Multivariate Statistical Analysis 多變量統計
分析擁有多個變數的資料
- 探討資料彼此之間的關聯性或是釐清資料的結構
Types of analysis
MANOVA - Multivariate analysis of variance
- extends the analysis of variance to cover cases where there is more than one dependent variable to be analyzed simultaneously; see also Multivariate analysis of covariance (MANCOVA).
Multivariate regression
- attempts to determine a formula that can describe how elements in a vector of variables respond simultaneously to changes in others. For linear relations, regression analyses here are based on forms of the general linear model. Some suggest that multivariate regression is distinct from multivariable regression, however, that is debated and not consistently true across scientific fields.
PCA - 主成分分析 Principal components analysis
- creates a new set of orthogonal variables that contain the same information as the original set. It rotates the axes of variation to give a new set of orthogonal axes, ordered so that they summarize decreasing proportions of the variation.
Factor analysis 因素分析
- is similar to PCA but allows the user to extract a specified number of synthetic variables, fewer than the original set, leaving the remaining unexplained variation as error. The extracted variables are known as latent variables or factors; each one may be supposed to account for covariation in a group of observed variables.
Clustering systems 聚類分析
- assign objects into groups (called clusters) so that objects (cases) from the same cluster are more similar to each other than objects from different clusters.
Canonical correlation analysis
- finds linear relationships among two sets of variables; it is the generalised (i.e. canonical) version of bivariate correlation.
RDA - Redundancy analysis
- is similar to canonical correlation analysis but allows the user to derive a specified number of synthetic variables from one set of (independent) variables that explain as much variance as possible in another (independent) set. It is a multivariate analogue of regression.
CA - Correspondence analysis, or reciprocal averaging
- finds (like PCA) a set of synthetic variables that summarise the original set. The underlying model assumes chi-squared dissimilarities among records (cases).
CCA - 典型相關分析 Canonical (or "constrained") correspondence analysis
- for summarising the joint variation in two sets of variables (like redundancy analysis); combination of correspondence analysis and multivariate regression analysis. The underlying model assumes chi-squared dissimilarities among records (cases).
Multidimensional scaling
- comprises various algorithms to determine a set of synthetic variables that best represent the pairwise distances between records. The original method is principal coordinates analysis (PCoA; based on PCA).
Discriminant analysis 判別分析, or canonical variate analysis
- attempts to establish whether a set of variables can be used to distinguish between two or more groups of cases.
LDA - Linear discriminant analysis
- computes a linear predictor from two sets of normally distributed data to allow for classification of new observations.
Recursive partitioning
- creates a decision tree that attempts to correctly classify members of the population based on a dichotomous dependent variable.
Artificial neural networks
- extend regression and clustering methods to non-linear multivariate models.
Statistical graphics
- such as tours, parallel coordinate plots, scatterplot matrices can be used to explore multivariate data.
Simultaneous equations models
- involve more than one regression equation, with different dependent variables, estimated together.
Vector autoregression
- involves simultaneous regressions of various time series variables on their own and each other's lagged values.
PRC - Principal response curves analysis
- is a method based on RDA that allows the user to focus on treatment effects over time by correcting for changes in control treatments over time.
SEM - 結構方程式模式 Structural Equation Model
LISREL - 線性結構相關模式 Linear Structure Relation