1 / 21

Introduction to Hierarchical Models. Lluís Coromina (Universitat de Girona)

Introduction to Hierarchical Models. Lluís Coromina (Universitat de Girona) Barcelona, 06/06/2005. Introduction. N=1371. Introduction. Introduction. 1. How frequently are you in contact with this person (personally, by mail, telephone or Internet)? 1 Less than once a year.

megara
Download Presentation

Introduction to Hierarchical Models. Lluís Coromina (Universitat de Girona)

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. Introduction to Hierarchical Models. Lluís Coromina (Universitat de Girona) Barcelona, 06/06/2005

  2. Introduction N=1371.

  3. Introduction

  4. Introduction 1. How frequently are you in contact with this person (personally, by mail, telephone or Internet)? 1 Less than once a year. 2 Several times a year. 3 About once a month. 4 Several times a month. 5 Several times a week. 6 Every day. 2. How close do you feel to this person? Please describe how close you feel on a scale from1 to 5, where 1 means not close and 5 means very close. 1 2 3 4 5 Not Close Very Close 3. How important is this person in your life? Please describe how close you feel on a scale from 1 to 5, where 1 means not important and 5 means very important. 1 2 3 4 5 Not important Very important 4. How often does this person upset you? 1 Never. 2 Rarely. 3 Sometimes. 4 Often.

  5. Model • Model • Yij = tij Ti + eij (1) • where: • Yij : response or measured variable “i” measured by method “j”. • Ti : unobserved variable of interest (trait). Related to validity. • eij : random error, which is related to lack of reliability.

  6. Model title: CLAS 2X4. TRAIT LOADS EQUAL. 1 nivell. RAW DATA FROM FILE dadesmodel.PSF LATENT VARIABLES T1 T2 T3 T4 RELATIONSHIPS M1T1 = 1*T1 M2T1 = T1 M1T2 = 1*T2 M2T2 = T2 M1T3 = 1*T3 M2T3 = T3 M1T4 = 1*T4 M2T4 = T4 SET THE ERROR VARIANCE OF M1T1 FREE SET THE ERROR VARIANCE OF M2T1 FREE SET THE ERROR VARIANCE OF M1T2 FREE SET THE ERROR VARIANCE OF M2T2 FREE SET THE ERROR VARIANCE OF M1T3 FREE SET THE ERROR VARIANCE OF M2T3 FREE SET THE ERROR VARIANCE OF M1T4 FREE SET THE ERROR VARIANCE OF M2T4 FREE SET THE VARIANCE OF T1 FREE SET THE VARIANCE OF T2 FREE SET THE VARIANCE OF T3 FREE SET THE VARIANCE OF T4 FREE T2 = T1 T4 T3 = T1 T4 LET T1 AND T4 CORRELATE LET T2 AND T3 CORRELATE LET THE PATH T1 -> M2T1 BE EQUAL TO THE PATH T2 -> M2T2 LET THE PATH T1 -> M2T1 BE EQUAL TO THE PATH T3 -> M2T3 LET THE PATH T1 -> M2T1 BE EQUAL TO THE PATH T4 -> M2T4 OPTIONS ND=3 sc RS PATH DIAGRAM END OF PROBLEM

  7. Model Figure I : Path diagram for the MTMM model

  8. Model Structural Equations T2 = 0.376*T1 - 0.00203*T4, Errorvar.= 0.490 , R² = 0.220 (0.0245) (0.0322) (0.0244) 15.388 -0.0629 20.030 T3 = 0.439*T1 + 0.0656*T4, Errorvar.= 0.566 , R² = 0.269 (0.0261) (0.0344) (0.0278) 16.795 1.906 20.323 Error Covariance for T3 and T2 = 0.533 (0.0242) 22.013 Lisrel Output in latent growth curve Var (Yij) = tij2Var (Ti) + Var (eij) (2) Table I: Decomposition variance components

  9. Multilevel model Multilevel analysis. Two-level model. The highest level: group level = egos = g The lowest level: individual level = alters = k

  10. Multilevel model • The mean centred individual scores for group “g” and individual “k” • can be decomposed into: • Between group component (3) • Within group component (4) • where: • is the total average over all alters and egos. • is the average of all alters of the gth ego. • Ygk is the score on the name interpreter of the kth alter chosen by the gth ego. • G is the total number of egos. • n is the number of alters within each ego, constant. • N=nG is the total number of alters.

  11. Multilevel model Sample covariance matrices: (5) (6) SW= SB= ST= SB+ SW = (7) Population covariance matrices: T= B+ W (8) Yij = tBijTBi + eBij + twijTwi + ewij(9) YBij YWij

  12. Multilevel model Härnqvist Method Separate analysis for SBand SW Group measures Sw is the ML estimator of ΣW SB is the ML estimator of ΣW+cΣB (10) Model estimated by Maximum Likelihood (ML).

  13. Multilevel model title: CLAS 2X4. TRAIT LOADS EQUAL. BETWEEN SIMPLIFICAT GROUP 1: BETWEEN RAW DATA FROM FILE dadesmodel.PSF $CLUSTER EGO LATENT VARIABLES T1 T2 T3 T4 RELATIONSHIPS M1T1 = 1*T1 M2T1 = 1*T1 M1T2 = 1*T2 M2T2 = 1*T2 M1T3 = 1*T3 M2T3 = 1*T3 M1T4 = 1*T4 M2T4 = 1*T4 SET THE ERROR VARIANCE OF M1T1 FREE SET THE ERROR VARIANCE OF M2T1 FREE SET THE ERROR VARIANCE OF M1T2 FREE SET THE ERROR VARIANCE OF M2T2 FREE SET THE ERROR VARIANCE OF M1T3 FREE SET THE ERROR VARIANCE OF M2T3 FREE SET THE ERROR VARIANCE OF M1T4 TO 0.00001 SET THE ERROR VARIANCE OF M2T4 FREE SET THE VARIANCE OF T1 FREE SET THE VARIANCE OF T2 FREE SET THE VARIANCE OF T3 FREE SET THE VARIANCE OF T4 FREE T2 = T1 T4 T3 = T1 T4 LET T1 AND T4 CORRELATE LET T2 AND T3 CORRELATE ...

  14. Multilevel model GROUP 2: WITHIN RAW DATA FROM FILE dadesmodel.PSF LATENT VARIABLES T1 T2 T3 T4 RELATIONSHIPS M1T1 = 1*T1 M2T1 = T1 M1T2 = 1*T2 M2T2 = T2 M1T3 = 1*T3 M2T3 = T3 M1T4 = 1*T4 M2T4 = T4 ... ... ... ... ... ... ... ... ... ... END OF PROBLEM

  15. Multilevel model CLAS 2X4. TRAIT LOADS EQUAL. BETWEEN SIMPLIFICAT GROUP 1: BETWEEN LISREL Estimates (Maximum Likelihood) Measurement Equations M1T2 = 1.000*T2, Errorvar.= 0.0321, R² = 0.689 M1T3 = 1.000*T3, Errorvar.= 0.0362, R² = 0.750 M2T2 = 1.000*T2, Errorvar.= 0.0257, R² = 0.734 M2T3 = 1.000*T3, Errorvar.= 0.0287, R² = 0.791 M1T1 = 1.000*T1, Errorvar.= 0.0175, R² = 0.913 M1T4 = 1.000*T4, Errorvar.= 0.000, R² = 1.00 M2T1 = 1.000*T1, Errorvar.= 0.0331, R² = 0.847 M2T4 = 1.000*T4, Errorvar.= 0.0683, R² = 0.653 Structural Equations T2 = - 0.0513*T1 - 0.224*T4, Errorvar.= 0.0634, R² = 0.107 T3 = 0.152*T1 - 0.160*T4, Errorvar.= 0.103, R² = 0.0560 Error Covariance for T3 and T2 = 0.0870 (0.0) Lisrel Output in latent growth curve

  16. Multilevel model GROUP 2: WITHIN LISREL Estimates (Maximum Likelihood) Measurement Equations M1T2 = 1.000*T2, Errorvar.= 0.184, R² = 0.759 M1T3 = 1.000*T3, Errorvar.= 0.193, R² = 0.782 M2T2 = 0.950*T2, Errorvar.= 0.151, R² = 0.775 M2T3 = 0.950*T3, Errorvar.= 0.151, R² = 0.804 M1T1 = 1.000*T1, Errorvar.= 0.154, R² = 0.842 M1T4 = 1.000*T4, Errorvar.= 0.225, R² = 0.684 M2T1 = 0.950*T1, Errorvar.= 0.167, R² = 0.815 M2T4 = 0.950*T4, Errorvar.= 0.181, R² = 0.708 Structural Equations T2 = 0.474*T1 + 0.0361*T4, Errorvar.= 0.386, R² = 0.334 T3 = 0.502*T1 + 0.114*T4, Errorvar.= 0.448, R² = 0.350 Error Covariance for T3 and T2 = 0.420 (0.0)

  17. Multilevel model Interpretation: To analyse each component separately: Yij = tBijTBi + eBij + twijTwi + ewij(11) YBij YWij Decompose the variance: Var (Yij) = tij2wVar (TiW) + tij2BVar (TiB) + (12) Var (eijw) + Var (eijB)

  18. Results and interpretation Table II: Decomposition into 4 variance components. * Boldfaced for small non-significant variances constrained to zero.

  19. Results and interpretation Table III: Percentages of decomposition into 4 variance components* * Boldfaced for small non-significant variances constrained to zero.

  20. Results and interpretation Table IV: Percentages of variance at within level form M1 and M2

  21. For further information and contact: http://www.udg.es/fcee/professors/llcoromina

More Related