ~ ses | Sex, wald.dd,
main= 'Increase in predicted mathach per unit increase in ses')
|
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