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