Introduction to principal component analysis (pca)

Introduction to principal component analysis (pca)

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  MOHAMMED BORHANDDEN MUSAH FACULTYOF EDUCATION UNIVERSITI TEKNOLOGI MALAYSIA Introduction to Principal Component Analysis (PCA)
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  OUTLINE Purpose Definition Procedure  Assumptions  Requirement Graphical Application
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  Purpose 1. Data reduction. redundant variables  unclear variables  irrelevant variables 2. Structural detection.
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  Definition PCA is alinear combination of weighted observed variables.
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  Note  PCA, PA,EFA and CFA  Measured variable, observed variable, indicator variable, item and manifest variable.
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  Cont.  Latent construct/variable,factor, component, underlying construct and unobserved variable.  Case, observation, respondent, participant and subject.
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  Procedure 1. Assumptions (datascreening) Normality; the assumption is that the combination of variables follows a multivariate normal distribution. Both graphical and statistical methods are used to evaluate normality.
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  Cont. Homoscedasticity, refers tothe assumption that the dependent variable exhibits similar amounts of variance across the range of values for an independent variable. Both graphical and statistical methods are used to evaluate homoscedasticity.
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  Cont. Linearity, assumes thatthe relationship between variables is linear, or they perform better if the relationships are linear. Both graphical and statistical methods are used to evaluate linearity.
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  Cont. 2. Requirements  Thevariables included must be metric level or dichotomous (dummy-coded) nominal level.  The sample size must be greater than 50 (preferably 100).  The ratio of cases to variables must be 5 to 1 or larger.  The correlation matrix for the variables must contain 2 or more correlations of 0.30 or greater.
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  Cont.  Variables withMSA less than 0.50 must be removed.  The overall MSA should be 0.50 or higher.  The Bartlett test of sphericity should statistically significant.  Components weighted with only one variable, should be discarded.
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  Graphical Application