multivariate statistical models’ symbols
TRANSCRIPT
MULTIVARIATE STATISTICAL MODELS’
SYMBOLSMultivariate Regression
Discriminant AnalysisMultivariate Discriminat Analysis
Factor AnalysisPrincipal Components AnalysisCanonical Correlation Analysis
Variance Analysis ModelsANCOVA-MANCOA
Relationshipsx y Two-way arrow
Explains just relationship between variable x and y. It doesn’t tell the causality.
x yOne-way arrowExplains causality between independent variable x and dependent variable y.
x1 y
x2
InteractionExplains both of two independent variables have influence on dependent variable y.
x1
x2
y
x1 x2Recursive ModelsExplains causality flows in only one direction.
Symbols of Variables
MANIFEST. Represents continuos variable.
LATENT VARIABLE. Represents latent variable.
Represents categorical (qualitative) variable.
Represents categorical (qualitative) variable that has three categories.
Student tAlthough Student t test is not a multivariate statistical analysis, it underlies the linear dependent multivariate statistical models.
1st group of independent variable X
2nd group of independent variable X
x
dependent variable Y
yindependentcategorical (2 categories)
dependentcontinuous
Multiple Regression Analysisx1
x2
xp
y
independentcontinuous variables
dependentcontinuous
variable
.
.
.
Discriminant Analysisx1
x2
xp
independentcontinuous variables
dependentcategorical variable
thathas two categories
.
.
.
y
Multivariate Discriminant Analysisx1
x2
xp
independentcontinuous variables
dependentcategorical variable
thathas categories higher than
two
.
.
.
y
Factor Analysisx1
x2
x3
x4
Latent
Latent
independentcontinuous variables
latent variables
Principal Components Analysisx1
x2
x3
x4
Latent
Latent
independentcontinuous variables
latent variables
Canonical Correlation Analysisx1
x2 Latent
x3
x4
x5Latent
x6
x7
independentcontinuous variables
independentcontinuous variables
there is a relationship between
latent variables
Variance Analysis Models
One-Way ANOVA
y
independentcategorical
variable has to have minimum 3 categories
x
Interactive Two-Way ANOVA
y
independentcategorical
variable has to have minimum 2 categories
x2
x1
One-Way MANOVAy1
y2
yp
independentcategorical
variables that have to have more than two categories(here as an example the
dependent variable x has 5 categories)
dependentcontinuous variables
.
.
.
y3
x
Two-way MANOVA
independentcategorical
variables has to have minimum 2 categories
x2
x1
y1
y2
yp
dependentcontinuous variables
.
.
.
y3
Two-Way MANOVA with interaction
independentcategorical
variables has to have minimum 2 categories
x2
x1
y1
y2
yp
dependentcontinuous variables
.
.
.
y3
x3
ANCOVA
x2
x1
covariate
factor
y
one categorical+ one continuosu covariate
variable
dependentcontinuous
variable