Multivariate Methods

Multivariate Methods Pattern Recognition and Hypothesis Testing

Goals in Multivariate Analysis • Model building – predicting metric variable from others • Predicting dichotomies and counts – generalized linear model • Testing/predicting groups • Reducing the number of dimensions • Exploring count data

Goals, cont • Distances between items, individuals, and assemblages • Grouping cases - classification

Model Building • Multiple Regression • Single response variable and multiple explanatory variables • Search for a parsimonious, meaningful model

Generalized Linear Model • A generalization of the linear model uses a link function to connect the linear model and the response • Logistic regression for predicting dichotomous data • Poisson regression to predict counts

Testing Groups • Discriminant Functions • Confirming groups defined on independent grounds • Matching new observations to existing groups • Applications – compositional analysis, sex determination, ethnicity • Problems – normal distributions assumed, sample size requirements

Reducing Dimensionality • Principal Components • Many correlated variables • Observed variables approximate what we want to study – grouping variables • Applications - assemblage data, measurement data on artifacts • Problems – evaluating significance of results and interpretation

Patterns in Count Data • Correspondence analysis • Examining variables and cases simultaneously • Applications – assemblage comparisons (sites, areas within sites, features) • Problems – Interpretation of the results

Measuring Distance • Multidimensional scaling • Variables converted to distances between cases • Applications – measurements • Problems - Interpretation

Classification (Grouping) • Cluster Analysis • Finding clusters in multi-dimensional space – grouping cases • Applications – assemblages, artifacts, features • Problems – “real” vs. created clusters, number of clusters

Multivariate Methods