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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)
1131211 SavingsLoanBranchonSatisfacti
221 onSatisfactiLoyalty
Loyalty
Branch
Loan
Savings
Satisfaction
Ulf H. Olsson
Univariate Normal Distribution•
•
Ulf H. Olsson
Bivariate normal distribution
Ulf H. Olsson
Standard Normal density functions
2
2
2
1)(
u
eu
)2()1(2
1
2
222
)1(2
1),(
vuvu
evu
),....,('
;)2(
1),...,.(
21
)'2
1(
2/12/21
1
n
nn
uuu
euuu
u
uu
Ulf H. Olsson
Regression Analysis/OLS-Regression
ikikiii xxxy .....2211
Ulf H. Olsson
Factor Analysis
pq
pi
x iqqi
,...,3,2,1
.....2211
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)