This document outlines the symbols and notation used in various multivariate statistical models. It describes models such as multiple regression, discriminant analysis, factor analysis, principal components analysis, and analysis of variance models. For each model, it shows the graphical representation of the variables involved, indicating which variables are independent, dependent, continuous, categorical, and latent. It provides examples of how multivariate statistical models can be represented using these standardized symbols.

1. MULTIVARIATE STATISTICAL
MODELS’ SYMBOLS
Multivariate Regression
Discriminant Analysis
Multivariate Discriminat Analysis
Factor Analysis
Principal Components Analysis
Canonical Correlation Analysis
Variance Analysis Models
ANCOVA-MANCOA

2. Relationships
x y Two-way arrow
Explains just relationship between variable x and y. It
doesn’t tell the causality.
x y
One-way arrow
Explains causality between independent variable x
and dependent variable y.
x1 y
x2
Interaction
Explains both of two independent variables have
influence on dependent variable y.
x1
x2
y
x1 x2
Recursive Models
Explains causality flows in only one direction.

3. Symbols ofVariables
MANIFEST. Represents continuos variable.
LATENTVARIABLE. Represents latent variable.
Represents categorical (qualitative) variable.
Represents categorical (qualitative) variable that has three categories.

4. Student t
Although 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
y
independent
categorical (2 categories)
dependent
continuous

5. Multiple Regression Analysis
x1
x2
xp
y
independent
continuous
variables
dependent
continuous
variable
.
.
.

6. Discriminant Analysis
x1
x2
xp
independent
continuous
variables
dependent
categorical variable
that
has two categories
.
.
.
y

7. Multivariate Discriminant Analysis
x1
x2
xp
independent
continuous
variables
dependent
categorical variable
that
has categories higher than
two
.
.
.
y

8. Factor Analysis
x1
x2
x3
x4
Latent
Latent
independent
continuous
variables
latent
variables

9. Principal Components Analysis
x1
x2
x3
x4
Latent
Latent
independent
continuous
variables
latent
variables

10. Canonical Correlation Analysis
x1
x2 Latent
x3
x4
x5Latent
x6
x7
independent
continuous
variables
independent
continuous
variables
there is a relationship
between
latent
variables

11. VarianceAnalysis Models

12. One-Way ANOVA
y
independent
categorical
variable has to have
minimum 3 categories
x

13. InteractiveTwo-Way ANOVA
y
independent
categorical
variable has to have
minimum 2 categories
x2
x1

14. One-Way MANOVA
y1
y2
yp
independent
categorical
variables that have to have
more than two categories
(here as an example the
dependent variable x has 5
categories)
dependent
continuous
variables
.
.
.
y3
x

15. Two-way MANOVA
independent
categorical
variables has to have
minimum 2 categories
x2
x1
y1
y2
yp
dependent
continuous
variables
.
.
.
y3

16. Two-Way MANOVA with interaction
independent
categorical
variables has to have
minimum 2 categories
x2
x1
y1
y2
yp
dependent
continuous
variables
.
.
.
y3
x3

17. ANCOVA
x2
x1
covariate
factor
y
one categorical
+ one continuosu covariate
variable
dependent
continuous
variable