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Multilevel Multitrait Multimethod model. Lluís Coromina (Universitat de Girona)

Multilevel Multitrait Multimethod model. Lluís Coromina (Universitat de Girona) Barcelona, 06/06/2005. Background. Measurement data quality in social networks analysis. Assess reliability and validity in egocentered social networks. Complete networks Egocentered networks. Index.

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Multilevel Multitrait Multimethod model. Lluís Coromina (Universitat de Girona)

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  1. Multilevel Multitrait Multimethod model. Lluís Coromina (Universitat de Girona) Barcelona, 06/06/2005

  2. Background • Measurement data quality in social networks analysis. • Assess reliability and validity in egocentered social networks. • Complete networks • Egocentered networks

  3. Index • Reliability and Validity • MTMM Model • Data • Multilevel analysis • Results and interpretation

  4. Reliability and Validity • Reliability and Validity • MTMM Model • Confirmatory Factor Analysis (CFA) specification of the MTMM model. • Yij = mij Mj + tij Ti + eij(1) • where: • Yij : response or measured variable “i” measured by method “j”. • Ti : unobserved variable of interest (trait). Related to validity. • Mj : variation in scores due to the method. Related to invalidity. • mij and tij : factor loadings on the method and trait factors. • eij : random error, which is related to lack of reliability.

  5. MTMM model Figure 1 : Path diagram for the MTMM model for trait (Ti) and method (Mj).

  6. MTMM model

  7. M1 M2 Y11 Y21 Y31 Y41 Y12 Y22 Y32 Y42 T1 T2 T3 T4 e11 e42 e41 e22 e21 e31 e12 e32 MTMM model Figure 2: Path diagram of a CFA MTMM model for two methods and four traits.

  8. MTMM model Var (Yij) = mij2Var (Mj) + tij2Var (Ti) + Var (eij) (2) Validity and Reliability for CFA MTMM model: Reliability coefficient = (3) Validity coefficient = (4)

  9. Data Kogovšek, et al., 2002: Estimating the reliability and validity of personal support measures: full information ML estimation with planned incomplete data. Social Networks, 24, 1-20. T1 Frequency of contact T3 Feeling of importance T2 Feeling of closeness T4 Frequency of the alter upsetting to ego Representative sample of inhabitants of Ljubljana Table 1: The design of the study

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

  11. Multilevel MTMM model • The mean centred individual scores for group “g” and individual “k” • can be decomposed into: • Within group component (5) • Between group component (6) • 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 (questions) 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. • N=nG is the total number of alters.

  12. Multilevel MTMM model Sample covariance matrices: (7) (8) SW= SB= ST= SB+ SW = (9) Population covariance matrices: T= B+ W (10) Yij = mBijMBj + tBijTBi + eBij + mwijMwj + twijTwi + ewij(11) YBij YWij

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

  14. Multilevel MTMM model Figure 3: Multilevel CFA MTMM Model.

  15. Multilevel MTMM model Interpretation: We can obtain 2 reliabilities and 2 validities for each trait-method combination. To analyse each component separately: Yij = mBijMBj + tBijTBi + eBij + mwijMwj + twijTwi + ewij(11) YBij YWij Decompose the variance: Var (Yij) = mij2wVar (MjW) + mij2BVar (MjB) + tij2wVar (TiW) + tij2BVar (TiB) + (13) Var (eijw) + Var (eijB)

  16. Multilevel MTMM model Analysis: • Analysis 1: traditional analysis on ST. ML estimation. • Analysis 2: traditional analysis on SW. ML estimation. • Analysis 3: traditional analysis on SB, which is a biased estimate of ΣB. ML estimation. Analyses 2 and 3 together constitute the recommendation of Härnqvist (1978). • Analysis 4: multilevel analysis, to fit ΣW and ΣB simultaneously. ML estimation.

  17. Results and interpretation Table 1: Goodness of fit statistics.

  18. Results and interpretation Table 2: Decomposition into 6 variance components. Analysis 4. * Boldfaced for small non-significant variances constrained to zero.

  19. Results and interpretation Table 3: Decomposition into 6 variance components* * Boldfaced for small non-significant variances constrained to zero.

  20. Results and interpretation Table 4: Multilevel reliabilities and validities* * Boldfaced for small non-significant variances constrained to zero.

  21. Results and interpretation Table 5: Within part. Comparison of analyses 2 (SW) and 4 (multilevel). * Boldfaced for small non-significant variances constrained to zero.

  22. Results and interpretation Table 6: Between part. Comparison of analyses 3 (SB) and 4 (multilevel). * Boldfaced for small non-significant variances constrained to zero.

  23. Results and interpretation Table 7: Overall analysis. Comparison of analyses 1 (ST) and 4 (multilevel). * Boldfaced for small non-significant variances constrained to zero.

  24. Results and interpretation Table 8: Percentages of variance at within level form M1 and M2

  25. Results and interpretation • Contribution: • To consider egocentered networks as hierarchical data. • To specify a multilevel MTMM. • Interpretation from measurement theory of different % of variance.

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

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