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