General Linear Model Flashcards
General Linear Model
Statistical model with one or more independent variable that predicts a dependent variable
Predictor
Independent variable
x
Outcome/ Criterion
Dependent variable
y
GLM goal
Try to account for as much variability as possible in the criterion/outcome
What kind of variable will the GLM not accept?
A categorical Y variable
What kind of scale of measurement is needed for the Y variable in the GLM
An interval or ratio Y variable
Nominal
Numbers are used to distinguish between objects
Classifying
Apples = 1, Oranges = 2
Ordinal
Numbers used to put items in order and to rank them
S = 0 M= 1 A= 2
1,0,2 (Ranked by age)
Interval
Equal intervals represent equal difference between items.
Differences are meaningful
A zero is not a true zero,
Ex: 0 degrees does not mean there is not any temperture
Ratio
Has a true zero
Meaningful zero point
Ex: time
Linear Regression
Simplest analysis in GLM
Foundation
Does length of relationship predict the degree of being upset after the breakup
Multiple Regression
Multiple predictors
Single DV
Does length of relationship, amount of commitment and age impact how sad you’ll be post a breakup
ANOVA’s
Analysis of categorical x variables
Look for or’s in the question
Do we tend to forgive parents, romantic partners or friends after a fight ?
One-way ANOVA
One categorical x variable and one continuous y variable
Critical factor in determining what analysis to use
Depends on how many x’s we have not how many levels x has
2 or more categorical x- variables and one continuous y-variable
m-way ANOVA
Mix of continuous and categorical x-variables
mixed-model regression
Mixed model regression
Analyzes cases when there is a combination of categorical and continuous x-variables
Difference between ANOVA’s and Regression
Regression: continuous x-variables
ANOVA’s: Categorical x-variables
ANCOVA
Deals with both types of variables
How can the GLM deal with multiple criterion variables
- Run multiple ANOVA’s/ Regression
Discriminant function analysis
Follow up on a multivariate test
Benefits of using the GLM
- Less formulas to remember
- Simplifies the math
- Clarifies similarities and differences between variables across a variety of tests
- Provides conceptual framework to work with
Data =
Model + Error
Data
Values obtained from scientific experiments
Scores on variable of interest for the researcher
Actual scores on Y
Y
Goal of collecting data
Explains why people score on the criterion the way they do
Build statistical models to explain and predict the scores on the criterion
Model
Prediction is a way of demonstrating an understanding of something
Combines one or more predictor variable to predict scores (y’)
Goal for the model
Build a statistical model that can accurately predict data
Types of models
Simple model
Less simple model
Little more complex model
Fairly complex model
Simple model
predicts a constant score for everyone
Everyone will get 85%
Less simple model
Predicts group mean for everyone
Class average was 82% after first exam so that is our prediction
Little more complex model
Adding an x variable to predict the outcome
Use study hours to predict grades
Fairly complex model
Add multiple predictors to predict outcome
Use study time, stress levels and sleep to predict grades
Error
Predicted scores compared to actual scores
Model’s accuracy in predicting y
Why study error?
To eliminate it and improve our model
Counting error
Counting the number of scores you got incorrect
100% error
Absolute error
Taking absolute values of the errors
Sum of the squared errors (SSE)
Square the error terms and then sum them
Why use the SSE?
Rewards for small error and punishes the model for large error
What is the SSE
Variance your data cannot explain
Accounted Variance + Error
100% variance
A model predicts a phenomenon well means
We understand our model
