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Multivariate Statistics Overview

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Multiple Regression

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Used to understand the relationship between one continuous dependent variable and two or more independent variables. It estimates how various independent variables are associated with the dependent variable.

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Multivariate Analysis of Variance (MANOVA)

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A statistical method that allows for simultaneous testing of the effects of one or more independent variables on two or more dependent variables. It extends ANOVA to multiple dependent variables.

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Principal Component Analysis (PCA)

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A dimension-reduction tool that can be used to reduce a large set of variables to a small set that still contains most of the information in the large set.

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Factor Analysis

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Used for investigating whether a number of variables of interest are linearly related to a smaller number of unobservable factors.

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Cluster Analysis

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A statistical method used to group similar objects into respective categories based on a set of measured variables.

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Discriminant Function Analysis

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A classification technique used to determine which variables discriminate between two or more naturally occurring groups.

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Canonical Correlation Analysis

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Used to understand the relationship between two multidimensional variables. It finds the linear combinations of each set of variables that are maximally correlated with each other.

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Path Analysis

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Used to provide estimates of the magnitude and significance of hypothesized causal connections between sets of variables.

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Logistic Regression

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Used to model the probability of a binary outcome based on one or more predictor variables. It expresses the relationship between a binary dependent variable and independent variables.

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Probit Analysis

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Similar to logistic regression but uses the probit link function instead of the logistic link, primarily used when modeling binary outcomes.

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Multidimensional Scaling (MDS)

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A set of related ordination techniques used in information visualization for exploring similarities or dissimilarities in data.

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Hierarchical Linear Modeling (HLM)

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Also known as multilevel modeling, used for data that are organized at more than one level, e.g., students within classes.

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Survival Analysis

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A set of statistical approaches used to investigate the time it takes for an event of interest to occur.

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Partial Least Squares (PLS)

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Statistical method that bears some relation to principal components regression; instead of finding hyperplanes of maximum variance, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space.

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Hotelling's T-squared

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A multivariate statistical test used in hypothesis testing that generalizes Student's t-test to more than one variable.

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