Answer to the question no. 1
The variate is simply a linear combination or set of variables along with their weights which are empirically determined. The variate is very often known as a random variable.
A simple variate equation could be: Y = w1X1 + w2X2 + w3X3 + ….. + wnXn
Here, Y is the variate and dependent of the independent variables Xs and ws are the weights which are determined to achieve the best of specific multivariate techniques.
Sometimes it might be a little bit confusing. Generally multiple refers to the right hand side dimensions but multivariate refers to the dimensions from the left hand side (dependent). When there are many Y variables and also many X variables that would be Multivariate Multiple Regression (MVMR). Again, a regression analysis with only one dependent variable and several independent variables is never a multivariate regression, just a multiple regression. Strictly speaking, multivariate regression should refer to cases where there are multiple dependent variables while multiple regressions refer to those with one dependent variable but multiple independent variables. No matter what, a Multivariate analysis will always be referring to the dependent variable.
The MVMR reduces to the univariate multiple regression since it doesn’t know about relationships among the Ys. Therefore to have a truly multivariate model we need restrictions of some type, for example, a rank reduction or an SEM (i.e. Structural Equations Modeling), etc.
Answer to the question no. 2
Two Broad Types of Multivariate Methods:
1. Dependence – analyze dependent and independent variables at the same time.
2. Interdependence – analyze dependent and independent variables separately
Dependence techniques: a variable or set of variables is identified as the dependent variable to be predicted or explained by other variables known as independent variables.
ü Multiple Regression
ü Multiple Discriminant Analysis
ü Logit/Logistic Regression
ü Multivariate Analysis of Variance (MANOVA) and Covariance
ü Conjoint Analysis
ü Canonical Correlation
ü Structural Equations Modeling (SEM)
Interdependence techniques: involve the simultaneous analysis of all variables in the set, without distinction between dependent variables and independent variables.
ü Principal Components and Common Factor Analysis
ü Cluster Analysis
ü Multidimensional Scaling (perceptual mapping)
ü Correspondence Analysis
In selecting a proper Multivariate Technique, we should keep in mind few things:
1. What type of relationship is being examined – dependence or interdependence?
2. Dependence relationship: How many variables are being predicted?
ü What is the measurement scale of the dependent variable?
ü What is the measurement scale of the predictor variable?
3. Interdependence relationship: Are you examining relationships between variables, respondents, or objects?