Summary of Advanced Procedures

The General Linear Model is “general” because it includes a broad group of procedures, including correlation, regression and the more complex linear models. And it includes both continues and discrete variables. It’s linear because it assumes that the relationship between model components is consistent. When one variable goes up (has larger numbers), the other variable consistent reacts. The reaction can be go the same way (positive) or go the opposite way (negative). But the assumption is that changes in one variable will be accompanied by changes in the other variable.

Another assumption is that causation may not be proved but it can be inferred. Although random assignment might increase one’s confidence in cause-effect conclusions, causation can be inferred based simply on consistency. Such an assumption can be risky but we do it all the time. We assume that the earth gets warm because the sun rises. We’ve never randomly assigned the sun to rising and now rising conditions. But we feel quite confident is our conclusion that the sun causes the heat, and no the other way around.

Here are nine applications of the General Linear Model

Continuous Models compare:

  a. frequency distribution        One variable (predictor or criterion)
  b. correlation                        Two regressions
  c. regression                         Single predictor; single criterion                 Same as F test or t-squared
  d. multiple regression            Multiple predictors; single criterion            Same as ANOVA
  e. multivariate analysis           Multiple predictors; multiple criteria 
  f. causal modeling                 Multiple measures of a factor

Discrete Models Compare:

  a. t-test                                 2 means; 1 independent variable 
  b. one-way ANOVA            3 or more means; 1 independent variable 
  c. factorial ANOVA             Multiple means on 2+ independent variables