7.1.15 - The Two-Sample Hotelling's T-Square Test Statistic.7.1.12 - Two-Sample Hotelling's T-Square.7.1.11 - Question 2: Matching Perceptions.7.1.8 - Multivariate Paired Hotelling's T-Square.7.1.7 - Question 1: The Univariate Case.7.1.4 - Example: Women’s Survey Data and Associated Confidence Intervals.7.1.1 - An Application of One-Sample Hotelling’s T-Square.Lesson 7: Inferences Regarding Multivariate Population Mean.6.2 - Example: Wechsler Adult Intelligence Scale.Lesson 6: Multivariate Conditional Distribution and Partial Correlation.5.2 - Interval Estimate of Population Mean.5.1 - Distribution of Sample Mean Vector.Lesson 5: Sample Mean Vector and Sample Correlation and Related Inference Problems.4.7 - Example: Wechsler Adult Intelligence Scale.4.6 - Geometry of the Multivariate Normal Distribution.4.4 - Multivariate Normality and Outliers.4.3 - Exponent of Multivariate Normal Distribution.Lesson 4: Multivariate Normal Distribution.Lesson 3: Graphical Display of Multivariate Data.Lesson 2: Linear Combinations of Random Variables.1.5 - Additional Measures of Dispersion.Lesson 1: Measures of Central Tendency, Dispersion and Association.Examples of fields where factor analysis is involved include physiology, health, intelligence, sociology, and sometimes ecology among others. A technique called factor rotation is employed toward that goal. Ideally, we like each variable to contribute significantly to only one component. A particular variable may, on occasion, contribute significantly to more than one of the components. Recall that in PCA, the interpretation of the principal components is often not very clean.
In both PCA and FA, the dimension of the data is reduced.
In factor analysis, we model the observed variables as linear functions of the “factors.” In principal components, we create new variables that are linear combinations of the observed variables. In one sense, factor analysis is an inversion of principal components. The method is similar to principal components although, as the textbook points out, factor analysis is more elaborate. It is a widely used tool and often controversial because the models, methods, and subjectivity are so flexible that debates about interpretations can occur. These unobserved factors are more interesting to the social scientist than the observed quantitative measurements.įactor analysis is generally an exploratory/descriptive method that requires many subjective judgments. For example, a basic desire of obtaining a certain social level might explain most consumption behavior. Factor Analysis is a method for modeling observed variables, and their covariance structure, in terms of a smaller number of underlying unobservable (latent) “factors.” The factors typically are viewed as broad concepts or ideas that may describe an observed phenomenon.
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