In factor analysis, variance refers to the amount of difference or spread observed in variables, which is attributed to underlying factors and measurement noise.
Understanding Variance in Factor Analysis
Variance, fundamentally, measures how much individual data points in a set differ from the average value of that set. In the context of factor analysis, this concept is applied to the variables you measure. These measured variables are often called observed variables or manifest variables.
According to the principles of factor analysis, the variability (or variance) we see in these observed variables isn't just random. Instead, it's systematically influenced by hidden or unmeasured variables called latent variables or factors.
The reference provided highlights this key concept:
Factors, or latent variables, systematically influence observed variables (i.e., when we measure observed variables, those measurements/observations are caused, at least in part, by latent variables) Inter-individual differences (i.e., variance) in observed variables are due to latent variables and measurement error.
This means that when different individuals score differently on an observed variable (e.g., a question on a survey), these differences (the variance) can be broken down into parts:
- Variance explained by latent factors: This is the portion of the variance in an observed variable that is systematically influenced by the underlying factors that the variable measures. For example, if a survey question measures "extraversion," the variance in responses might be partly due to individuals' actual levels of extraversion (the latent factor).
- Variance due to measurement error: This is the portion of the variance that is random or unsystematic. It could be due to temporary mood, misunderstandings of the question, inconsistent testing conditions, or other random influences.
Components of Variance
In factor analysis, the total variance of an observed variable is typically partitioned into these components:
- Common Variance: The variance shared with other observed variables because they are influenced by the same latent factors. This is the part we are often most interested in when identifying factors.
- Unique Variance: The variance that is specific to that observed variable and not shared with others. It includes both:
- Specific Variance: Variance influenced by reliable, but unique, aspects not captured by the common factors.
- Error Variance (Measurement Error): Unreliable, random variance.
Practical Implications
Understanding variance in this way is crucial for factor analysis because:
- It helps determine how well the latent factors explain the observed data.
- It allows researchers to estimate the reliability of observed variables (how much variance is due to true scores vs. error).
- It guides the interpretation of factors – identifying which variables load onto which factors based on their shared variance.
For example, if you measure several different aspects of "customer satisfaction" (observed variables), factor analysis can help determine if the variance across these measures is largely explained by one or two underlying factors (like "product quality" and "service experience"), plus some random error. The higher the proportion of variance in the observed variables explained by the factors (common variance), the stronger the evidence for those underlying constructs.
