Lecture 7 - Latent Variables

Question 1

What is a latent variable?

Answer 1

-a latent variable cannot be measured; or at least not directly.

Question 2

What is a psychological/latent construct?

Answer 2

-an abstract entity that was created to reflect a set of behaviors that tend to co-occur with one another

Question 3

How is a psychological construct assessed?

Answer 3

-by soliciting a representative sample of these behaviors. This sample should be both limitative (i.e., parsimony, time constraints) and inclusive (i.e., cover all relevant aspects)

Question 4

Which test allows us to measure psychological constructs?

Answer 4

-the test is designed to solicit this sample of behavior.
-the factor analytic model allows us to measure this psychological construct.
-the factors, or latent variables, is the statistical representation, or expression of the psychological construct

Question 5

Which assumption is made in psychology about latent construct/factor and behaviours? (which one causes which?)

Answer 5

-the “presence” of the latent construct (e.g., intelligence) that predicts the emergence of the observed behaviors (e.g., vocabulary)
[its because of the construct/factor that we behave in a certain way (not the opposite)]
-factor is a predictor of the behaviours

Question 6

What are the 2 types of factor analyses used to estimate latent variables?

Answer 6

-confirmatory factor analysis [recommended when you have more evidence on the test; replication studies]
-exploratory factor analysis [recommended in early stages of test development]

Question 7

How does the Exploratory Factor Analysis work (EFA)?

Answer 7

-will assess the link between each of your items and each of the factors;
-then, look at results and assign the item to the factor on which it has the highest factor loading [strength of association between item and factor]

Question 8

How does the Confirmatory Factor Analysis work?

Answer 8

-tell the statistical package how your items should be grouped
-then it tells you if your model fits the data (if its an adequate representation of the data)
-when your structure doesn’t work, you start exploring (which isn’t an ideal method)

Question 9

What is the equation that summarizes the 2 factor analysis models?

Answer 9

This is Factor Analysis:
-Х = τ + Λξ + δ
-X = Tau + Lambda * Xi + Delta

Question 10

What is the point of a correlation matrix?

Answer 10

-looks at the correlation of all your items and tries to find out which ones go together

Question 11

What are the 3 goals/components of a factor analysis?

Answer 11

To analyse a set of continuous observed variables in order to:
-see whether they form relatively independent, and meaningful, subsets.
-understand the underlying structure/organization of this set of variables.
-provide a synthesis of a larger set of variables

Question 12

When is factor analysis used?

Answer 12

-factor analyses are a critical component of psychometric validation studies, aiming to verify whether the various items forming a questionnaire do indeed help to assess the expected underlying constructs (aka factors).
-factor analyses can also be conducted with ordinal (specialized applications) or nominal (correspondence analyses) indicators.

Question 13

How does factor analysis work and the goal?

Answer 13

-we extract factors from the real correlation matrix and if we consider only these factors, they’re connected to a model implied correlation matrix
-the goal is to maximally reduce the size of this residual matrix, using a variety of “estimators”
-but here, the latent factors are the predictors, and the observed variables are the outcomes, as in a regression

Question 14

What is the simplified factor analysis equation and what does it mean?

Answer 14

-Х = Λξ + δ
-X = observed scores
-Λ = matrix of Factor Loadings [strength of association between factor and item]
-ξ = latent Variables
-δ = vector of Residuals
[τ = vector of Intercepts; intercept not included because the variables are all standardized –> all have a mean of zero]

Question 15

What does the simplified factor analysis lead us to? (what are the 2 causes of items)

Answer 15

-this model looks at each specific item/variable and assumes that it has only 2 causes: the factor and random measurement error
-the residual describes wtv is unique to the item and a factor captures everything that is shared among the item

Question 16

What is the conditional independence assumption?

Answer 16

-factor analysis assumes that all of the covariance will be absorbed by the factor (no residual correlations among the uniquenesses) [since there are only 2 causes]

Question 17

What is the main advantage of factor analysis and latent variables?

Answer 17

-that they are completely corrected for measurement error
-factor analysis separates the true underlying factor (latent variable) from random measurement errors that are unique to each item, making the factor perfectly reliable.
-however, reliability doesn’t guarantee validity—it just ensures the factor is consistently measured.

Question 18

What is the difference between reliability and random measurement error?

Answer 18

-reliability: the factor captures the true score variance, which is the consistent part of the measurement
-random measurement error: reflects the fact that each item is more or less representative of the construct [automatically separated into uniqueness]

Question 19

How do latent variables handle random error to improve validity?

Answer 19

-reliability used to limit validity because random error reduced the true score variance, making it hard to assess how constructs relate.
-latent variables solve this by separating random error, allowing for better assessment of validity.

Question 20

What is structural equation modeling?

Answer 20

-provides a way to estimate relations among constructs corrected for random measurement errors
-it is a combination of factor analysis [find underlying concepts behind data] and regression [estimate how these concepts are related to each other]

Question 21

To summarize, what is a factor analysis?

Answer 21

-focuses on the covariance matrix: what is shared among the indicators
-a reflective model: the indicators are seen as providing a reflection of the latent construct.
-the indicators are assumed to have 2 causes: the latent
construct, and the uniqueness (which includes random error, and all that is specific to the item)

Question 22

What is the Principle Component Analysis? [other option instead of factor analysis]

Answer 22

-aims to reproduces the complete variance-covariance matrix, thus what is shared among the indicators and what is unique to them.
-formative model: Indicators “form” the latent variable.
-useful as a way to obtain a “summary” index of otherwise unrelated indicators (e.g., life events: divorce, marriage, death of a loved one, imprisonment).
-assumes that you are interested in all that is in the indicators.