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

show_html(
  cbind(ftab.Survived.Age,
      ftab.Survived.Sex,
      Total=tab.Survived),
  varontop=FALSE
)

		Age:	Child			Adult			Sex:	Male			Female			Total
Survived	No		52			1438				1364			126			1490
	Yes		57			654				367			344			711

Of course it is also possible to combine flat contingency tables rowwise:

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 ftables 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}