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  1. Why Factor Analysis? 1. Testing of theory ! Explain covariation among multiple observed variables by ! Mapping variables to latent constructs (called “factors”) 2. Understanding the structure underlying a set of measures ! Gain insight to dimensions ! Construct validation (e.g., convergent validity) 3. Scale development

  2. q factors, rather than components, that F is the matrix of factor scores and w is the matrix of factor loadings. The variables in X are called observable or manifest variables, those in F are hidden or latent. (Technically ε is also latent.) Before we can actually do much with this model, we need to say more about the

  3. Factor Analysis (FA) assumes the covariation structure among a set of variables can be described via a linear combination of unobservable (latent) variables called factors. FA and PCA have similar themes, i.e., to explain covariation between variables via linear combinations of other variables.

  4. Methods of Estimating the Factor Analysis Model: Principal Factor Analysis • The Principal Factor Analysis approach to estimation relies on estimating the communalities. • It uses the reduced covariance matrix S∗ = S−Ψˆ. • The diagonal elements of S∗ are s2 i − ψˆi = ˆh2 i, the (estimated) communality for the i-th variable.

  5. Factor Analysis can beExploratory: The goal is to describe and summarize the data by explaining a large number of observed variables in terms of a smaller number of latent variables (factors). The factors are the reason the observable variables have the

  6. Shan-Yu Chou 1 Factor Analysis • Combines questions or variables to create new factors • Combines objects to create new groups • Uses in Data Analysis – To identify underlying constructs in the data from the groupings of variables that emerge – To reduce the number of variables to a more manageable set Shan-Yu Chou 2 1. Introduction ...

  7. Factor Analysis (FA) assumes the covariation structure among a set of variables can be described via a linear combination of unobservable (latent) variables called factors. FA and PCA have similar themes, i.e., to explain covariation between variables via linear combinations of other variables.

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