General Linear Models -- #2 2x2 – main effects 2x2 with interactions 2x3 – main effects 2x3 with interactions 3x3 – main effects 3x3 with interactions.

Slides:

Advertisements

Similar presentations

Overview of Techniques Case 1 Independent Variable is Groups, or Conditions Dependent Variable is continuous ( ) One sample: Z-test or t-test Two samples:

Advertisements

P u t y o u r h e a d o n m y s h o u l d e r.

Solving Linear Programming Problems Shubhagata Roy.

1 1 Chapter 5: Multiple Regression 5.1 Fitting a Multiple Regression Model 5.2 Fitting a Multiple Regression Model with Interactions 5.3 Generating and.

FACTORIAL ANOVA Overview of Factorial ANOVA Factorial Designs Types of Effects Assumptions Analyzing the Variance Regression Equation Fixed and Random.

ANCOVA Workings of ANOVA & ANCOVA ANCOVA, Semi-Partial correlations, statistical control Using model plotting to think about ANCOVA & Statistical control.

Linear vs. exponential growth Linear vs. exponential growth: t = 0 A = 1x(1+1) 0 = 1 A = 1x0 + 1 = 1.

Regression Models w/ k-group & Quant Variables Sources of data for this model Variations of this model Main effects version of the model –Interpreting.

1 Chapter 3 Multiple Linear Regression Ray-Bing Chen Institute of Statistics National University of Kaohsiung.

Introduction to the General Linear Model (GLM) l 1 quantitative variable & 1 2-group variable l 1a  main effects model with no interaction l 1b  interaction.

A 1 A 2 A 3 A 4 B B B

ANCOVA Workings of ANOVA & ANCOVA ANCOVA, Semi-Partial correlations, statistical control Using model plotting to think about ANCOVA & Statistical control.

Statistics 350 Lecture 16. Today Last Day: Introduction to Multiple Linear Regression Model Today: More Chapter 6.

Introduction the General Linear Model (GLM) l what “model,” “linear” & “general” mean l bivariate, univariate & multivariate GLModels l kinds of variables.

1 BA 275 Quantitative Business Methods Simple Linear Regression Introduction Case Study: Housing Prices Agenda.

Psychology 202b Advanced Psychological Statistics, II March 1, 2011.

DATA ANALYSIS III MKT525. Multiple Regression Simple regression:DV = a + bIV Multiple regression: DV = a + b 1 IV 1 + b 2 IV 2 + …b n IV n b i = weight.

Completely Randomized Factorial Design With Two Factors Example A police department in a big city want to assess their human relations course for new officers.

General Linear Models -- #1 things to remember b weight interpretations 1 quantitative predictor 1 quantitative predictor & non-linear component 1 2-group.

Bivariate & Multivariate Regression correlation vs. prediction research prediction and relationship strength interpreting regression formulas process of.

Introduction the General Linear Model (GLM) l 2 quantitative variables l 3a  main effects model with no interaction l 3b  interaction model l 2 categorical.

How Well Can You Measure?

Drawing Linear Graphs Starter: Multiplying Negative Numbers (1) -3 x 4 = (4) = (7) -6 x = (10) -3 x 3 +9 = (13) 7 x = (16) 4 x

Completing the ANOVA From the Summary Statistics.

Difference of Squares Chapter 8.8. Difference of Squares (Definition)

Coding Multiple Category Variables for Inclusion in Multiple Regression More kinds of predictors for our multiple regression models Some review of interpreting.

Factor: Factor: 1. s 2 r 2 – 4s 4 1. s 2 r 2 – 4s b b 3 c + 18b 2 c b b 3 c + 18b 2 c 2 3. xy + 3x – 2y xy + 3x – 2y -

Regression Models w/ 2 Quant Variables Sources of data for this model Variations of this model Main effects version of the model –Interpreting the regression.

Regression Models w/ 2-group & Quant Variables Sources of data for this model Variations of this model Main effects version of the model –Interpreting.

Plotting Linear Main Effects Models Interpreting 1 st order terms w/ & w/o interactions Coding & centering… gotta? oughta? Plotting single-predictor models.

Analysis of Covariance Combines linear regression and ANOVA Can be used to compare g treatments, after controlling for quantitative factor believed to.

Examples of the Unification Algorithm { X = int, Y = X  X } unify({ X = int, Y = X  X }) S=X, T=int, C’={Y = X  X} = [ X  int ] ; unify({ Y = int 

Natural Deduction for Predicate Logic Bound Variable: A variable within the scope of a quantifier. – (x) Px – (  y) (Zy · Uy) – (z) (Mz  ~Nz) Free Variable:

Psychology 202a Advanced Psychological Statistics November 12, 2015.

From Theory to Practice: Efficient Join Query Processing in a Parallel Database System Shumo Chu, Magdalena Balazinska and Dan Suciu Database Group, CSE,

2-2 Linear Equations Obj: identify linear equations/functions Write linear equations in standard form.

“GLMrous designs” “GLMrous designs” “Are you regressed or something?” “Pseudonyms & aliases” “Pseudonyms & aliases” Models I Models II.

Variance Stabilizing Transformations. Variance is Related to Mean Usual Assumption in ANOVA and Regression is that the variance of each observation is.

ANCOVA Workings of ANOVA & ANCOVA ANCOVA, partial correlations & multiple regression Using model plotting to think about ANCOVA & Statistical control Homogeneity.

Derivative Examples 2 Example 3

Partial Fractions. After completing this chapter you should be able to: Add and subtract two or more fractions Convert an expression with linear factors.

Topics, Summer 2008 Day 1. Introduction Day 2. Samples and populations Day 3. Evaluating relationships Scatterplots and correlation Day 4. Regression and.

Effect Sizes & Power Analyses for k-group Designs Effect Size Estimates for k-group ANOVA designs Power Analysis for k-group ANOVA designs Effect Size.

S ystems Analysis Laboratory Helsinki University of Technology 1 Harri Ehtamo Kimmo Berg Mitri Kitti On Tariff Adjustment in a Principal Agent Game Systems.

Goals:  Solve linear inequalities using multiplication and division  Use inequalities to solve real life problems. Eligible Content:  A / A

Human Communication Models and Theories. How can we describe the process of communication?

Plotting Non-linear & Complex Main Effects Models

An Adjustment Scheme for a Buyer-Seller Game

Inference in Simple Linear Regression

Systems of Linear Equations

Quantitative Methods Dr. Aravind Banakar –

Quantitative Methods Dr. Aravind Banakar –

Quantitative Methods

Quantitative Methods

Quantitative Methods

Quantitative Methods

Quantitative Methods

Quantitative Methods

پروتكل آموزش سلامت به مددجو

مبررات إدخال الحاسوب في رياض الأطفال

How to Interpret a 2-Way ANOVA

SPECIMEN HL1. SPECIMEN HL1 SPECIMEN HL1 SPECIMEN HL1.

Reaction time زمن الرجع.

Soc 3306a Lecture 11: Multivariate 4

Simple Linear Regression

21twelveinteractive.com/ twitter.com/21twelveI/ facebook.com/21twelveinteractive/ linkedin.com/company/21twelve-interactive/ pinterest.com/21twelveinteractive/

Sihua Peng, PhD Shanghai Ocean University

Cases. Simple Regression Linear Multiple Regression.

Welcome to EDP/EPE 660 Kelly Bradley, Ph.D..

Sergey Gorbunov Ivan Kisel DESY, Zeuthen KIP, Uni-Heidelberg

Presentation transcript:

General Linear Models -- #2 2x2 – main effects 2x2 with interactions 2x3 – main effects 2x3 with interactions 3x3 – main effects 3x3 with interactions

b0b0 b1b1 b2b2 2-group (Tx Cx) & 2-group (Tz Cz) predictors Main Effects Model 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz = simple effects (no interaction) X = Tx vs. Cx y’ = b 0 + b 1 X + b 2 Z Z = Tz vs. Cz X C T T Z C CxCz CxTz TxCz CxCz CxTz TxTz Z Tz = 1 Cz = 0 X Tx = 1 Cx = 0

group (Tx Cx) & 2-group (Tz Cz) predictors Main Effects Model 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz = simple effects (no interaction) X = Tx vs. Cx y’ = b 0 + b 1 X + b 2 Z Z = Tz vs. Cz X C T T Z C CxCz CxTz TxCz TxTz Z Tz = 1 Cz = 0 X Tx = 1 Cx = 0

b0b0 b1b1 b2b2 Models with 2-group (Tx Cx) & 2-group (Tz Cz) predictors  2x2 ANOVA 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz X = Tx vs. Cx y’ = b 0 + b 1 X + b 2 Z + b 3 XZ Z = Tz vs. Cz TxCz CxCz CxTz TxTz Z Tz = 1 Cz = 0 X Tx = 1 Cx = 0 XZ = X * Z b 3 = dif htdifs of CxCz - TxCz & CxTz - TxTz b3b3 vs.

Models with 2-group (Tx Cx) & 2-group (Tz Cz) predictors  2x2 ANOVA 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz X = Tx vs. Cx y’ = b 0 + b 1 X + b 2 Z + b 3 XZ Z = Tz vs. Cz Z Tz = 1 Cz = 0 X Tx = 1 Cx = 0 XZ = X * Z b 3 = dif htdifs of CxCz - TxCz & CxTz - TxTz

b0b0 b1b1 b2b2 Models with 2-group (Tx Cx) & 3-group (Tz 1 Tz 2 Cz) predictors  ME model 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz 1 = simple effects (no interaction) y’ = b 0 + b 1 X + b 2 Z 1 + b 3 Z 2 b3b3 CxCz CxTz 1 CxTz 2 TxCz TxTz 1 TxTz 2 b 3 = htdifs of CxCz & CxTz 2 Z C T 1 T 2 C X T CxCz TxCzTxTz 1 CxTz 1 CxTz 2 TxTz 2 Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X = Tx vs. Cx X Tx = 1 Cx = 0

Models with 2-group (Tx Cx) & 3-group (Tz 1 Tz 2 Cz) predictors  ME model 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz 1 = simple effects (no interaction) y’ = b 0 + b 1 X + b 2 Z 1 + b 3 Z 2 b 3 = htdifs of CxCz & CxTz 2 Z C T 1 T 2 C X T CxCz TxCzTxTz 1 CxTz 1 CxTz 2 TxTz 2 Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X = Tx vs. Cx X Tx = 1 Cx = 0

b0b0 b1b1 b2b2 Models with 2-group (Tx Cx) & 3-group (Tz 1 Tz 2 Cz) predictors  2x3 ANOVA 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz 1 y’ = b 0 + b 1 X + b 2 Z 1 + b 3 Z 2 +b 4 XZ 1 + b 5 XZ 2 b3b3 CxCz CxTz 1 CxTz 2 TxCz TxTz 1 TxTz 2 b 3 = htdifs of CxCz & CxTz 2 Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X = Tx vs. Cx X Tx = 1 Cx = 0 XZ 1 = X * Z 1 XZ 2 = X * Z 2 b 4 = dif htdifs of CxCz - TxCz & CxTz 1 – TxTz 1 b 5 = dif htdifs of CxCz - TxCz & CxTz 2 – TxTz 2 b4b4 vs. b5b5

Models with 2-group (Tx Cx) & 3-group (Tz 1 Tz 2 Cz) predictors  2x3 ANOVA 0 1  X b 0 = mean of CxCz b 1 = htdif of CxCz & TxCz b 2 = htdifs of CxCz & CxTz 1 y’ = b 0 + b 1 X + b 2 Z 1 + b 3 Z 2 +b 4 XZ 1 + b 5 XZ 2 b 3 = htdifs of CxCz & CxTz 2 Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X = Tx vs. Cx X Tx = 1 Cx = 0 XZ 1 = X * Z 1 XZ 2 = X * Z 2 b 4 = dif htdifs of CxCz - TxCz & CxTz 1 – TxTz 1 b 5 = dif htdifs of CxCz - TxCz & CxTz 2 – TxTz 2

 X 3-group (Tx 1 Tx 2 Cx) & 3-group (Tz 1 Tz 2 Cz) predictors  ME Model y’ = b 0 + b 1 X + b 2 X + b 3 Z 1 + b 4 Z 2 X C T 1 T 2 T2ZT1CT2ZT1C CxTz 2 CxCz Tx 1 Cz Tx 1 Tz 2 Tx 2 Tz 2 Tx 2 Cz CxTz 1 Tx 1 Tz 1 b 0 = mean of CxCz b 1 = htdif of CxCz & Tx 1 Cz b 2 = htdifs of CxCz & Tz 2 Cz = simple effects (no interaction) b 3 = htdifs of CxCz & CxTz 1 b0b0 b1b1 b2b2 b3b3 CxCz CxTz 1 CxTz 2 Tx 2 Cz Tx 2 Tz 1 Tx 2 Tz 2 Tx 1 Cz Tx 1 Tz 1 Tx 1 Tz 2 b 4 = htdifs of CxCz & CxTz 2 b4b4 X1 Tx 1 =1 Tx 2 =0 Cx=0 X2 Tx 1 =0 Tx 2 =1 Cx=0 X 1 = Tx 1 vs. CxX 2 = Tx 2 vs. Cx Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0

 X 3-group (Tx 1 Tx 2 Cx) & 3-group (Tz 1 Tz 2 Cz) predictors  ME Model y’ = b 0 + b 1 X + b 2 X + b 3 Z 1 + b 4 Z 2 X C T 1 T 2 T2ZT1CT2ZT1C CxTz 2 CxCz Tx 1 Cz Tx 1 Tz 2 Tx 2 Tz 2 Tx 2 Cz CxTz 1 Tx 1 Tz 1 b 0 = mean of CxCz b 1 = htdif of CxCz & Tx 1 Cz b 2 = htdifs of CxCz & Tz 2 Cz = simple effects (no interaction) b 3 = htdifs of CxCz & CxTz 1 b 4 = htdifs of CxCz & CxTz 2 X1 Tx 1 =1 Tx 2 =0 Cx=0 X2 Tx 1 =0 Tx 2 =1 Cx=0 X 1 = Tx 1 vs. CxX 2 = Tx 2 vs. Cx Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0

 X 3-group (Tx 1 Tx 2 Cx) & 3-group (Tz 1 Tz 2 Cz) predictors w/ interaction  3x3 ANOVA y’ = b 0 + b 1 X + b 2 X + b 3 Z 1 + b 4 Z 2 + b 5 X 1 Z 1 + b 6 X 1 Z 2 + b 7 X 2 Z 1 + b 8 X 2 Z 2 b 0 = mean of CxCz b 1 = htdif of CxCz & Tx 1 Cz b 2 = htdifs of CxCz & Tz 2 Cz b 3 = htdifs of CxCz & CxTz 1 b0b0 b1b1 b2b2 b3b3 CxCz CxTz 1 CxTz 2 Tx 2 Cz Tx 2 Tz 1 Tx 2 Tz 2 Tx 1 Cz Tx 1 Tz 1 Tx 1 Tz 2 b 4 = htdifs of CxCz & CxTz 2 b4b4 X 1 Tx 1 =1 Tx 2 =0 Cx=0 X 2 Tx 1 =0 Tx 2 =1 Cx=0 X 1 = Tx 1 vs. CxX 2 = Tx 2 vs. Cx Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X 1 Z 1 = X 1 * Z 1 X 1 Z 2 = X 1 * Z 2 X 2 Z 1 = X 2 * Z 1 X 2 Z 2 = X 2 * Z 2 Main Effects terms

 X 3-group (Tx 1 Tx 2 Cx) & 3-group (Tz 1 Tz 2 Cz) predictors w/ interaction  3x3 ANOVA y’ = b 0 + b 1 X + b 2 X + b 3 Z 1 + b 4 Z 2 + b 5 X 1 Z 1 + b 6 X 1 Z 2 + b 7 X 2 Z 1 + b 8 X 2 Z 2 b5b5 CxCz CxTz 1 CxTz 2 Tx 2 Cz Tx 2 Tz 1 Tx 2 Tz 2 Tx 1 Cz Tx 1 Tz 1 Tx 1 Tz 2 X 1 Tx 1 =1 Tx 2 =0 Cx=0 X 2 Tx 1 =0 Tx 2 =1 Cx=0 X 1 = Tx 1 vs. CxX 2 = Tx 2 vs. Cx Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X 1 Z 1 = X 1 * Z 1 X 1 Z 2 = X 1 * Z 2 X 2 Z 1 = X 2 * Z 1 X 2 Z 2 = X 2 * Z 2 Interaction terms b 5 = dif htdifs of CxCz - TxCz & CxTz 1 – TxTz 1 b 6 = dif htdifs of CxCz - TxCz & CxTz 2 – TxTz 2 b 7 = dif htdifs of CxCz – Tx 2 Cz & CxTz 1 – Tx 2 Tz 1 b 8 = dif htdifs of CxCz – Tx 2 Cz & CxTz 2 – Tx 2 Tz 2 vs. b6b6 b7b7 b8b8

 X 3-group (Tx 1 Tx 2 Cx) & 3-group (Tz 1 Tz 2 Cz) predictors w/ interaction  3x3 ANOVA y’ = b 0 + b 1 X + b 2 X + b 3 Z 1 + b 4 Z 2 + b 5 X 1 Z 1 + b 6 X 1 Z 2 + b 7 X 2 Z 1 + b 8 X 2 Z 2 b 0 = mean of CxCz b 1 = htdif of CxCz & Tx 1 Cz b 2 = htdifs of CxCz & Tz 2 Cz b 3 = htdifs of CxCz & CxTz 1 b 4 = htdifs of CxCz & CxTz 2 X 1 Tx 1 =1 Tx 2 =0 Cx=0 X 2 Tx 1 =0 Tx 2 =1 Cx=0 X 1 = Tx 1 vs. CxX 2 = Tx 2 vs. Cx Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X 1 Z 1 = X 1 * Z 1 X 1 Z 2 = X 1 * Z 2 X 2 Z 1 = X 2 * Z 1 X 2 Z 2 = X 2 * Z 2 Main Effects terms

 X 3-group (Tx 1 Tx 2 Cx) & 3-group (Tz 1 Tz 2 Cz) predictors w/ interaction  3x3 ANOVA y’ = b 0 + b 1 X + b 2 X + b 3 Z 1 + b 4 Z 2 + b 5 X 1 Z 1 + b 6 X 1 Z 2 + b 7 X 2 Z 1 + b 8 X 2 Z 2 X 1 Tx 1 =1 Tx 2 =0 Cx=0 X 2 Tx 1 =0 Tx 2 =1 Cx=0 X 1 = Tx 1 vs. CxX 2 = Tx 2 vs. Cx Z 1 = Tz 1 vs. CzZ 2 = Tz 2 vs. Cz Z 1 Tz 1 =1 Tz 2 =0 Cx=0 Z 2 Tz 1 =0 Tx 2 =1 Cx=0 X 1 Z 1 = X 1 * Z 1 X 1 Z 2 = X 1 * Z 2 X 2 Z 1 = X 2 * Z 1 X 2 Z 2 = X 2 * Z 2 Interaction terms b 5 = dif htdifs of CxCz - TxCz & CxTz 1 – TxTz 1 b 6 = dif htdifs of CxCz - TxCz & CxTz 2 – TxTz 2 b 7 = dif htdifs of CxCz – Tx 2 Cz & CxTz 1 – Tx 2 Tz 1 b 8 = dif htdifs of CxCz – Tx 2 Cz & CxTz 2 – Tx 2 Tz 2