Latent Variables

In this tutorial we discuss latent variables. We will look at what latent variables are, how we can turn these invisible characteristics into numbers, and how we know whether we can trust the resulting measures.

What Are Latent Variables?

Latent variables are like ghosts: you cannot see or measure them directly, but you can look for patterns in observable data that may reflect them. A latent variable is an unobserved construct that is inferred from measured variables. Think of traits like extraversion, intelligence, or anxiety. There is no simple "extraversion thermometer" we can just point at someone.

Instead of measuring the ghost itself, we use indicators — the observable reactions, behaviors, or responses that we can measure.

An Example: Extraversion and Salary

Imagine you're a researcher who has the following hypothesis:

"Extroverted people earn higher salaries than introverted people."

To test this, you design a questionnaire and collect data on two things:

• People's extraversion
• Their salary

But that raises a big question: How do we measure salary and extraversion? One part is more direct: salary can be recorded as an observed variable, for example by asking, "What is your monthly salary?" Self-reported salary can still contain measurement error, but it is not a latent construct in this example.

But what about extraversion? You could try asking: "How extroverted are you?" — but that's not a great idea.

People do not always know objectively how extroverted they are. Their self-image can differ from how others see them. Some people underestimate themselves, some overestimate.

In short: Extraversion is a latent variable. It cannot be measured directly with a single, simple question.

From Ghosts to Data: Using Observable Indicators

Instead of asking about extraversion in one vague question, we ask about behaviors and feelings that are expected to reflect extraversion. For example:

• How much people like parties
• How talkative they are
• How comfortable they feel in groups

These observable responses are indicators of the latent variable. They are imperfect measures: each response can also be affected by the wording of the item, the situation, and measurement error.

Items and Scales

Instead of measuring the latent variable directly, we need a set of statements, or items, that everyone answers.

What is an Item?

In survey research, an item is a single question or statement where respondents indicate how strongly they agree or disagree.

For example:

"I enjoy going to large social gatherings."
Response options: Strongly disagree, Disagree, Neutral, Agree, Strongly agree.

Each item captures one tiny aspect of the latent variable (here: extraversion).

What is a Scale?

A scale is a group of several items where respondents indicate how much they agree or disagree. For example:

• Question 1: "I enjoy going to parties."
• Question 2: "I find it easy to start conversations with strangers."
• Question 3: "I feel comfortable speaking in front of a group."
• Question 4: "I am lively and full of energy."

Together, these items form an extraversion scale. People simply answer all the items.

If we assign numbers to the response options, we can calculate the average of the responses, provided that all items are scored in the same direction. Negatively worded items must first be reverse-scored.

This average can then be used as a scale score that estimates the latent variable, for example, how extroverted a person is. If the scale has been designed and validated so that higher values indicate more extraversion, a higher score indicates more extraversion.

So, each item is usually answered on a rating scale, often from 1 to 5:

• 1 - Strongly disagree
• 2 - Disagree
• 3 - Neither agree nor disagree
• 4 - Agree
• 5 - Strongly agree

Now imagine a person answers the four extraversion items with scores 4, 4, 3, 4. We can average these:

Average score: (4 + 4 + 3 + 4) / 4 = 3.75
The higher the score, the more extroverted the person is.

That average is our estimate of the latent variable for that person.

How do we know which questions to ask?

The good news is: you usually do not have to invent all the questions yourself. In most cases, psychologists use existing, validated questionnaires that have already been tested in many studies.

These scales are:

• Published
• Well-documented
• Known to measure the latent variable reasonably well

How do we easily build a survey?

That is easy: we just create one with numiqo. Here you can create a scale with the different items.

In our example, the instruction could be: Please indicate how strongly the following attributes apply to you. "I am ..."

• outgoing
• sociable
• lively
• full of energy

Rating options could be: Does not apply, Somewhat applies, Rather applies, Fully applies.

This gives us one part of our questionnaire: a structured way to turn the extraversion ghost into numbers we can analyze.

Can We Trust the Scale?

Once we have built a scale with several items, one big question remains: Can we trust this scale? Are all these items really measuring the same underlying construct?

This is where Cronbach's Alpha comes in. It helps us assess the internal consistency of the item scores. However, a high Cronbach's alpha does not by itself prove that the scale measures one latent variable or that it measures the intended construct. Evidence from the content of the items, factor analysis, and relationships with other measures is also needed to assess validity.