OVERVIEW OF MULTIVARIATE STATISTICAL DATA ANALYSIS

	EXPLORATORY/DESCRIPTIVE MULTIVARIATE ANALYSIS					CONFIRMATORY/INFERENTIAL MULTIVARIATE ANALYSIS
	DATA MINING					DATA CRAFTING
		DATA EXPLORATION PATTERN RECOGNITION					STATISTICAL INFERENCE
			LOOKING FOR PATTERNS					TEST HYPOTHESES
			EXPLORING RELATIONSHIPS					FIT & TEST THE MODELS
			FORM HYPOTHESES
			SELECT MODELS

PATTERN RECOGNITION
	UNSUPERVISED (NO PRIOR KNOWLEDGE)	SUPERVISED ( PRIOR KNOWLEDGE)
PATTERNS OF "SIMILARITY" BETWEEN VARIABLES	ORDINATION PCA FACTOR ANALYSIS	DISCRIMINANT ANALYSIS GLM REGRESSION PATH ANALYSIS
PATTERNS OF "SIMILARITY" BETWEEN INDIVIDUALS	ORDINATION PRINCIPAL COMPONENT ANALYSIS MDS CLUSTER ANALYSIS

 

MULTIVARIATE TECHNIQUE		EXPLORATORY VS CONFIRMATORY	DATA TYPES Dependent/Independent	USE
Basic Numerical Multivariate Data Exploration
	Sample Mean Vector Sample Covariance Sample Correlation	EXPLORATORY	Interval, ratio	* Data exploration, description, understanding relationships
Bssic Graphical Multivariate Data Exploration
	The scatterplot	EXPLORATORY	interval, ratio/interval, ratio	* Data exploration, description, understanding relationships
	Scatterplot Matrix		interval, ratio/interval, ratio	* Assessment of many bivariate relationship at the same time
	Enhanced Scatterplots			* Add of univariate behaviour (boxplots, histograms, density estimates) * Simplify functional relation (data smoothing) * Summarize bivariate behaviour (bi-boxplots)
	Coplots and Trellis Graphics		interval, ratio/any	* Understand Conditional joint relationship of two variables given another set of variables (coplots) * Understand higher dimensional dependence structure by using lower dimensional graphs (trellis graphics)
	Probability Plots		interval, ratio	* Check distributional assumptions
	Other Plots: Star plots, Chernoff's Faces etc.		interval, ratio/any	* View the multivariate data in a easier way to understand
Principal Components Analysis
		EXPLORATORY	interval, ratio	* Reduce the dimension of the data, deal with less number of variables * Seek one- or two- dimensional projection of the data that maximizes some measure of "interestingness" (Projection Pursuit) * Ease the interpretation
Correspondence  Analysis
		EXPLORATORY	nominal,ordinal/nominal, ordinal	* Display the association among a set of categorical variables in a type of scatterplot or map. * Obtain low dimensional representation of multivariate categorical data
Multidimensional Scaling (MDS)
		EXPLORATORY	any/any	* Extract a structure in observed proximity matrces * Identify the dimension on which the subjects make their similarity judgements
Cluster Analysis
		EXPLORATORY	any/any	* Classification of individuals to clusters
The Generalized Linear Models (GLM)
		CONFIRMATORY	interval, ratio/any	* Predict and/or explain the relationship between explanatory and response variables linearly.
Regression and MANOVA
		CONFIRMATORY		* Explain the relationship between explanatory and response variables by using GLM with identity link function and a normal error term
Log-Linear and Logistic Models
		CONFIRMATORY	nominal, ordinal/nominal, ordinal	* Examine the relationship between categorical variables
Multivariate Response Models
	Repeated Measures	CONFIRMATORY		* Predict multivariate response, not only single response given multiple explanatory variables
	Random Effects
	Logistic Models
	Marginal Models for Binary Response
	Marginal Modelling
	Generalized Random Effects
Discrimination, Classification, and Pattern Recognition
	Allocation Rules	CONFIRMATORY		* For known groups, devise rules which can allocate previously unclassified objects or individuals into these groups
	Logistic Discrimination
	Pattern Recognition, Neural Networks
Exploratory Factor Analysis
		EXPLORATORY	interval, ratio	* Investigate the relationship between measured/manifest variables and factors without making any prior assumptions about which manifest variables are related with to which factors
Confirmatory Factor Analysis
		CONFIRMATORY	interval, ratio	* Test a specific factor structure in which particular manifest variables relate to particular factors NOTE: Factor analysis postulates a model for the data, PCA does not
Covariance Structure Models
	Path Analysis	CONFIRMATORY	interval, ratio	* Design FA model in which particular manifest variables are allowed to relate to particular latent variables

 

 

Engin A. Sungur, Spring 2005