1 / 15

General Linear Models -- #2

General Linear Models -- #2. 2x2 – main effects 2x2 with interactions 2x3 – main effects 2x3 with interactions 3x3 – main effects 3x3 with interactions. 2-group (Tx Cx) & 2-group (Tz Cz) predictors Main Effects Model. Z Tz = 1 Cz = 0. X Tx = 1 Cx = 0. X C T.

sadah
Télécharger la présentation

General Linear Models -- #2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 2-group (Tx Cx) & 2-group (Tz Cz) predictors Main Effects Model Z Tz = 1 Cz = 0 X Tx = 1 Cx = 0 X C T X = Tx vs. Cx Z = Tz vs. Cz TxTz CxTz T Z C TxCz CxCz y’ = b0 + b1X + b2Z TxTz b0 = mean of CxCz CxTz b1 = htdif of CxCz & TxCz TxCz b2 0 10 20 30 40 50 60 b1 b2 = htdifs of CxCz & CxTz CxCz b0 = simple effects (no interaction) 0 1  X

  3. 2-group (Tx Cx) & 2-group (Tz Cz) predictors Main Effects Model Z Tz = 1 Cz = 0 X Tx = 1 Cx = 0 X C T X = Tx vs. Cx Z = Tz vs. Cz TxTz CxTz T Z C TxCz CxCz y’ = b0 + b1X + b2Z b0 = mean of CxCz b1 = htdif of CxCz & TxCz 0 10 20 30 40 50 60 b2 = htdifs of CxCz & CxTz = simple effects (no interaction) 0 1  X

  4. Models with 2-group (Tx Cx) & 2-group (Tz Cz) predictors  2x2 ANOVA Z Tz = 1 Cz = 0 XZ = X * Z X Tx = 1 Cx = 0 X = Tx vs. Cx Z = Tz vs. Cz y’ = b0 + b1X + b2Z + b3XZ b0 = mean of CxCz b1 = htdif of CxCz & TxCz CxTz b3 TxTz vs. b2 = htdifs of CxCz & CxTz b2 0 10 20 30 40 50 60 TxCz b1 b3 = dif htdifs of CxCz - TxCz & CxTz - TxTz CxCz b0 0 1  X

  5. Models with 2-group (Tx Cx) & 2-group (Tz Cz) predictors  2x2 ANOVA Z Tz = 1 Cz = 0 XZ = X * Z X Tx = 1 Cx = 0 X = Tx vs. Cx Z = Tz vs. Cz y’ = b0 + b1X + b2Z + b3XZ b0 = mean of CxCz b1 = htdif of CxCz & TxCz b2 = htdifs of CxCz & CxTz 0 10 20 30 40 50 60 b3 = dif htdifs of CxCz - TxCz & CxTz - TxTz 0 1  X

  6. Z C T1 T2 Models with 2-group (Tx Cx) & 3-group (Tz1 Tz2 Cz) predictors  ME model CxTz2 CxTz1 CxCz C X T TxCz TxTz1 TxTz2 X Tx = 1 Cx = 0 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz X = Tx vs. Cx y’ = b0 + b1X + b2Z1 + b3Z2 b0 = mean of CxCz TxTz2 b1 = htdif of CxCz & TxCz TxTz1 CxTz2 b3 b2 = htdifs of CxCz & CxTz1 CxTz1 TxCz 0 10 20 30 40 50 60 b1 b2 b3 = htdifs of CxCz & CxTz2 CxCz = simple effects (no interaction) b0 0 1  X

  7. Z C T1 T2 Models with 2-group (Tx Cx) & 3-group (Tz1 Tz2 Cz) predictors  ME model CxTz2 CxTz1 CxCz C X T TxCz TxTz1 TxTz2 X Tx = 1 Cx = 0 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz X = Tx vs. Cx y’ = b0 + b1X + b2Z1 + b3Z2 b0 = mean of CxCz b1 = htdif of CxCz & TxCz b2 = htdifs of CxCz & CxTz1 0 10 20 30 40 50 60 b3 = htdifs of CxCz & CxTz2 = simple effects (no interaction) 0 1  X

  8. Models with 2-group (Tx Cx) & 3-group (Tz1 Tz2 Cz) predictors  2x3 ANOVA X Tx = 1 Cx = 0 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 XZ1 = X * Z1 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz XZ2 = X * Z2 X = Tx vs. Cx b0 = mean of CxCz y’ = b0 + b1X + b2Z1 + b3Z2 +b4XZ1 + b5XZ2 b1 = htdif of CxCz & TxCz TxTz2 b2 = htdifs of CxCz & CxTz1 b5 CxTz2 vs. b3 = htdifs of CxCz & CxTz2 b3 TxTz1 b4 CxTz1 TxCz vs. 0 10 20 30 40 50 60 b4 = dif htdifs of CxCz - TxCz & CxTz1 – TxTz1 b2 b1 CxCz b5 = dif htdifs of CxCz - TxCz & CxTz2 – TxTz2 b0 0 1  X

  9. Models with 2-group (Tx Cx) & 3-group (Tz1 Tz2 Cz) predictors  2x3 ANOVA X Tx = 1 Cx = 0 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 XZ1 = X * Z1 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz XZ2 = X * Z2 X = Tx vs. Cx b0 = mean of CxCz y’ = b0 + b1X + b2Z1 + b3Z2 +b4XZ1 + b5XZ2 b1 = htdif of CxCz & TxCz b2 = htdifs of CxCz & CxTz1 b3 = htdifs of CxCz & CxTz2 0 10 20 30 40 50 60 b4 = dif htdifs of CxCz - TxCz & CxTz1 – TxTz1 b5 = dif htdifs of CxCz - TxCz & CxTz2 – TxTz2 0 1  X

  10. 3-group (Tx1 Tx2 Cx) & 3-group (Tz1 Tz2 Cz) predictors  ME Model X C T1 T2 X1 Tx1=1 Tx2=0 Cx=0 X2 Tx1=0 Tx2=1 Cx=0 X1 = Tx1 vs. Cx X2 = Tx2 vs. Cx Tx1Tz2 CxTz2 Tx2Tz2 T2 Z T1 C Tx1Tz1 Tx1Tz1 CxTz1 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz CxCz Tx1Cz Tx2Cz y’ = b0 + b1X + b2X + b3Z1 + b4Z2 b0 = mean of CxCz Tx1Tz2 Tx2Tz2 b1 = htdif of CxCz & Tx1Cz CxTz2 Tx1Tz1 Tx2Tz1 b4 b2 = htdifs of CxCz & Tz2Cz Tx1Cz CxTz1 Tx2Cz 0 10 20 30 40 50 60 b3 = htdifs of CxCz & CxTz1 b3 b1 b2 b4 = htdifs of CxCz & CxTz2 CxCz b0 = simple effects (no interaction) 0 1 2  X

  11. 3-group (Tx1 Tx2 Cx) & 3-group (Tz1 Tz2 Cz) predictors  ME Model X C T1 T2 X1 Tx1=1 Tx2=0 Cx=0 X2 Tx1=0 Tx2=1 Cx=0 X1 = Tx1 vs. Cx X2 = Tx2 vs. Cx Tx1Tz2 CxTz2 Tx2Tz2 T2 Z T1 C Tx1Tz1 Tx1Tz1 CxTz1 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz CxCz Tx1Cz Tx2Cz y’ = b0 + b1X + b2X + b3Z1 + b4Z2 b0 = mean of CxCz b1 = htdif of CxCz & Tx1Cz b2 = htdifs of CxCz & Tz2Cz 0 10 20 30 40 50 60 b3 = htdifs of CxCz & CxTz1 b4 = htdifs of CxCz & CxTz2 = simple effects (no interaction) 0 1 2  X

  12. 3-group (Tx1 Tx2 Cx) & 3-group (Tz1 Tz2 Cz) predictors w/ interaction  3x3 ANOVA X1Z1 = X1 * Z1 X1 Tx1=1 Tx2=0 Cx=0 X2 Tx1=0 Tx2=1 Cx=0 X1 = Tx1 vs. Cx X2 = Tx2 vs. Cx X1Z2 = X1 * Z2 X2Z1 = X2 * Z1 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 X2Z2 = X2 * Z2 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz y’ = b0 + b1X + b2X + b3Z1 + b4Z2 + b5X1Z1 + b6X1Z2 + b7X2Z1 + b8X2Z2 Main Effects terms Tx1Tz2 Tx2Tz2 b0 = mean of CxCz CxTz2 Tx2Tz1 b1 = htdif of CxCz & Tx1Cz b4 Tx1Tz1 Tx2Cz CxTz1 0 10 20 30 40 50 60 b2 = htdifs of CxCz & Tz2Cz Tx1Cz b3 b1 b2 b3 = htdifs of CxCz & CxTz1 CxCz b0 b4 = htdifs of CxCz & CxTz2 0 1 2  X

  13. 3-group (Tx1 Tx2 Cx) & 3-group (Tz1 Tz2 Cz) predictors w/ interaction  3x3 ANOVA X1Z1 = X1 * Z1 X1 Tx1=1 Tx2=0 Cx=0 X2 Tx1=0 Tx2=1 Cx=0 X1 = Tx1 vs. Cx X2 = Tx2 vs. Cx X1Z2 = X1 * Z2 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 X2Z1 = X2 * Z1 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz X2Z2 = X2 * Z2 y’ = b0 + b1X + b2X + b3Z1 + b4Z2 + b5X1Z1 + b6X1Z2 + b7X2Z1 + b8X2Z2 Interaction terms b5 = dif htdifs of CxCz - TxCz & CxTz1 – TxTz1 Tx1Tz2 Tx2Tz2 CxTz2 vs. vs. b6 = dif htdifs of CxCz - TxCz & CxTz2 – TxTz2 Tx2Tz1 b6 b8 Tx1Tz1 CxTz1 Tx2Cz 0 10 20 30 40 50 60 Tx1Cz vs. vs. b7 = dif htdifs of CxCz – Tx2Cz & CxTz1 – Tx2Tz1 b5 b7 CxCz b8 = dif htdifs of CxCz – Tx2Cz & CxTz2 – Tx2Tz2 0 1 2  X

  14. 3-group (Tx1 Tx2 Cx) & 3-group (Tz1 Tz2 Cz) predictors w/ interaction  3x3 ANOVA X1Z1 = X1 * Z1 X1 Tx1=1 Tx2=0 Cx=0 X2 Tx1=0 Tx2=1 Cx=0 X1 = Tx1 vs. Cx X2 = Tx2 vs. Cx X1Z2 = X1 * Z2 X2Z1 = X2 * Z1 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 X2Z2 = X2 * Z2 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz y’ = b0 + b1X + b2X + b3Z1 + b4Z2 + b5X1Z1 + b6X1Z2 + b7X2Z1 + b8X2Z2 Main Effects terms b0 = mean of CxCz b1 = htdif of CxCz & Tx1Cz 0 10 20 30 40 50 60 b2 = htdifs of CxCz & Tz2Cz b3 = htdifs of CxCz & CxTz1 b4 = htdifs of CxCz & CxTz2 0 1 2  X

  15. 3-group (Tx1 Tx2 Cx) & 3-group (Tz1 Tz2 Cz) predictors w/ interaction  3x3 ANOVA X1Z1 = X1 * Z1 X1 Tx1=1 Tx2=0 Cx=0 X2 Tx1=0 Tx2=1 Cx=0 X1 = Tx1 vs. Cx X2 = Tx2 vs. Cx X1Z2 = X1 * Z2 Z1 Tz1=1 Tz2=0 Cx=0 Z2 Tz1=0 Tx2=1 Cx=0 X2Z1 = X2 * Z1 Z1 = Tz1 vs. Cz Z2 = Tz2 vs. Cz X2Z2 = X2 * Z2 y’ = b0 + b1X + b2X + b3Z1 + b4Z2 + b5X1Z1 + b6X1Z2 + b7X2Z1 + b8X2Z2 Interaction terms b5 = dif htdifs of CxCz - TxCz & CxTz1 – TxTz1 b6 = dif htdifs of CxCz - TxCz & CxTz2 – TxTz2 0 10 20 30 40 50 60 b7 = dif htdifs of CxCz – Tx2Cz & CxTz1 – Tx2Tz1 b8 = dif htdifs of CxCz – Tx2Cz & CxTz2 – Tx2Tz2 0 1 2  X

More Related