met 2212 multivariate statistics
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Met 2212Multivariate 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
Bivariate normal distribution
Ulf H. Olsson
Regression Analysis
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)
Ulf H. Olsson
STATISTICAL SYMBOLS - NOTATION
Estimator
VectorParameter
MatrixianceCoPopulation
MatrixianceCoSampleS
MatrixDataX
:
:
var:
var:
:
Ulf H. Olsson
STATISTICAL SYMBOLS - NOTATION
ij
ij
ij
Ulf H. Olsson
STATISTICAL SYMBOLS - NOTATION
iablesdependenterrortmeasuremen
iablestindependenerrortmeasuremen
termerrorrandom
iablelatentdependent
iablelatenttindependen
iableobserveddependentYy
iableobservedtindependenXx
i
i
i
i
i
ij
ij
var
var
var
var
var
var
ε
δ
ζ
η
ξ
Ulf H. Olsson
STATISTICAL SYMBOLS - NOTATION
),(
),cov(
),cov(
),cov(
ji
ji
ji
ji
cor
Ulf H. Olsson
True Process
TheoreticalDomain
Empirical Domain
)()(,,
andS
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