Combining Flattened Contingency Tables (and Other Tables)

This vignette demonstrates how flattened contingency tables can be combined into more complex tables. For starters, we create a few contingendy tables.

tab.Class.Age <- xtabs(Freq~Class+Age,data=Titanic)
tab.Survived.Class.Age <- xtabs(Freq~Survived+Class+Age,data=Titanic)
tab.Survived.Class.Sex <- xtabs(Freq~Survived+Class+Sex,data=Titanic)
tab.Survived.Class <- xtabs(Freq~Survived+Class,data=Titanic)
tab.Survived.Sex <- xtabs(Freq~Survived+Sex,data=Titanic)
tab.Survived.Age <- xtabs(Freq~Survived+Age,data=Titanic)
tab.Survived <- xtabs(Freq~Survived,data=Titanic)

Then we load the memisc package:

library(memisc)

Next, we create a few flattened contingency tables:

(ftab.Survived.Age <- ftable(tab.Survived.Age))
         Age Child Adult
Survived
No              52  1438
Yes             57   654
(ftab.Survived.Sex <- ftable(tab.Survived.Sex))
         Sex Male Female
Survived
No           1364    126
Yes           367    344

Since these tables have the same row variables, we can combine them columnwise:

cbind(ftab.Survived.Age,
      ftab.Survived.Sex)
         Age Child Adult  Sex Male Female
Survived
No              52  1438      1364    126
Yes             57   654       367    344

We can even add a simple table of counts:

cbind(ftab.Survived.Age,
      ftab.Survived.Sex,
      Total=tab.Survived)
         Age Child Adult  Sex Male Female   Total
Survived
No              52  1438      1364    126    1490
Yes             57   654       367    344     711

Of course, it is not enough to see such tables on screen, we also may need them in a presentable format, such as LaTeX or HTML. For the latter format we again have format_html and show_html. To see how this works, we first look at the individual ftables:

show_html(ftab.Survived.Age)
Age
Survived Child Adult
No 52 1438
Yes 57 654
show_html(ftab.Survived.Sex)
Sex
Survived Male Female
No 1364 126
Yes 367 344

… and then at their combination

show_html(
  cbind(ftab.Survived.Age,
      ftab.Survived.Sex,
      Total=tab.Survived)
)
Age Sex
Child Adult Male Female Total
Survived No 52 1438 1364 126 1490
Yes 57 654 367 344 711

To make, in “knitr”, the creation of HTML-versions automatic one can use the following little trick:

knit_print.ftable_matrix <-function(x,options,...)
  knitr::asis_output(
    format_html(x,
                digits=if(length(options$ftable.digits))
                          options$ftable.digits
                       else 0,
                ...))

Now we do not need to call show_html while using “knitr”:

cbind(ftab.Survived.Age,
      ftab.Survived.Sex,
      Total=tab.Survived)
Age Sex
Child Adult Male Female Total
Survived No 52 1438 1364 126 1490
Yes 57 654 367 344 711

This can be undone by removing the method function of knit_print:

rm(knit_print.ftable_matrix)

For show_html and toLatex there are some variants in how the variable names are positioned, for example:

show_html(
  cbind(ftab.Survived.Age,
      ftab.Survived.Sex,
      Total=tab.Survived),
  varinfront=FALSE
)
Age Sex
Survived Child Adult Male Female Total
No 52 1438 1364 126 1490
Yes 57 654 367 344 711
ftab.Age.Survived <- ftable(tab.Survived.Age,col.vars=1)
ftab.Sex.Survived <- ftable(tab.Survived.Sex,col.vars=1)
ftab.Class.Survived <- ftable(tab.Survived.Class,col.vars=1)

rbind(
  ftab.Age.Survived,
  ftab.Sex.Survived,
  ftab.Class.Survived,
  Total=tab.Survived
)
       Survived   No Yes
Age
Child             52  57
Adult           1438 654

Sex
Male            1364 367
Female           126 344

Class
1st              122 203
2nd              167 118
3rd              528 178
Crew             673 212


Total           1490 711
show_html(
  rbind(
    ftab.Age.Survived,
    ftab.Sex.Survived,
    ftab.Class.Survived,
    Total=tab.Survived
  )
)
Survived
No Yes
Age Child 52 57
Adult 1438 654
Sex Male 1364 367
Female 126 344
Class 1st 122 203
2nd 167 118
3rd 528 178
Crew 673 212
Total 1490 711

It is also possible to create the ftable`s from tables of percentages or generic tables (created with `genTable) etc.

ptab.Survived.Age<-percentages(Survived~Age,data=Titanic)
ptab.Survived.Sex<-percentages(Survived~Sex,data=Titanic)
ptab.Survived.Class<-percentages(Survived~Class,data=Titanic)

fptab.Age.Survived <- ftable(ptab.Survived.Age,col.vars=1)
fptab.Sex.Survived <- ftable(ptab.Survived.Sex,col.vars=1)
fptab.Class.Survived <- ftable(ptab.Survived.Class,col.vars=1)

show_html(
  rbind(
    fptab.Age.Survived,
    fptab.Sex.Survived,
    fptab.Class.Survived
  ),
  digits=1
)
Survived
No Yes
Age Child 47 . 7 52 . 3
Adult 68 . 7 31 . 3
Sex Male 78 . 8 21 . 2
Female 26 . 8 73 . 2
Class 1st 37 . 5 62 . 5
2nd 58 . 6 41 . 4
3rd 74 . 8 25 . 2
Crew 76 . 0 24 . 0

It is also possible to combine rbind and cbind:

tab.Age <- xtabs(Freq~Age,data=Titanic)
tab.Sex <- xtabs(Freq~Sex,data=Titanic)
tab.Class <- xtabs(Freq~Class,data=Titanic)


show_html(
  rbind(
    cbind(fptab.Age.Survived,Total=tab.Age),
    cbind(fptab.Sex.Survived,Total=tab.Sex),
    cbind(fptab.Class.Survived,Total=tab.Class)
  ),
  digits=c(1,0) # One digit after dot for percentages
                # no digits for total counts.
)
Survived
No Yes Total
Age Child 47 . 7 52 . 3 109
Adult 68 . 7 31 . 3 2092
Sex Male 78 . 8 21 . 2 1731
Female 26 . 8 73 . 2 470
Class 1st 37 . 5 62 . 5 325
2nd 58 . 6 41 . 4 285
3rd 74 . 8 25 . 2 706
Crew 76 . 0 24 . 0 885

The same construct as LaTeX code:

toLatex(
  rbind(
    cbind(fptab.Age.Survived,Total=tab.Age),
    cbind(fptab.Sex.Survived,Total=tab.Sex),
    cbind(fptab.Class.Survived,Total=tab.Class)
  ),
  digits=c(1,0) # One digit after dot for percentages
                # no digits for total counts.
)
\begin{tabular}{llD{.}{.}{1}D{.}{.}{1}cD{.}{.}{0}}
\toprule
&&\multicolumn{2}{c}{Survived}&&\\
\cmidrule{3-4}
&&\multicolumn{1}{c}{No}&\multicolumn{1}{c}{Yes}&&\multicolumn{1}{c}{Total}\\
\midrule
Age&Child&47.7&52.3&&109\\
&Adult&68.7&31.3&&2092\\
\midrule Sex&Male&78.8&21.2&&1731\\
&Female&26.8&73.2&&470\\
\midrule Class&1st&37.5&62.5&&325\\
&2nd&58.6&41.4&&285\\
&3rd&74.8&25.2&&706\\
&Crew&76.0&24.0&&885\\
\bottomrule
\end{tabular}

and typeset with LaTeX

../../../_images/ftable-matrix-xmpl.png