Date post: | 07-Apr-2018 |
Category: |
Documents |
Upload: | arvind-yadav |
View: | 228 times |
Download: | 0 times |
of 12
8/3/2019 Multivariate - Dependence Methods
1/12
DATA ANALYSISMultivariate dependence methods
8/3/2019 Multivariate - Dependence Methods
2/12
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
8/3/2019 Multivariate - Dependence Methods
3/12
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
8/3/2019 Multivariate - Dependence Methods
4/12
MULTICOLLINEARITY
Where two or more of theindependent variables are highlycorrelated can damage the effects
on multiple regression multicollinearity or collinearity
29 April 2012 4
8/3/2019 Multivariate - Dependence Methods
5/12
EXAMPLE
29 April 2012 5
http://example%20multreg.docx/http://example%20multreg.docx/8/3/2019 Multivariate - Dependence Methods
6/12
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.,
29 April 2012 6
8/3/2019 Multivariate - Dependence Methods
7/12
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
29 April 2012 7
8/3/2019 Multivariate - Dependence Methods
8/12
8/3/2019 Multivariate - Dependence Methods
9/12
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
29 April 2012 9
8/3/2019 Multivariate - Dependence Methods
10/12
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
8/3/2019 Multivariate - Dependence Methods
11/12
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
8/3/2019 Multivariate - Dependence Methods
12/12
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