# Analyzing Multiple Response Questions

There are at least two main approaches for storing multiple response questions in a data set. The indicator mode and the polytomous mode.

## 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"))
```

Freq | |
---|---|

Python | 3 |

R | 7 |

SPSS | 4 |

Stata | 4 |

#Total cases | 9 |

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

Percent of responses | |
---|---|

Python | 16.7 |

R | 38.9 |

SPSS | 22.2 |

Stata | 22.2 |

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

Percent of cases | |
---|---|

Python | 33.3 |

R | 77.8 |

SPSS | 44.4 |

Stata | 44.4 |