Measuring height example

It is easy to be skeptical about the ability of our model in measuring latent constructs like mathematical or verbal ability, depression, fatigue, or resilience. However, it is remarkable how well this model works.

To illustrate this, let’s imagine a world without a measuring tape. That means that we cannot do our favorite thing (i.e., directly measure peoples’ height). Instead, we will have to rely on people answering multiple questions to try to measure this “latent” construct. More specifically, we rely on the following questionnaire:

1. When I lay down in my bed, I frequently feel cold in my foot
2. I often go down the stairs skipping every 2 steps
3. I think that I would do great in a basketball team
4. I would impress many people as a police officer
5. I feel uncomfortable in most cars
6. I literally look down on my colleagues
7. Can you get an object on a cabinet at your kitchen without using a stool?
8. Do you lower your head when going through the door?
9. Can you store your luggage in the luggage compartment of a bus or airplane?
10. Do you have to move the seat back in your car?
11. When you get a ride, do people typically offer the front passenger seat for you?
12. When people take a photo of a group, do you typically stand in the back?
13. Do you have difficulty in feeling comfortable in the bus?
14. When people create a line in order of size (shortest to tallest), are you typically in the end of the line?

These are all “yes” and “no” questions, where “yes” answers were coded as ones and “no” answers are zeroes. This example was created by Dalton Andrade and Heliton Tavares, two professors of statistics in Brazil. They actually had multiple people answer these questions (i.e., these data are real, not made up). The data for this is provided in the file “Height_data.csv”. On total, we have 211 participants and these data are organized as shown below:

setwd('/Volumes/drvalle/uf/courses/bayesian course/group activities/6 example educ/Dalton')
dat=read.csv('Height_data.csv',as.is=T)
nrow(dat)

## [1] 211

head(dat)

##   ID Height.meters i01 i02 i03 i04 i05 i06 i07 i08 i09 i10 i11 i12 i13 i14
## 1  1          1.81   0   1   0   1   1   1   1   0   1   1   1   0   1   0
## 2  2          1.64   0   0   0   0   0   0   0   0   1   0   0   0   0   0
## 3  3          1.80   0   0   1   1   0   0   1   0   1   1   0   1   0   1
## 4  4          1.78   0   1   1   1   1   0   1   0   1   1   0   1   0   1
## 5  5          1.66   0   0   0   0   0   0   1   0   1   1   0   0   0   0
## 6  6          1.67   0   0   0   0   0   0   1   0   1   1   0   0   0   0

Try analyzing these data with the model that you created in class. Do our estimates of the “latent construct” correlate well with the height information that participants provided? If they do, this indicates that our model is working well.

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