Multiple linear indicators. A better scenario, but one that is more challenging to use, is to work with multiple linear indicators. Example: Attraction.
We assume that when someone is attracted to someone else (a latent variable), that person is more likely to have an increased heart rate, talk more, and make more phone calls (all observable variables).
let’s assume an interval scale ranging from –4 (not at all attracted) to + 4 (highly attracted)
heart beat x10 latent variable), that person is more likely to have an increased heart rate, talk more, and make more phone calls (all observable variables).
We assume that each observed variable has a linear relationship with the latent variable.
Note, however, that each observed variable has a different metric (one is heart beats per minute, another is time spent talking). Thus, we need a different metric for the latent variable.
Allow the lowest measured value to represent the lowest value of the latent variable
Allow the highest measured value to represent the highest value of the latent variable
The line between these points maps the relationship between them
heart beat x 10 value of the latent variable
Now we can map the observed scores for each measured variable onto the scale for the latent variable. For example, the observed heart rate score of 120 maps onto an attraction score of 2. Ten-minutes of talking maps onto an attraction score of zero. Thirteen phone calls maps to a high attraction score of 3. (Russ on The Bachelorette)
heart beat value of the latent variable
This mapping process provides us with three estimates of the latent score: 2, 0, and 3. Because we are trying to estimate a single number for attraction, we can simply average these three estimates to obtain our measurement of attraction.
In this example: (2 + 0 + 3)/3 = 5/3 = 1.67 (somewhat attracted)
(time spent talking + heart rate)/2 = attraction
Person A: (2 + 80)/2 = 82/2 = 41
Person B: (3 + 120)/2 = 123/2 = 62
Person A: 2 minutes talking + 80 beats per minute
= 41 minutes talking/beats per minute???
Person Heart rate Time spent talking Average
A 80 2 41
B 80 3 42
C 120 2 61
D 120 3 62
* Moving between lowest to highest scores matters more for one variable than the other
* Heart rate has a greater range than time spent talking and, therefore, influences the total score more (i.e., the score on the latent variable)
Mapping the relationship by placing anchors at the highest and lowest values helps to minimize this problem
Preview: Standardization and z-scores
Observed: Hours of Lost Sleep
Latent: Stress Level
Observed: Things to do
Latent: Stress Level