anova.rms

0th

Percentile

Analysis of Variance (Wald and F Statistics)

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 $\chi^2$, $\chi^2$ 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.

Keywords
models, regression, htest, aplot
Usage
## S3 method for class 'rms':
anova(object, \ldots, 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, \dots)

Arguments
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 ma
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
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="sub
what
what type of statistic to plot. The default is the Wald $\chi^2$ 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 <
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 $\chi^2$s (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< code=""> to print as <0.0001< code="">. Set to FALSE to print as 0.0000.
dec.chisq
number of places to the right of the decimal place for typesetting $\chi^2$ 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
Details

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.

Value

  • anova.rms returns a matrix of class anova.rms containing factors as rows and $\chi^2$, 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.

Side Effects

print prints, latex creates a file with a name of the form "title.tex" (see the title argument above).

concept

bootstrap

See Also

rms, rmsMisc, lrtest, rms.trans, summary.rms, solvet, locator, dotchart2, latex, Dotplot, anova.lm, contrast.rms, pantext

Aliases
  • anova.rms
  • print.anova.rms
  • plot.anova.rms
  • latex.anova.rms
Examples
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.')
Documentation reproduced from package rms, version 2.0-2, License: GPL (>= 2)

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