Which test: Predict the value (or group membership) of one variable based on the value of another based on their relationship / association

When the research objective is to use one or more predictor variables to predict the values (or group membership) of one or more outcome variables, we have a choice among different statistical procedures, depending on the following variable characteristics:
 
Number of variables
One (or more) dependent / outcome variable(s) and one (or more) independent / predictor variable(s)
 
Examples: 
  1. To what extent can we use the values of a predictor variable to predict the values of an outcome variable? (predict the values)
  2. Which predictor variables best predict whether a respondent will be a buyer or a non-buyer? (predict group membership)
  3. Based on the values of the predictor variables, can we estimate the probability that a respondent will be a buyer or a non-buyer (predict group membership)


When the dependent variable is BINOMIAL / BINARY / DICHOTOMOUS

  1. Binary Discriminant Analysis (predicts group membership)
  2. Simple Binary Logistic Regression (predicts group membership)
  3. Multiple Binary Logistic Regression (predicts group membership)
  4. Note that logistic regression is generally preferred over discriminant analysis for a binary outcome variable due to fewer assumptions by logistic regression. However, if data assumptions of discriminant analysis are met, it is preferred to use discriminant analysis.
 
When the dependent variable is NOMINAL
  1. Multiple Discriminant Analysis (predicts group membership)
  2. Multinomial Logistic Regression (predicts group membership)
  3. Preference is for Discriminant Analysis rather than Logistic Regression for a nominally (>2 levels) scaled outcome variable.
 
When the dependent variable is ORDINAL / RANK-DATA
  1. Ordinal Logistic Regression (predicts group membership)
  2. Categorical Regression (CATREG) (predicts values along a categorical outcome variable)
 
When the dependent variable is INTERVAL and passed the assumption of normality (parametric data)
  1. Simple Linear Regression (single predictor of values)
  2. Multiple Linear Regression (more than one predictors of values)
  3. Multivariate Multiple Linear Regression (more than one outcome and more than one predictors of values)
 
When the dependent variable is INTERVAL but failed the assumption of normality (non-parametric data)
  1. Non-parametric Regression (e.g. kernel estimation, local polynomal regression and smoothing splines to predict values). 
______________________________________________________________
zza57a