Module 6 Flashcards
What is the main purpose of FA? What is the main purpose of PCA?
The aim of FA is to identify latent constructs underlying variables, while the aim of PCA is to reduce a large number of variables down to a smaller, more general set of variables. FA and PCA are basically the same, but have different practical applications
What technique is used to perform exploratory FA? What technique is used to perform confirmatory FA?
Exploratory = FA, more common Confirmatory = PCA, produces components. Confirmatory is often performed after exploratory, to see if your hypothesis eventuated.
What is an eigenvector? What is an eigenvalue?
An eigenvector represents an orientation, which remains unchanged when a linear transformation is applied to it. It is composed of correlated variables and is distinguished from other eigenvectors.
An eigenvalue represents the magnitude of the relevant eigenvector
What does orthogonal rotation assume? What does oblique rotation assume?
Orthogonal rotation assumes factors/components are not correlated.
Oblique rotation assumes factors/components are correlated
What is the meaningful loading cutoff for a factor/component?
.3/.4
What is the key difference between FA and PCA?
The key difference is in their goals for explaining variance. FA produces factors that only account for variance shared between variables. PCA produces components that account for all the variance in the variables.
What does Field (2013) suggest are the 3 main uses of FA?
1) To understand the structure of a set of variables
2) To develop a questionnaire to measure a variable
3) To reduce a data set to a more manageable size, while retaining the data set’s essential qualities
What are the five key decisions that must be considered before a researcher decides to use FA?
1) Study design, and particularly what variables are to be measured
2) Determining whether EFA is appropriate
3) Choice of model fitting procedure
4) Number of factors
Factor/component loading can be seen as the Pearson correlation between…?
A factor (eg: sociability) and a variable (eg: social skills). It represents the importance of a particular variable in explaining the variance in a factor. If we square the factor loading we obtain a measure of the substantive importance
What are the 3 ways to visualise factor analysis?
R-matrices, plots, mathematically.
R-matrix - cluster = bunch of highly correlated variables, can be considered a ‘factor’
Plots - the two axes represent two ‘factors’, the dots represent variables, the plot shows how each variable is related to each factor
Mathematically - think of FA and PCA as linear models. The factor/component loadings are the actual weights in the model. Equations - eg: comparing equation for sociability vs. equation for consideration. Each factor is a straight line (axis) when we think about it graphically, thus each can be written as an equation. Each equation will contain all the variables that were measured, but the b values next to each variable will be different for the two different factors/components (sociability and consideration)
With regards to the mathematical visualisation of factor analysis, what is the controversial assumption that underlies FA, but not PCA?
The assumption is that the ‘algebraic factors’ in the model represent real-world dimensions, such as sociability and consideration
What do we mean when we say the factor analysis model flips PCA on its head?
In PCA we predict components from measured variables, but in factor analysis we predict the measured variables from the underlying factors
What do the columns in a matrix represent? What do the rows represent?
Columns = factors/components
Rows = variables
Thus, each element in the matrix is a loading for a particular variable on one of the factors/components
In terms of discovering factors, if you want to generalise your results for a population, what do you need to use? If you only want to apply your findings to your sample, what do you need to use?
Generalise to population = inferential methods
Apply to sample = descriptive factors
What 3 types of variance comprise in a model?
Common variance, unique variance, and random variance.
Common variance = shared with other variables
Unique variance = only explained by that variable, not shared
Random variance = error variance (specific to one measure, but no reliably so)
The proportion of common variance = communality
