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Multivariate Statistics Overview
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Multiple Regression
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.
Multivariate Analysis of Variance (MANOVA)
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.
Principal Component Analysis (PCA)
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.
Factor Analysis
Used for investigating whether a number of variables of interest are linearly related to a smaller number of unobservable factors.
Cluster Analysis
A statistical method used to group similar objects into respective categories based on a set of measured variables.
Discriminant Function Analysis
A classification technique used to determine which variables discriminate between two or more naturally occurring groups.
Canonical Correlation Analysis
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.
Path Analysis
Used to provide estimates of the magnitude and significance of hypothesized causal connections between sets of variables.
Logistic Regression
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.
Probit Analysis
Similar to logistic regression but uses the probit link function instead of the logistic link, primarily used when modeling binary outcomes.
Multidimensional Scaling (MDS)
A set of related ordination techniques used in information visualization for exploring similarities or dissimilarities in data.
Hierarchical Linear Modeling (HLM)
Also known as multilevel modeling, used for data that are organized at more than one level, e.g., students within classes.
Survival Analysis
A set of statistical approaches used to investigate the time it takes for an event of interest to occur.
Partial Least Squares (PLS)
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.
Hotelling's T-squared
A multivariate statistical test used in hypothesis testing that generalizes Student's t-test to more than one variable.
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