multivariate - dependence methods

8/3/2019 Multivariate - Dependence Methods

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DATA ANALYSISMultivariate dependence methods


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MULTIPLE REGRESSION

Used as a descriptive tool in threetypes of situations It is used to develop a self weighing

estimating equation by which to predictvalues for a criterion variable from thevalues for several predictor variables

Controlling for confounding variables to

better evaluate the contribution of othervariables

To test and explain the casual theories,which is often referred to as path

analysis 29 April 2012 2


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When there are two or more than twoindependent variables, the analysis

concerning relationship is known as multiplecorrelation and the equation describing suchrelationship as the multiple regressionequation

When the independent variables are

regressed jointly against the dependentvariable, the individual correlations collapseinto what is called a multiple r or multiplecorrelation

The square of multiple r (R2) is the amount ofvariance explained in the dependent variableby the predictors

Such analysis when more than one predictoris jointly regressed against the criterion

variable is known as multiple regression29 April 2012 3


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MULTICOLLINEARITY

Where two or more of theindependent variables are highlycorrelated can damage the effects

on multiple regression multicollinearity or collinearity

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EXAMPLE

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http://example%20multreg.docx/http://example%20multreg.docx/


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DISCRIMINANT ANALYSIS

Researcher may classify individuals orobjects into one of two or more mutuallyexclusive and exhaustive groups on thebasis of a set of independent variables

It requires interval independent variablesand a nominal dependent variable Ex:- Brand preference and relationship toindividuals age, income, education etc.,

is to be studied Dependent variable brand preference Interval independent variable age, income,

etc.,

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Discriminant analysis is considered anappropriate technique when single dependentvariable happens to be non-metric and is to

be classified into two or more groups,depending upon its relationship with severalindependent variables which all happen to bemetric

Objective to predict an objects likelihood of

belonging to a particular group based onseveral independent variable i.e., to establisha procedure to find the predictors that bestclassify subjects

In case the dependent variable is classifiedinto more than two groups, we call multiDiscriminant analysis.

In case only two groups are to be formed, wecall Discriminant analysis

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It is an appropriate one when severalmetric dependent variables are

involved along with many non-metricexplanatory variables

MANOVA is specially applied

whenever the researcher wants to testhypotheses concerning multivariatedifferences in group responses to

experimental manipulations

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CANONICAL CORRELATIONANALYSIS

To simultaneously predict a set ofcriterion variables from their joint co-variance with a set of explanatoryvariables

To obtain a set of weights for thedependent and independent variables insuch a way that linear composite of the

criterion variables has a maximumcorrelation with the linear composite ofthe explanatory variables

The relationship between two or more

dependent variables and several29 April 2012 10


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Canonical correlation analysis (CCA) is a way of measuring thelinear relationship between two multidimensional variables.

It finds two bases, one for each variable, that are optimal with

respect to correlations and, at the same time, it finds thecorresponding correlations.

In other words, it finds the two bases in which the correlation matrixbetween the variables is diagonal and the correlations on thediagonal are maximized. The dimensionality of these new bases isequal to or less than the smallest dimensionality of the two variables.

An important property of canonical correlations is that they areinvariant with respect to affine transformations of the variables. Thisis the most important difference between CCA and ordinarycorrelation analysis which highly depend on the basis in which thevariables are described.

CCA was developed by H. Hotelling . Although being a standard tool in statistical analysis, where

canonical correlation has been used for example in economics,medical studies, meteorology and even in classification of maltwhisky,

It is surprisingly unknown in the fields of learning and signalprocessing. 29 April 2012 11


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Relate Grade school adjustment to health and physical

maturity of the child

provided Each child has a adjustment scores (tests,teachers ratings, parents ratings and so on)

Physical maturity scores (heart rate, height,weight, index of intensity of illness and so on)

Objective to discover factors separately inthe two sets of variables such that themultiple correlation between sets of factorswill be the maximum possible

Common variance Finding the weights requires factor analysis with

two matrices Results in over all description of the presence or

absence a relationship between the sets of

variables 29 April 2012 12

multivariate - dependence methods

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