Multivariate Data Analysis refers to any
statistical technique used to analyze data that arises from more than one
variable.
Canonical Correlation/Regression
It is also known as multiple multiple
regression or multivariate multiple regression. All other multivariate techniques
may be viewed as simplifications or special cases of this “fully multivariate
general linear model.”
We have two sets of variables (set X and
set Y). We wish to create a linear combination of the X variables (b1X1 + b2X2
+ .... + bpXp), called a canonical variate, that is maximally correlated with a
linear combination of the Y variables (a1Y1 + a2Y2 + .... + aqYq). The
coefficients used to weight the X’s and the Y’s are chosen with one criterion,
maximize the correlation between the two linear combinations.
Logistic Regression
Logistic regression is used to predict a
categorical (usually dichotomous) variable from a set of predictor variables.
With a categorical dependent variable, discriminant function analysis is
usually employed if all of the predictors are continuous and nicely
distributed; logit analysis is usually employed if all of the predictors are
categorical; and logistic regression is often chosen if the predictor variables
are a mix of continuous and categorical variables and/or if they are not nicely
distributed (logistic regression makes no assumptions about the distributions
of the predictor variables).
Principal Components
and Factor Analysis
Here we start out with one set of
variables. The variables are generally correlated with one another. We wish to
reduce the (large) number of variables to a smaller number of components or
capture most of the variance in the observed variables. Each factor (or
component) is estimated as being a linear (weighted) combination of the
observed variables. We could extract as many factors as there are variables,
but generally most of them would contribute little, so we try to get a few
factors that capture most of the variance. Our initial extraction generally
includes the restriction that the factors be orthogonal, independent of one
another.
Discriminant Function
Analysis
It is to predict group membership from a
set of two or more continuous variables. The analysis creates a set of
discriminant functions (weighted combinations of the predictors) that will
enable us to predict into which group a case falls, based on scores on the
predictor variables (usually continuous, but could include dichotomous
variables and dummy coded categorical predictors). The total possible number of
discriminant functions is one less than the number of groups, or the number of
predictor variables, whichever is less.
Multiple Analysis Of
Variance, MANOVA
In MANOVA the Y’s are weighted to
maximize the correlation between their linear combination and the X’s. A
different linear combination (canonical variate) is formed for each effect
(main effect or interaction—in fact, a different linear combination is formed
for each treatment df—thus, if an independent variable consists of four groups,
three df, there are three different linear combinations constructed to
represent that effect, each orthogonal to the others). Standardized
discriminant function coefficients (weights for predicting X from the Y’s) and
loadings (for each linear combination of Y’s, the correlations between the
linear combination and the Y’s themselves) may be used better to define the
effects of the factors and their interactions. One may also do a “step down
analysis” where one enters the Y’s in an a priori order of importance (or based
solely on statistical criteria, as in stepwise multiple regression). At each
step one evaluates the contribution of the newly added Y, above and beyond that
of the Y’s already entered.
Cluster Analysis
In a cluster analysis the goal is to
cluster cases (research units) into groups that share similar characteristics.
Contrast this goal with the goal of principal components and factor analysis,
where one groups variables into components or factors based on their having
similar relationships with latent
variables.
Tidak ada komentar:
Posting Komentar