# anova.rms

##### 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`

##### 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)*