anova.rms {rms} | R Documentation |
The anova
function automatically tests most meaningful hypotheses
in a design. For example, suppose that age and cholesterol are
predictors, and that a general interaction is modeled using a restricted
spline surface. anova
prints Wald statistics (F statistics
for an ols
fit) for testing linearity of age, linearity of
cholesterol, age effect (age + age by cholesterol interaction),
cholesterol effect (cholesterol + age by cholesterol interaction),
linearity of the age by cholesterol interaction (i.e., adequacy of the
simple age * cholesterol 1 d.f. product), linearity of the interaction
in age alone, and linearity of the interaction in cholesterol
alone. Joint tests of all interaction terms in the model and all
nonlinear terms in the model are also performed. For any multiple
d.f. effects for continuous variables that were not modeled through
rcs
, pol
, lsp
, etc., tests of linearity will be
omitted. This applies to matrix predictors produced by e.g.
poly
or ns
. print.anova.rms
is the printing
method. plot.anova.rms
draws dot charts depicting the importance
of variables in the model, as measured by Wald chi-square,
chi-square minus d.f., AIC, P-values, partial
R^2, R^2 for the whole model after deleting the effects in
question, or proportion of overall model R^2 that is due to each
predictor. latex.anova.rms
is the latex
method. It
substitutes Greek/math symbols in column headings, uses boldface for
TOTAL
lines, and constructs a caption. Then it passes the result
to latex.default
for conversion to LaTeX.
## S3 method for class 'rms': anova(object, ..., main.effect=FALSE, tol=1e-9, test=c('F','Chisq'), ss=TRUE) ## S3 method for class 'anova.rms': print(x, which=c('none','subscripts','names','dots'), ...) ## S3 method for class 'anova.rms': plot(x, what=c("chisqminusdf","chisq","aic","P","partial R2","remaining R2", "proportion R2"), xlab=NULL, pch=16, rm.totals=TRUE, rm.ia=FALSE, rm.other=NULL, newnames, sort=c("descending","ascending","none"), pl=TRUE, ...) ## S3 method for class 'anova.rms': latex(object, title, psmall=TRUE, dec.chisq=2, dec.F=2, dec.ss=NA, dec.ms=NA, dec.P=4, ...)
object |
a rms fit object. object must
allow vcov to return the variance-covariance matrix. For
latex is the result of anova .
|
... |
If omitted, all variables are tested, yielding tests for individual factors
and for pooled effects. Specify a subset of the variables to obtain tests
for only those factors, with a pooled Wald tests for the combined effects
of all factors listed. Names may be abbreviated. For example, specify
anova(fit,age,cholesterol) to get a Wald statistic for testing the joint
importance of age, cholesterol, and any factor interacting with them.
Can be optional graphical parameters to send to dotchart2 , or other parameters to send to latex.default .
Ignored for print .
|
main.effect |
Set to TRUE to print the (usually meaningless) main effect tests even when
the factor is involved in an interaction. The default is FALSE , to print only
the effect of the main effect combined with all interactions involving that
factor.
|
tol |
singularity criterion for use in matrix inversion |
test |
For an ols fit, set test="Chisq" to use Wald chi^2 tests rather than F-tests.
|
ss |
For an ols fit, set ss=FALSE to suppress printing partial sums of squares, mean
squares, and the Error SS and MS.
|
x |
for print,plot,text is the result of anova .
|
which |
If which is not "none" (the default), print.anova.rms will
add to the rightmost column of the output the list of parameters being
tested by the hypothesis being tested in the current row. Specifying
which="subscripts" causes the subscripts of the regression
coefficients being tested to be printed (with a subscript of one for
the first non-intercept term). which="names" prints the names of
the terms being tested, and which="dots" prints dots for terms being
tested and blanks for those just being adjusted for.
|
what |
what type of statistic to plot. The default is the Wald
chi-square
statistic for each factor (adding in the effect of higher-ordered
factors containing that factor) minus its degrees of freedom. The
last three choice for what only apply to ols models.
|
xlab |
x-axis label, default is constructed according to what .
plotmath symbols are used for R, by default.
|
pch |
character for plotting dots in dot charts. Default is 16 (solid dot). |
rm.totals |
set to FALSE to keep total chi-squares (overall, nonlinear, interaction totals)
in the chart.
|
rm.ia |
set to TRUE to omit any effect that has "*" in its name
|
rm.other |
a list of other predictor names to omit from the chart |
newnames |
a list of substitute predictor names to use, after omitting any. |
sort |
default is to sort bars in descending order of the summary statistic |
pl |
set to FALSE to suppress plotting. This is useful when you only wish to
analyze the vector of statistics returned.
|
title |
title to pass to latex , default is name of fit object passed to
anova prefixed with "anova." . For Windows, the default is
"ano" followed by the first 5 letters of the name of the fit
object.
|
psmall |
The default is psmall=TRUE , which causes P<0.00005 to print as <0.0001 .
Set to FALSE to print as 0.0000 .
|
dec.chisq |
number of places to the right of the decimal place for typesetting
chi-square values (default is 2 ). Use zero for integer, NA for
floating point.
|
dec.F |
digits to the right for F statistics (default is 2 )
|
dec.ss |
digits to the right for sums of squares (default is NA , indicating
floating point)
|
dec.ms |
digits to the right for mean squares (default is NA )
|
dec.P |
digits to the right for P-values |
If the statistics being plotted with plot.anova.rms
are few in
number and one of them is negative or zero, plot.anova.rms
will quit because of an error in dotchart2
.
anova.rms
returns a matrix of class anova.rms
containing factors
as rows and chi-square, d.f., and P-values as
columns (or d.f., partial SS, MS, F, P).
plot.anova.rms
invisibly returns the vector of quantities
plotted. This vector has a names attribute describing the terms for
which the statistics in the vector are calculated.
print
prints, latex
creates a
file with a name of the form "title.tex"
(see the title
argument above).
Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu
rms
, rmsMisc
, lrtest
,
rms.trans
, summary.rms
,
solvet
, locator
,
dotchart2
, latex
,
xYplot
, anova.lm
,
contrast.rms
, pantext
n <- 1000 # define sample size set.seed(17) # so can reproduce the results treat <- factor(sample(c('a','b','c'), n,TRUE)) num.diseases <- sample(0:4, n,TRUE) age <- rnorm(n, 50, 10) cholesterol <- rnorm(n, 200, 25) weight <- rnorm(n, 150, 20) sex <- factor(sample(c('female','male'), n,TRUE)) label(age) <- 'Age' # label is in Hmisc label(num.diseases) <- 'Number of Comorbid Diseases' label(cholesterol) <- 'Total Cholesterol' label(weight) <- 'Weight, lbs.' label(sex) <- 'Sex' units(cholesterol) <- 'mg/dl' # uses units.default in Hmisc # Specify population model for log odds that Y=1 L <- .1*(num.diseases-2) + .045*(age-50) + (log(cholesterol - 10)-5.2)*(-2*(treat=='a') + 3.5*(treat=='b')+2*(treat=='c')) # Simulate binary y to have Prob(y=1) = 1/[1+exp(-L)] y <- ifelse(runif(n) < plogis(L), 1, 0) fit <- lrm(y ~ treat + scored(num.diseases) + rcs(age) + log(cholesterol+10) + treat:log(cholesterol+10)) anova(fit) # Test all factors anova(fit, treat, cholesterol) # Test these 2 by themselves # to get their pooled effects g <- lrm(y ~ treat*rcs(age)) dd <- datadist(treat, num.diseases, age, cholesterol) options(datadist='dd') p <- Predict(g, age=., treat="b") s <- anova(g) # Usually omit fontfamily to default to 'Courier' # It's specified here to make R pass its package-building checks plot(p, addpanel=pantext(s, 28, 1.9, fontfamily='Helvetica')) plot(s) # new plot - dot chart of chisq-d.f. # latex(s) # nice printout - creates anova.g.tex options(datadist=NULL) # Simulate data with from a given model, and display exactly which # hypotheses are being tested set.seed(123) age <- rnorm(500, 50, 15) treat <- factor(sample(c('a','b','c'), 500,TRUE)) bp <- rnorm(500, 120, 10) y <- ifelse(treat=='a', (age-50)*.05, abs(age-50)*.08) + 3*(treat=='c') + pmax(bp, 100)*.09 + rnorm(500) f <- ols(y ~ treat*lsp(age,50) + rcs(bp,4)) print(names(coef(f)), quote=FALSE) specs(f) anova(f) an <- anova(f) options(digits=3) print(an, 'subscripts') print(an, 'dots') an <- anova(f, test='Chisq', ss=FALSE) plot(0:1) # make some plot tab <- pantext(an, 1.2, .6, lattice=FALSE, fontfamily='Helvetica') # create function to write table; usually omit fontfamily tab() # execute it; could do tab(cex=.65) plot(an) # new plot - dot chart of chisq-d.f. # latex(an) # nice printout - creates anova.f.tex # Suppose that a researcher wants to make a big deal about a variable # because it has the highest adjusted chi-square. We use the # bootstrap to derive 0.95 confidence intervals for the ranks of all # the effects in the model. We use the plot method for anova, with # pl=FALSE to suppress actual plotting of chi-square - d.f. for each # bootstrap repetition. We rank the negative of the adjusted # chi-squares so that a rank of 1 is assigned to the highest. # It is important to tell plot.anova.rms not to sort the results, # or every bootstrap replication would have ranks of 1,2,3 for the stats. mydata <- data.frame(x1=runif(200), x2=runif(200), sex=factor(sample(c('female','male'),200,TRUE))) set.seed(9) # so can reproduce example mydata$y <- ifelse(runif(200)<=plogis(mydata$x1-.5 + .5*(mydata$x2-.5) + .5*(mydata$sex=='male')),1,0) require(boot) b <- boot(mydata, function(data, i, ...) rank(-plot(anova( lrm(y ~ rcs(x1,4)+pol(x2,2)+sex,data,subset=i)), sort='none', pl=FALSE)), R=25) # should really do R=500 but will take a while Rank <- b$t0 lim <- t(apply(b$t, 2, quantile, probs=c(.025,.975))) # Use the Hmisc Dotplot function to display ranks and their confidence # intervals. Sort the categories by descending adj. chi-square, for ranks original.chisq <- plot(anova(lrm(y ~ rcs(x1,4)+pol(x2,2)+sex,data=mydata)), sort='none', pl=FALSE) predictor <- as.factor(names(original.chisq)) predictor <- reorder.factor(predictor, -original.chisq) Dotplot(predictor ~ Cbind(Rank, lim), pch=3, xlab='Rank', main=if(.R.) expression(paste( 'Ranks and 0.95 Confidence Limits for ',chi^2,' - d.f.')) else 'Ranks and 0.95 Confidence Limits for Chi-square - d.f.')