Analyzing Multiple Response Questions

Polytomous mode

The polytomous mode is suitable when the possible response categories are not fixed and the responses are recorded according to their order of appearance.

For example, consider the following question.

What are your favorite statistical software package? (allow up to two answers)

Response 1: _____________

Response 2: _____________

The collected data would then look like the following:

polytomous <- data.frame(
  response1 = c("R", "Python","R", "Stata", "SPSS","Python","Stata","SPSS","R"),
  response2 = c("Python", "R", "Stata", "SPSS", "R", "R", "R", "Stata", "SPSS")
)
polytomous

##   response1 response2
## 1         R    Python
## 2    Python         R
## 3         R     Stata
## 4     Stata      SPSS
## 5      SPSS         R
## 6    Python         R
## 7     Stata         R
## 8      SPSS     Stata
## 9         R      SPSS

Indicator mode

The indicator mode refers to the situation where the data are stored as a set of indicator variables/columns. Consider the above question as following:

Which of the followings are your favorite statistical packages?

a) R
b) Stata
c) Python
d) SPSS

The most straightforward way to store the above data is to construct a set of indicator or dummy variables.

One variable/column for each response.

In this case, the data would like the following:

indicator <- data.frame(
  R = c("Yes","Yes","Yes", "No", "Yes","Yes","Yes","No","Yes"),
  Stata = c("No","No","Yes","Yes","No","No","Yes","Yes","No"),
  Python = c("Yes","Yes","No","No","No","Yes","No","No","No"),
  SPSS = c("No","No","No","Yes","Yes","No","No","Yes","Yes")
)
indicator

##     R Stata Python SPSS
## 1 Yes    No    Yes   No
## 2 Yes    No    Yes   No
## 3 Yes   Yes     No   No
## 4  No   Yes     No  Yes
## 5 Yes    No     No  Yes
## 6 Yes    No    Yes   No
## 7 Yes   Yes     No   No
## 8  No   Yes     No  Yes
## 9 Yes    No     No  Yes

Analyzing multiple response questions

If the data are stored as indicator mode, the common way is to tabulate each variable separately.

# install.packages("dplyr")
library(dplyr)

# R
# round(prop.table(table(indicator$R))*100,1)
count(indicator, R, name = "Freq") %>% mutate(Percent = round(Freq/sum(Freq)*100, 1))

# Stata
# round(prop.table(table(indicator$Stata))*100,1)
count(indicator, Stata, name = "Freq") %>% mutate(Percent = round(Freq/sum(Freq)*100, 1))

# Python
# round(prop.table(table(indicator$Python))*100,1)
count(indicator, Python, name = "Freq") %>% mutate(Percent = round(Freq/sum(Freq)*100, 1))

# SPSS
# round(prop.table(table(indicator$SPSS))*100,1)
count(indicator, SPSS, name = "Freq") %>% mutate(Percent = round(Freq/sum(Freq)*100, 1))

##     R Freq Percent
## 1  No    2    22.2
## 2 Yes    7    77.8

##   Stata Freq Percent
## 1    No    5    55.6
## 2   Yes    4    44.4

##   Python Freq Percent
## 1     No    6    66.7
## 2    Yes    3    33.3

##   SPSS Freq Percent
## 1   No    5    55.6
## 2  Yes    4    44.4

If the data are stored as polytomous mode even a simple descriptive analysis like tabulating frequency distributions could be quite tricky and complicated. In this case, we can use calc_cro() function from the expss package for tabulating multiple response questions.

# install.packages(expss)
library(expss)

# Frequency

calc_cro(polytomous, mrset(response1 %to% response2), total(label = "Freq"))

# Percent of responses
calc_cro_cpct_responses(polytomous, mrset(response1 %to% response2), total_row_position = "none", total(label = "Percent of responses"))

# Percent of cases
calc_cro_cpct(polytomous, mrset(response1 %to% response2), total_row_position = "none", total(label = "Percent of cases"))