\name{summary.formula}
\alias{summary.formula}
\alias{stratify}
\alias{print.summary.formula.response}
\alias{plot.summary.formula.response}
\alias{latex.summary.formula.response}
\alias{print.summary.formula.reverse}
\alias{plot.summary.formula.reverse}
\alias{latex.summary.formula.reverse}
\alias{[.summary.formula.response}
\alias{print.summary.formula.cross}
\alias{latex.summary.formula.cross}
\alias{formula.summary.formula.cross}
\alias{na.retain}
\alias{cumcategory}
\alias{mChoice}
\alias{as.character.mChoice}
\title{
Summarize Data for Making Tables and Plots
}
\description{
\code{summary.formula} summarizes the variables listed in an S-Plus formula,
computing descriptive statistics (including ones in a
user-specified function).  The summary statistics may be passed to
\code{print} methods, \code{plot} methods for making annotated dot charts, and
\code{latex} methods for typesetting tables using LaTeX. 
\code{summary.formula} has three methods for computing descriptive
statistics on univariate or multivariate responses, subsetted by
categories of other variables.  The method of summarization is
specified in the parameter \code{method} (see details below).  For the
\code{response} and \code{cross} methods, the statistics used to
summarize the data 
may be specified in a very flexible way (e.g., the geometric mean,
33rd percentile, Kaplan-Meier 2-year survival estimate, mixtures of
several statistics).  The default summary statistic for these methods
is the mean (the proportion of positive responses for a binary
response variable).  The \code{cross} method is useful for creating data
frames which contain summary statistics that are passed to \code{trellis}
as raw data (to make multi-panel dot charts, for example).  The
\code{print} methods use the \code{print.char.matrix} function to print boxed
tables, if it is available (it is included in S-Plus versions 3.2 and
later).


For \code{method="response"} and \code{method="reverse"} the right hand side of
\code{formula} may contain "multiple choice" variables.  These are denoted
by matrices whose elements are logical (\code{FALSE},\code{TRUE}) values, 0/1 values,
or character strings in which values of \code{"present"} or \code{"yes"} (case
is ignored) denote positive and anything else denotes a negative
answer.  The columns of such matrices correspond to basic categories
(e.g., symptoms), and the matrices are often created by applying the
\code{mChoice} function to a series of factor or character vectors.  See
the first example.  When \code{test=TRUE} each choice is tested separately as
a binary categorical response.


The \code{plot} method for \code{method="reverse"} creates a temporary
function \code{Key} in frame 0 as is done by the \code{xYplot} and
\code{ecdf.formula} functions.  After \code{plot} runs, you can type
\code{Key()} to put a legend in a default location, or
e.g. \code{Key(locator(1))} to draw a legend where you click the left
mouse button.  This key is for categorical variables, so to have the
opportunity to put the key on the graph you will probably want to use
the command \code{plot(object, which="categorical")} [Note however that
in Windows S-Plus you can switch back and forth between multiple pages
on a graph sheet, and issue a \code{Key()} or \code{Key2()} command
according to which graph sheet page is active.].  A second function
\code{Key2} is created if continuous variables are being plotted.  It is
used the same as \code{Key}.  If the \code{which} argument is not
specified to \code{plot}, two pages of plots will be produced.  If you
don't define \code{par(mfrow=)} yourself,
\code{plot.summary.formula.reverse} will try to lay out a multi-panel
graph to best fit all the individual dot charts for continuous
variables.

There is a subscripting method for objects created with
\code{method="response"}. 
This can be used to print or plot selected variables or summary statistics
where there would otherwise be too many on one page.

\code{cumcategory} is a utility function useful when summarizing an ordinal
response variable.  It converts such a variable having \code{k} levels to a
matrix with \code{k-1} columns, where column \code{i} is a vector of zeros and
ones indicating that the categorical response is in level \code{i+1} or
greater.  When the left hand side of \code{formula} is \code{cumcategory(y)},
the default \code{fun} will summarize it by computing all of the relevant
cumulative proportions.

\code{mChoice} is a function that is useful for defining a group of
variables on the right side of the formula.  The variables can represent
individual choices on a multiple choice question.  These choices are
typically factor or character values but may be of any type.  Levels
of component factor variables need not be the same; all unique levels
(or unique character values) are collected over all of the multiple
variables.  Then a new matrix is formed that has one column per unique
value of all of these variables.  For each column, the row values are
logical \code{TRUE} or \code{FALSE} if any of the component choice variables equal
level for the new matrice's current column.  By default, NAs in the
choice variables are ignored.  Set \code{na.result=TRUE} to set results to NA
for a row and column where at least one of the choice
variables is NA but none of them equals the current column category.
When a matrix like one created by \code{mChoice} appears in a formula
processed by \code{summary.formula} you can easily obtain descriptive
statistics for categories where subjects can be in more than one
category.

\code{as.character.mChoice} will convert a matrix representing an
\code{mChoice} object into a character vector by concatenating the
categories present per observation.  This makes \code{summarize} work
when stratifying by \code{mChoice} variables.
}
\synopsis{
\method{summary}{formula}(formula, data, subset, na.action, 
           fun=NULL,
           method=c('response','reverse','cross'),
           overall=method=='response'|method=='cross', 
           continuous=10, na.rm=method=='reverse', g=4, 
           quant=c(.025,.05,.125,.25,.375,.5,.625,.75,.875,.95,.975),
           nmin=0, test=FALSE,
           conTest=function(group,x) {
             st <- spearman2(group,x)
             list(P=st['P'], stat=st['F'],
                  df=st[c('df1','df2')],
                  testname=if(st['df1']==1)'Wilcoxon' else
                  'Kruskal-Wallis',
                  statname='F', latexstat='F_{df}',
                  plotmathstat='F[df]')
           },
           catTest=function(tab) {
             st <- if(!is.matrix(tab) || nrow(tab) < 2)
               list(p.value=NA, statistic=NA, parameter=NA) else
             chisq.test(tab, correct=FALSE)
             list(P=st$p.value, stat=st$statistic,
                  df=st$parameter,
                  testname='Pearson', statname='Chi-square',
                  latexstat='\\chi^{2}_{df}',
                  plotmathstat='chi[df]^2')
           }, \dots)
}
\usage{
\method{summary}{formula}(formula, data, subset, na.action, fun, method='response',
              overall=TRUE, continuous=10, na.rm=FALSE, g=4, nmin=0, \dots)
\method{print}{summary.formula.response}(x, vnames=c('labels','names'), prUnits=TRUE,
      abbreviate.dimnames=FALSE,
      prefix.width, min.colwidth, formatArgs, \dots)
\method{plot}{summary.formula.response}(x, which=1, vnames=c('labels','names'), xlim, xlab, 
     pch=c(16,1,2,17,15,3,4,5,0), superposeStrata=TRUE,
     dotfont=1, add=FALSE, main, subtitles=TRUE, xaxis=TRUE,
     \dots)
\method{latex}{summary.formula.response}(object, title=first.word(expr=substitute(object)),
      caption, trios, vnames=c('labels','names'), prUnits=TRUE,
      rowlabel='', cdec=2, ncaption=FALSE,
      \dots)
x[i,j]


\method{summary}{formula}(formula, data, subset, na.action, method='reverse',
              overall=FALSE, continuous=10, na.rm=TRUE,
              quant=c(0.025, 0.05, 0.125, 0.25, 0.375, 0.5,
                      0.625, 0.75, 0.875, 0.95, 0.975),
              test=FALSE,
              conTest=function(group,x) {
                 st <- spearman2(group,x)
                 list(P=st['P'], stat=st['F'], df=st[c('df1','df2')],
                      testname=if(st['df1']==1)'Wilcoxon' else
                                            'Kruskal-Wallis',
                      statname='F', latexstat='F_{df}', plotmathstat='F[df]')
                 },
              catTest=function(tab) {
                 st <- if(!is.matrix(tab) || nrow(tab) < 2)
                   list(p.value=NA, statistic=NA, parameter=NA) else
                   chisq.test(tab, correct=FALSE)
                 list(P=st$p.value, stat=st$statistic,
                      df=st$parameter,
                      testname='Pearson', statname='Chi-square',
                      latexstat='\\chi^{2}_{df}', plotmathstat='chi[df]^2')
              })

\method{print}{summary.formula.reverse}(x, digits, prn=!all(n==N), pctdig=0,
      npct=c('numerator','both','denominator','none'),
      exclude1=TRUE, vnames=c('labels','names'), prUnits=TRUE, sep='/',
      abbreviate.dimnames=FALSE, prefix.width=max(nchar(lab)),
      min.colwidth, formatArgs,  prtest=c('P','stat','df','name'),
      prmsd=FALSE, long=FALSE, pdig=3, eps=.001, \dots)

\method{plot}{summary.formula.reverse}(x, vnames=c('labels','names'), what=c('proportion','\%'),
  which=c('both','categorical','continuous'),
  xlim=if(what=='proportion') c(0,1) else c(0,100), 
  xlab=if(what=='proportion')'Proportion' else 'Percentage', 
  pch=c(16,1,2,17,15,3,4,5,0), exclude1=TRUE,
  dotfont=1, main, subtitles=TRUE,
  prtest=c('P','stat','df','name'), pdig=3, eps=.001,
  conType=c('dot','bp'), cex.means=.5, \dots)

\method{latex}{summary.formula.reverse}(object,
     title=first.word(expr=substitute(object)), digits,
     prn=!all(n==N), pctdig=0,
     npct=c('numerator','both','denominator','none'),
     npct.size='scriptsize', Nsize='scriptsize',
     exclude1=TRUE, vnames=c('labels','names'),
     middle.bold=FALSE, outer.size='scriptsize',
     caption, rowlabel='', insert.bottom=TRUE, dcolumn=FALSE,
     prtest=c('P','stat','df','name'),
     prmsd=FALSE, msdsize=NULL, long=FALSE, pdig=3, eps=.001, \dots)


\method{summary}{formula}(formula, data, subset, na.action, fun, method='cross',
              overall=TRUE, continuous=10, g=4, \dots)
\method{print}{summary.formula.cross}(x, twoway=nvar==2, prnmiss=any(x$Missing>0), prn=TRUE,
      abbreviate.dimnames=FALSE, prefix.width=max(nchar(v)), 
      min.colwidth, formatArgs, \dots) 
\method{latex}{summary.formula.cross}(object,
      title=first.word(expr=substitute(object)),
      twoway=nvar==2, prnmiss=TRUE, prn=TRUE,
      caption=attr(object,'heading'),
      vnames=c('labels','names'), rowlabel='', \dots)


stratify(\dots, na.group=FALSE, shortlabel=TRUE)

\method{formula}{summary.formula.cross}(x, ...)

cumcategory(y)


mChoice(\dots, label='', 
        sort.levels=c('original','alphabetic'), 
        add.none=TRUE, none.name='none', na.result=FALSE, drop=TRUE)

\method{as.character}{mChoice}(x)
}
\arguments{
\item{formula}{
An S formula with additive effects.  For \code{method="response"} or
\code{"cross"}, the dependent variable has the usual connotation.  For
\code{method="reverse"}, the dependent variable is what is usually thought
of as an independent variable, and it is one that is used to stratify
all of the right hand side variables.  For \code{method="response"}
(only), the \code{formula} may contain one or more invocations of the
\code{stratify} function whose arguments are defined below.  This causes
the entire analysis to be stratified by cross-classifications of the
combined list of stratification factors.  This stratification will be
reflected as major column groupings in the resulting table, or as more
response columns for plotting.  If \code{formula} has no dependent variable
\code{method="reverse"} is the only legal value and so \code{method} defaults to
\code{"reverse"} in this case.
}
\item{x}{an object created by \code{summary.formula} or \code{mChoice}}
\item{y}{
a numeric, character, category, or factor vector for \code{cumcategory}.
Is converted to a categorical variable is needed.
}
\item{data}{
name or number of a data frame.  Default is the current frame.
}
\item{subset}{
a logical vector or integer vector of subscripts used to specify the
subset of data to use in the analysis.  The default is to use all
observations in the data frame.
}
\item{na.action}{
function for handling missing data in the input data.  The default is
a function defined here called \code{na.retain}, which keeps all
observations for processing, with missing variables or not.
}
\item{fun}{
function for summarizing data in each cell.  Default is to take the
mean of each column of the possibly multivariate response variable.
You can specify \code{fun="\%"} to compute percentages (100 times the mean of a 
series of logical or binary variables).
User--specified functions can also return a matrix.  For example, you might 
compute quartiles on a bivariate response.
}
\item{method}{
The default is \code{"response"}, in which case the response variable may
be multivariate and any number of statistics may be used to summarize
them.  Here the responses are summarized separately for each of any
number of independent variables.  Continuous independent variables
(see the \code{continuous} parameter below) are automatically stratified
into \code{g} (see below) quantile groups (if you want to control the
discretization for selected variables, use the \code{cut2} function on them).  
Otherwise, the data are
subsetted by all levels of discrete right hand side variables.  For
multivariate responses, subjects are considered to be missing if any
of the columns is missing.  


The \code{method="reverse"} option is
typically used to make baseline characteristic tables, for example.
The single left hand side variable must be categorical (e.g.,
treatment), and the right hand side variables are broken down one at a
time by the "dependent" variable.  Continuous variables are described
by three quantiles (quartiles by default) along with 
outer quantiles (used only for scaling x-axes when plotting quartiles;
all are used when plotting box-percentile plots), and
categorical ones are
described by counts and percentages.  If there is no left hand side
variable, \code{summary} assumes that there is only one group in the data,
so that only one column of summaries will appear.
If there is no dependent variable in \code{formula}, \code{method} defaults to
\code{"reverse"} automatically.


The \code{method="cross"} option allows for a multivariate dependent
variable and for up to three independents.  Continuous independent
variables (those with at least \code{continuous} unique values) are
automatically divided into \code{g} quantile groups.
The independents are cross-classified, and marginal statistics may optionally be computed.
The output of \code{summary.formula} in this case is a data frame
containing the independent variable combinations (with levels of
\code{"All"} corresponding to marginals) and the corresponding summary
statistics in the matrix \code{S}.  The output data frame is suitable for
direct use in \code{trellis}.  The \code{print} and \code{latex} typesetting methods for this
method allows for a special two-way format if there are two right
hand variables.
}
\item{overall}{
For \code{method="reverse"}, setting \code{overall=TRUE} makes a new column with
overall statistics for the whole sample.  For \code{method="cross"},
\code{overall=TRUE} (the default) results in all marginal statistics being
computed.  For \code{trellis} displays (usually multi-panel dot plots), 
these marginals just form other categories.  For \code{"response"}, the
default is \code{overall=TRUE}, causing a final row of global summary
statistics to appear in tables and dot charts.  If \code{test=TRUE} these
marginal statistics are ignored in doing statistical tests.
}
\item{continuous}{
specifies the threshold for when a variable is considered to be
continuous (when there are at least \code{continuous} unique values).
\code{factor} variables are always considered to be categorical no matter
how many levels they have.
}
\item{na.rm}{
for \code{method="response"}, set \code{na.rm=TRUE} to exclude missing values from
being counted as their own category when subsetting the response(s)
by levels of a categorical variable.  For \code{method="reverse"} set
\code{na.rm=FALSE} to keep missing values of categorical variables from
being excluded from the table.  \code{na.rm} also applies to summary
statistic functions such as \code{smean.cl.normal}.  For these \code{na.rm}
defaults to \code{TRUE} unlike built-in S-Plus functions.
}
\item{g}{
number of quantile groups to use when variables are automatically
categorized with \code{method="response"} or \code{"cross"} using \code{cut2}
}
\item{nmin}{
if fewer than \code{nmin} observations exist in a category for \code{"response"}
(over all strata combined), that category will be ignored
}
\item{test}{
applies if \code{method="reverse"}.  Set to \code{TRUE} to compute test
statistics using tests specified in \code{conTest} and \code{catTest}.
}
\item{conTest}{
a function of two arguments (grouping variable and a continuous
variable) that returns a list with components \code{P} (the computed
P-value), \code{stat} (the test statistic, either chi-square or F),
\code{df} (degrees of freedom), \code{testname} (test name), \code{statname}
(statistic name), an optional component \code{latexstat} (LaTeX
representation of \code{statname}), an optional component
\code{plotmathstat} (for R - the \code{plotmath} representation of
\code{statname}, as a character string),  and an
optional component \code{note} 
that contains a character string note about the test (e.g., \code{"test not
done because n < 5"}).  \code{conTest} is applied to continuous variables
on the right-hand-side of the formula when \code{method="reverse"}.  The
default uses the \code{spearman2} function to run the Wilcoxon or
Kruskal-Wallis test using the F distribution.
}
\item{catTest}{
a function of a frequency table (an integer matrix) that returns a
list with the same components as created by \code{conTest}.  By default,
the Pearson chi-square test is done, without continuity correction
(the continuity correction would make the test conservative like the
Fisher exact test).
}
\item{...}{
for \code{summary.formula} these are optional
arguments for \code{cut2} when variables are automatically categorized.
For \code{plot} methods these arguments are passed to \code{dotchart2}.
For \code{Key} and \code{Key2} these arguments are passed to \code{key},
\code{text}, or \code{mtitle}.  For \code{print} methods these are
optional arguments to \code{print.char.matrix}. For \code{latex} methods
these are passed to \code{latex.default}.  One of the most important of
these is \code{file}.  Specifying \code{file=""} will cause LaTeX code
to just be printed to standard output rather than be stored in a
permanent file.
Is a series of vectors for \code{mChoice}, or one or more stratification
variables (separated by commas) (which will be cross-classified) for
\code{stratify}.
}
\item{object}{an object created by \code{summary.formula}}
\item{quant}{
vector of quantiles to use for summarizing data with
\code{method="reverse"}.  This must be numbers between 0 and 1
inclusive and must include the numbers 0.5, 0.25, and 0.75 which are
used for printing and for plotting 
quantile intervals.  The outer quantiles are used for scaling the x-axes
for such plots.  Specify outer quantiles as \code{0} and \code{1} to
scale the x-axes using the whole observed data ranges instead of the
default (a 0.95 quantile interval).  Box-percentile plots are drawn
using all but the outer quantiles.
}
\item{vnames}{
By default, tables and plots are usually labeled with variable labels
(see the \code{label} and \code{sas.get} functions).  To use the shorter
variable names, specify \code{vnames="name"}.
}
\item{pch}{
  vector of plotting characters to represent different groups, in order
  of group levels.  For \code{method="response"} the characters
  correspond to levels of the \code{stratify} variable if
  \code{superposeStrata=TRUE}, and if no 
  \code{strata} are used or if \code{superposeStrata=FALSE}, the 
  \code{pch} vector corresponds to the \code{which} argument for
  \code{method="response"}.
}
\item{superposeStrata}{
  If \code{stratify} was used, set \code{superposeStrata=FALSE} to make
  separate dot charts for each level of the \code{stratification}
  variable, for \code{method='response'}.  The default is to
  superposition all strata on one dot chart.
}
\item{dotfont}{font for plotting points}
\item{xaxis}{set to \code{FALSE} to suppress drawing x-axis in
  \code{plot.summary.formula.response}}

\item{abbreviate.dimnames}{see \code{print.char.matrix}}
\item{prefix.width}{see \code{print.char.matrix}}
\item{min.colwidth}{
minimum column width to use for boxes printed with \code{print.char.matrix}.
The default is the maximum of the minimum column label length and the minimum
length of entries in the data cells.
}
\item{formatArgs}{
a list containing other arguments to pass to \code{format.default} such as
\code{scientific}, e.g., \code{formatArgs=list(scientific=c(-5,5))}.  For
\code{print.summary.formula.reverse}, \code{formatArgs} applies only to
statistics computed on continuous variables, not to percents,
numerators, and denominators.
}
\item{digits}{
number of significant digits to print.  Default is to use the current
value of the \code{digits} system option.
}
\item{prn}{
set to \code{TRUE} to print the number of non-missing observations on the
current (row) variable.  The default is to print these only if any of
the counts of non-missing values differs from the total number of
non-missing values of the left-hand-side variable.
For \code{method="cross"} the default is to always print \code{N}.
}
\item{prnmiss}{
set to \code{FALSE} to suppress printing counts of missing values for \code{"cross"}
}
\item{pctdig}{
number of digits to the right of the decimal place for printing
percentages. The default is zero, so percents will be rounded to the
nearest percent.
}
\item{npct}{
specifies which counts are to be printed to the right of percentages.
The default is to print the frequency (numerator of the percent) in
parentheses.  You can specify \code{"both"} to print both numerator and
denominator, \code{"denominator"}, or \code{"none"}.
}
\item{npct.size}{
the size for typesetting \code{npct} information which appears after percents.
The default is \code{"scriptsize"}.
}
\item{Nsize}{
  When a second row of column headings is added showing sample sizes,
  \code{Nsize} specifies the LaTeX size for these subheadings.  Default
  is \code{"scriptsize"}.
  }
\item{exclude1}{
by default, \code{method="reverse"} objects will be printed, plotted,  or typeset by
removing redundant entries from percentage tables for categorical
variables.  For example, if you print the percent of females, you
don't need to print the percent of males.  To override this, set \code{exclude1=FALSE}.
}
\item{prUnits}{
  set to \code{FALSE} to suppress printing or latexing \code{units}
  attributes of variables, when \code{method='reverse'} or \code{'response'}
  }
\item{sep}{
character to use to separate quantiles when printing
\code{method="reverse"} tables
}
\item{prtest}{
a vector of test statistic components to print if \code{test=TRUE} was in
effect when \code{summary.formula} was called.  Defaults to printing all
components.  Specify \code{prtest=FALSE} or \code{prtest="none"} to not
print any tests.  This applies to \code{print}, \code{latex}, and
\code{plot} methods for \code{method='reverse'}.
}
\item{prmsd}{
  set to \code{TRUE} to print mean and SD after the three quantiles, for
  continuous variables with \code{method="reverse"}
}
\item{msdsize}{
  defaults to \code{NULL} to use the current font size for the mean and
  standard deviation if \code{prmsd} is \code{TRUE}.  Set to a character
  string to specify an alternate LaTeX font size.
  }
\item{long}{
  set to \code{TRUE} to print the results for the first category on its own
  line, not on the same line with the variable label (for
  \code{method="reverse"} with \code{print} and \code{latex} methods)
}
\item{pdig}{
  number of digits to the right of the decimal place for printing
  P-values.  Default is \code{3}.  This is passed to \code{format.pval}.
}
\item{eps}{
  P-values less than \code{eps} will be printed as \code{< eps}.  See
  \code{format.pval}.
  }
\item{what}{
for \code{method="reverse"} specifies whether proportions or percentages
are to be plotted
}
\item{twoway}{
for \code{method="cross"} with two right hand side variables, \code{twoway}
controls whether the resulting table will be printed in enumeration
format or as a two-way table (the default)
}
\item{which}{
For \code{method="response"} specifies the sequential number or a vector of
subscripts of response variables to plot.  If you had any \code{stratify}
variables, these are counted as if multiple response variables were
analyzed.  For \code{method="reverse"} specifies whether to plot results
for categorical variables, continuous variables, or both (the default).
}
\item{conType}{
  For plotting \code{method="reverse"} plots for continuous variables,
  dot plots showing quartiles are drawn by default.  Specify
  \code{conType='bp'} to draw box-percentile plots using all the
  quantiles in \code{quant} except the outermost ones.  Means are drawn
  with a solid dot and vertical reference lines are placed at the three
  quartiles.}
\item{cex.means}{
character size for means in box-percentile plots; default is .5}
\item{xlim}{
vector of length two specifying x-axis limits.  For
\code{method="reverse"}, this is only used for plotting categorical
variables.  Limits for continuous variables are determined by the
outer quantiles specified in \code{quant}.
}
\item{xlab}{
x-axis label
}
\item{add}{
set to \code{TRUE} to add to an existing plot
}
\item{main}{
a main title.  For \code{method="reverse"} this applies only to the plot
for categorical variables.
}
\item{subtitles}{
set to \code{FALSE} to suppress automatic subtitles
}
\item{label}{
a character string \code{label} attribute to attach to the matrix created
by \code{mChoice}
}
\item{sort.levels}{
set \code{sort.levels="alphabetic"} to sort the columns of the matrix
created by \code{mChoice} alphabetically by category rather than by the
original order of levels in component factor variables (if there were
any input variables that were factors)
}
\item{add.none}{
set to \code{FALSE} to keep \code{mChoice} from adding a final column to the
matrix named \code{none.name}.  The logical values in this column are
set to \code{TRUE} when none of the defined choices apply for the
observation and \code{FALSE} otherwise. If every observation used at least
one of the choices, the "none" column is not added regardless of the
value of \code{add.none}. 
}
\item{none.name}{
a character string defining the name of the column added if
\code{add.none=TRUE} and some observations did not select any choices.  The
default column name is \code{none.name="none"}.
}
\item{na.result}{
set to \code{TRUE} to set elements of columns of the matrix computed by
\code{mChoice} to \code{NA} when no input variable values equalled the current
category and at least one of them was NA
}
\item{drop}{
set \code{drop=FALSE} to keep unused factor levels as columns of the matrix
produced by \code{mChoice}
}
\item{caption}{
character string containing LaTeX table captions.
}
\item{title}{
name of resulting LaTeX file omitting the \code{.tex} suffix.  Default
is the name of the \code{summary} object.  If \code{caption} is specied,
\code{title} is also used for the table's symbolic reference label. 
}
\item{trios}{
If for \code{method="response"} you summarized the response(s) by using
three quantiles, specify \code{trios=TRUE} or \code{trios=v} to group each set of
three statistics into one column for \code{latex} output, using the format
a B c, where the outer quantiles are in smaller font
(\code{scriptsize}).  For \code{trios=TRUE}, the overall column names are taken
from the column names of the original data matrix.  To give new
column names, specify \code{trios=v}, where \code{v} is a vector of column
names, of length \code{m/3}, where \code{m} is the original number of columns
of summary statistics.
}
\item{rowlabel}{
see \code{latex.default} (under the help file \code{latex})
}
\item{cdec}{
number of decimal places to the right of the decimal point for
\code{latex}.  This value should be a scalar (which will be properly
replicated), or a vector with length equal to the number of columns
in the table.  For \code{"response"} tables, this length does not count
the column for \code{N}.
}
\item{ncaption}{
  set to \code{FALSE} to not have \code{latex.summary.formula.response}
  put sample sizes in captions
  }
\item{i}{
a vector of integers, or character strings containing variable names
to subset on.  Note that each row subsetted on in an \code{summary.formula.reverse}
object subsets on all the levels that make up the corresponding variable
(automatically).
}
\item{j}{
a vector of integers representing column numbers
}
\item{middle.bold}{
set to \code{TRUE} to have LaTeX use bold face for the middle quantile for
\code{method="reverse"} 
}
\item{outer.size}{
the font size for outer quantiles for \code{"reverse"} tables
}
\item{insert.bottom}{
  set to \code{FALSE} to suppress inclusion of definitions placed at the
  bottom of LaTeX tables for \code{method="reverse"}
  }
\item{dcolumn}{
  see \code{latex}
  }
\item{na.group}{
set to \code{TRUE} to have missing stratification variables given their own
category (\code{NA})
}
\item{shortlabel}{
set to \code{FALSE} to include stratification variable names and equal signs
in labels for strata levels
}
}
\value{
\code{summary.formula} returns a data frame or list depending on
\code{method}.  \code{plot.summary.formula.reverse} returns the number
of pages of plots that were made.
}
\section{Side Effects}{
\code{plot.summary.formula.reverse} creates a function \code{Key} and
\code{Key2} in frame 0 that will draw legends.
}
\author{
Frank Harrell
\cr
Department of Biostatistics
\cr
Vanderbilt University
\cr
f.harrell@vanderbilt.edu
}
\references{
Harrell FE (2004): Statistical tables and plots using S and LaTeX.
Document available from \url{http://biostat.mc.vanderbilt.edu/twiki/pub/Main/StatReport/summary.pdf}.
}
\seealso{
\code{\link{smean.sd}}, \code{\link{summarize}},
\code{\link{label}}, \code{\link[survival]{strata}}, \code{\link{dotchart2}},
\code{\link{print.char.matrix}}, \code{\link{update}},
\code{\link{formula}}, \code{\link{cut2}}, \code{\link{llist}},
\code{\link{format.default}}, \code{\link{latex}},
\code{\link{latexTranslate}} \code{\link{bpplt}}
}
\examples{
options(digits=3)
set.seed(173)
sex <- factor(sample(c("m","f"), 500, rep=TRUE))
age <- rnorm(500, 50, 5)
treatment <- factor(sample(c("Drug","Placebo"), 500, rep=TRUE))


# Generate a 3-choice variable; each of 3 variables has 5 possible levels
symp <- c('Headache','Stomach Ache','Hangnail',
          'Muscle Ache','Depressed')
symptom1 <- sample(symp, 500,TRUE)
symptom2 <- sample(symp, 500,TRUE)
symptom3 <- sample(symp, 500,TRUE)
Symptoms <- mChoice(symptom1, symptom2, symptom3, label='Primary Symptoms')
table(as.character(Symptoms))

# Note: In this example, some subjects have the same symptom checked
# multiple times; in practice these redundant selections would be NAs
# mChoice will ignore these redundant selections
# If the multiple choices to a single survey question were already
# stored as a series of T/F yes/no present/absent questions we could do:
# Symptoms <- cbind(headache,stomach.ache,hangnail,muscle.ache,depressed)
# where the 5 input variables are all of the same type: 0/1,logical,char.
# These variables cannot be factors in this case as cbind would
# store integer codes instead of character strings.
# To give better column names can use 
# cbind(Headache=headache, 'Stomach Ache'=stomach.ache, \dots)


# Following 8 commands only for checking mChoice
data.frame(symptom1,symptom2,symptom3)[1:10,]
Symptoms[1:10,]  # Print first 10 subjects' new binary indicators


meanage <- if(.R.)double(5) else single(5)
for(j in 1:5) meanage[j] <- mean(age[Symptoms[,j]])
names(meanage) <- dimnames(Symptoms)[[2]]
meanage


# Manually compute mean age for 2 symptoms
mean(age[symptom1=='Headache' | symptom2=='Headache' | symptom3=='Headache'])
mean(age[symptom1=='Hangnail' | symptom2=='Hangnail' | symptom3=='Hangnail'])


#Frequency table sex*treatment, sex*Symptoms
summary(sex ~ treatment + Symptoms, fun=table)
# could also do summary(sex ~ treatment + mChoice(symptom1,\dots),\dots)


#Compute mean age, separately by 3 variables
summary(age ~ sex + treatment + Symptoms)


summary(age ~ sex + treatment, method="cross")
# Note: method="cross" will not allow mChoice variables


f <- summary(treatment ~ age + sex + Symptoms, method="reverse", test=TRUE)
f
# trio of numbers represent 25th, 50th, 75th percentile
print(f, long=TRUE)
plot(f)
plot(f, conType='bp', prtest='P')
bpplt()    # annotated example showing layout of bp plot

#Compute predicted probability from a logistic regression model
#For different stratifications compute receiver operating
#characteristic curve areas (C-indexes)
predicted <- plogis(.4*(sex=="m")+.15*(age-50))
positive.diagnosis <- ifelse(runif(500)<=predicted, 1, 0)
roc <- function(z) {
   x <- z[,1];
   y <- z[,2];
   n <- length(x);
   if(n<2)return(c(ROC=NA));
   n1 <- sum(y==1);
   c(ROC= (mean(rank(x)[y==1])-(n1+1)/2)/(n-n1) );
 }
y <- cbind(predicted, positive.diagnosis)
options(digits=2)
summary(y ~ age + sex, fun=roc)


options(digits=3)
summary(y ~ age + sex, fun=roc, method="cross")


#Plot estimated mean life length (assuming an exponential distribution) 
#separately by levels of 4 other variables.  Repeat the analysis
#by levels of a stratification variable, drug.  Automatically break
#continuous variables into tertiles.
#We are using the default, method='response'
\dontrun{
life.expect <- function(y) c(Years=sum(y[,1])/sum(y[,2]))
attach(pbc)
S <- Surv(follow.up.time, death)
s2 <- summary(S ~ age + albumin + ascites + edema + stratify(drug),
                         fun=life.expect, g=3)


#Note: You can summarize other response variables using the same 
#independent variables using e.g. update(s2, response~.), or you 
#can change the list of independent variables using e.g. 
#update(s2, response ~.- ascites) or update(s2, .~.-ascites)
#You can also print, typeset, or plot subsets of s2, e.g.
#plot(s2[c('age','albumin'),]) or plot(s2[1:2,])


s2    # invokes print.summary.formula.response


#Plot results as a separate dot chart for each of the 3 strata levels
par(mfrow=c(2,2))
plot(s2, cex.labels=.6, xlim=c(0,40), superposeStrata=FALSE)


#Typeset table, creating s2.tex
w <- latex(s2, cdec=1)
#Typeset table but just print LaTeX code
latex(s2, file="")    # useful for Sweave


#Take control of groups used for age.  Compute 3 quartiles for
#both cholesterol and bilirubin (excluding observations that are missing
#on EITHER ONE)


age.groups <- cut2(age, c(45,60))
g <- function(y) apply(y, 2, quantile, c(.25,.5,.75))
y <- cbind(Chol=chol,Bili=bili)
label(y) <- 'Cholesterol and Bilirubin'
#You can give new column names that are not legal S-Plus names
#by enclosing them in quotes, e.g. 'Chol (mg/dl)'=chol


s <- summary(y ~ age.groups + ascites, fun=g)


par(mfrow=c(1,2), oma=c(3,0,3,0))   # allow outer margins for overall
for(ivar in 1:2) {                  # title 
  isub <- (1:3)+(ivar-1)*3          # *3=number of quantiles/var.
  plot(s3, which=isub, main='', 
       xlab=c('Cholesterol','Bilirubin')[ivar],
       pch=c(91,16,93))            # [, closed circle, ]
  }
mtext(paste('Quartiles of', label(y)), adj=.5, outer=TRUE, cex=1.75)  
#Overall (outer) title


prlatex(latex(s3, trios=TRUE)) 
# trios -> collapse 3 quartiles


#Summarize only bilirubin, but do it with two statistics:
#the mean and the median.  Make separate tables for the two randomized
#groups and make plots for the active arm.


g <- function(y) c(Mean=mean(y), Median=median(y))


for(sub in c("D-penicillamine", "placebo")) {
  ss <- summary(bili ~ age.groups + ascites + chol, fun=g,
                subset=drug==sub)
  cat('\n',sub,'\n\n')
  print(ss)


  if(sub=='D-penicillamine') {
    par(mfrow=c(1,1))
    plot(s4, which=1:2, dotfont=c(1,-1), subtitles=FALSE, main='')
    #1=mean, 2=median     -1 font = open circle
    title(sub='Closed circle: mean;  Open circle: median', adj=0)
    title(sub=sub, adj=1)
  }


  w <- latex(ss, append=TRUE, fi='my.tex', 
             label=if(sub=='placebo') 's4b' else 's4a',
             caption=paste(label(bili),' {\\\\em (',sub,')}', sep=''))
  #Note symbolic labels for tables for two subsets: s4a, s4b
  prlatex(w)
}


#Now consider examples in 'reverse' format, where the lone dependent
#variable tells the summary function how to stratify all the 
#'independent' variables.  This is typically used to make tables 
#comparing baseline variables by treatment group, for example.


s5 <- summary(drug ~ bili + albumin + stage + protime + sex + 
                     age + spiders,
              method='reverse')
#To summarize all variables, use summary(drug ~., data=pbc)
#To summarize all variables with no stratification, use
#summary(~a+b+c) or summary(~.,data=\dots)


options(digits=1)
print(s5, npct='both')
#npct='both' : print both numerators and denominators
plot(s5, which='categorical')
Key(locator(1))  # draw legend at mouse click
par(oma=c(3,0,0,0))  # leave outer margin at bottom
plot(s5, which='continuous')
Key2()           # draw legend at lower left corner of plot
                 # oma= above makes this default key fit the page better


options(digits=3)
w <- latex(s5, npct='both', here=TRUE)     
# creates s5.tex


#Turn to a different dataset and do cross-classifications on possibly 
#more than one independent variable.  The summary function with 
#method='cross' produces a data frame containing the cross-
#classifications.  This data frame is suitable for multi-panel 
#trellis displays, although `summarize' works better for that.


attach(prostate)
size.quartile <- cut2(sz, g=4)
bone <- factor(bm,labels=c("no mets","bone mets"))


s7 <- summary(ap>1 ~ size.quartile + bone, method='cross')
#In this case, quartiles are the default so could have said sz + bone


options(digits=3)
print(s7, twoway=FALSE)
s7   # same as print(s7)
w <- latex(s7, here=TRUE)   # Make s7.tex


library(trellis,TRUE)
invisible(ps.options(reset=TRUE))
trellis.device(postscript, file='demo2.ps')


dotplot(S ~ size.quartile|bone, data=s7, #s7 is name of summary stats
                  xlab="Fraction ap>1", ylab="Quartile of Tumor Size")
#Can do this more quickly with summarize:
# s7 <- summarize(ap>1, llist(size=cut2(sz, g=4), bone), mean,
#                 stat.name='Proportion')
# dotplot(Proportion ~ size | bone, data=s7)


summary(age ~ stage, method='cross')
summary(age ~ stage, fun=quantile, method='cross')
summary(age ~ stage, fun=smean.sd, method='cross')
summary(age ~ stage, fun=smedian.hilow, method='cross')
summary(age ~ stage, fun=function(x) c(Mean=mean(x), Median=median(x)),
        method='cross')
#The next statements print real two-way tables
summary(cbind(age,ap) ~ stage + bone, 
        fun=function(y) apply(y, 2, quantile, c(.25,.75)),
        method='cross')
options(digits=2)
summary(log(ap) ~ sz + bone,
        fun=function(y) c(Mean=mean(y), quantile(y)),
        method='cross')


#Summarize an ordered categorical response by all of the needed
#cumulative proportions
summary(cumcategory(disease.severity) ~ age + sex)

}
}
\keyword{category}
\keyword{interface}
\keyword{hplot}
\keyword{manip}
\concept{grouping}
\concept{stratification}
\concept{aggregation}
\concept{cross-classification}