GRA 6020 Multivariate Statistics

GRA 6020Multivariate Statistics

Ulf H. Olsson

Professor of Statistics

Ulf H. Olsson

Multivariate Statistics

• 1) Examining relationships with respect to a single variable

• Univariate Analysis• Univariate Distributions

• 2) Examining relationships with respect to two or more variables simultaneously

• Multivariate Analysis• Multivariate Distributions

Ulf H. Olsson

Statistical Models

• Statistical models are mathematical representations of population behavior; they describe salient features of the hypothesized process of interest among individuals in the target population. When you use a particular statistical model to analyze a particular set of data, you implicitly declare that this population model gave rise to these sample data.

Ulf H. Olsson

True Process

TheoreticalDomain

Empirical Domain

Making Sense

Ulf H. Olsson

Relationships (Stochastic)

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Loyalty

Branch

Loan

Savings

Satisfaction

Ulf H. Olsson

Univariate Normal Distribution•

•

Ulf H. Olsson

Bivariate normal distribution

Ulf H. Olsson

Standard Normal density functions

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Ulf H. Olsson

Regression Analysis/OLS-Regression

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Ulf H. Olsson

Factor Analysis

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pi

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Ulf H. Olsson

Structure Equation Modeling

Ulf H. Olsson

Regression Models

•All variables, both ys and xs, are directly observed

Ulf H. Olsson

Factor Models

•Observed variables are ”linked” to latent variables (factors)

Ulf H. Olsson

Structural Equation Models

•Regression models where all variables are latent (factors)