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'), india=TRUE, indnl=TRUE, 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, table.env=TRUE, caption=NULL, ...)
object |
a |
... |
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
Can be optional graphical parameters to send to
|
main.effect |
Set to |
tol |
singularity criterion for use in matrix inversion |
test |
For an |
india |
set to |
indnl |
set to |
ss |
For an |
x |
for |
which |
If |
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 |
xlab |
x-axis label, default is constructed according to |
pch |
character for plotting dots in dot charts. Default is 16 (solid dot). |
rm.totals |
set to |
rm.ia |
set to |
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 |
title |
title to pass to |
psmall |
The default is |
dec.chisq |
number of places to the right of the decimal place for typesetting
chi-square values (default is |
dec.F |
digits to the right for F statistics (default is |
dec.ss |
digits to the right for sums of squares (default is |
dec.ms |
digits to the right for mean squares (default is |
dec.P |
digits to the right for P-values |
table.env |
see |
caption |
caption for table if |
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 ## Example to save partial R^2 for all predictors, along with overall ## R^2, from two separate fits, and to combine them with a lattice plot require(lattice) set.seed(1) n <- 100 x1 <- runif(n) x2 <- runif(n) y <- (x1-.5)^2 + x2 + runif(n) group <- c(rep('a', n/2), rep('b', n/2)) A <- NULL for(g in c('a','b')) { f <- ols(y ~ pol(x1,2) + pol(x2,2) + pol(x1,2) %ia% pol(x2,2), subset=group==g) a <- plot(anova(f), what='partial R2', pl=FALSE, rm.totals=FALSE, sort='none') a <- a[-grep('NONLINEAR', names(a))] d <- data.frame(group=g, Variable=factor(names(a), names(a)), partialR2=unname(a)) A <- rbind(A, d) } dotplot(Variable ~ partialR2 | group, data=A, xlab=ex <- expression(partial~R^2)) dotplot(group ~ partialR2 | Variable, data=A, xlab=ex) dotplot(Variable ~ partialR2, groups=group, data=A, xlab=ex, auto.key=list(corner=c(.5,.5))) # 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) if(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(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.') }