1 / 31

Multilevel Modeling

Multilevel Modeling. Soc 543 Fall 2004. Presentation overview. What is multilevel modeling? Problems with not using multilevel models Benefits of using multilevel models Basic multilevel model Variation one: person and time Variation two: person, time, and space. Multilevel models.

kaya
Download Presentation

Multilevel Modeling

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. Multilevel Modeling Soc 543 Fall 2004

  2. Presentation overview • What is multilevel modeling? • Problems with not using multilevel models • Benefits of using multilevel models • Basic multilevel model • Variation one: person and time • Variation two: person, time, and space

  3. Multilevel models • Units of analysis are nested within higher-level units of analysis • Students within schools • Observations with person

  4. Problems without MLM • If we ignore higher-level units of analysis => cannot account for context (individualistic approach) • If we ignore individual-level observation and rely on higher-level units of analysis, we may commit ecological fallacy (aggregated data approach) • Without explicit modeling, sampling errors at second level may be large =>unreliable slopes • Homoscedasticity and no serial correlation assumptions of OLS are violated (an efficiency problem). • No distinction between parameter and sampling variances

  5. Advantages of MLM • Cross-level comparisons • Controls for level differences

  6. General MLM • Example: Raudenbush and Bryk, 1986 • Dependent variable: • Continuous • Observed

  7. General MLM • High school and beyond (HSB) survey • 10,231 students from 82 Catholic and 94 public schools • Dependent variable: standardized math achievement score • Independent variable: SES

  8. General MLM Variability among schools • Level one: within schools mathij = b0j + b1j (SESij - SES•j) + rij

  9. General MLM Variability among schools • Level two: between schools b0j = g00 + u0j b1j = g10 + u1j

  10. General MLM Variability among schools • Combined model mathij = g00 + u0j + g10(SESij - SES•j) + u1j(SESij - SES•j) + rij = g00 + g10(SESij - SES•j) + u0j + vij (Easy interpretation given the “centering” parameterization)

  11. General MLM Variability among schools • Combined model mathij = 100.74 + 4.52(SESij - SES•j) + u0j + vij • There is a positive relation between SES and math score

  12. General MLM Variability among schools • Results: math score means • school means are different • 90% of the variance is parameter variance • 10% is sampling variance • Results: math score-SES relation • school relations are different • 35% is parameter variance (this requires additional assumption and analysis) • 65% is sampling variance

  13. General MLM Covariates at level 2 Level one: within schools mathij = b0j + b1j (SESij - SES•j) + rij

  14. General MLM Covariates at level 2 • Level two: between schools b0j = g00 + g01sectj+ u0j b1j = g10 + g11sectj+ u1j

  15. General MLM Covariates at level 2 • Combined model: mathij = g00 + g01sectj + g10 (SESij - SES•j) + g11sectj(SESij - SES•j) + rij + vj

  16. General MLM • Combined model: mathij = 98.37 + 5.06sectj + 6.23(SESij - SES•j) - 3.86sectj(SESij - SES•j) + rij + vj

  17. General MLM Variability as a function of sector • Results: math score means • 80.7% is parameter variance • differences in school means is not entirely accounted for by sector • Results: SES-math score relation • 9.7% is parameter variance • differences in school SES-math score relation may be accounted for by sector

  18. General MLM Sector effects • Cannot say that previous relations are causal – may be selection effects • Use example of homework to explain sector differences

  19. General MLM Sector effects • Results: • school SES is strongly related to mean math score, but SES composition accounts for Catholic difference • schools with lower SES had weaker SES-math score relation than higher SES schools

  20. General MLM Sector effects • Results: • variation in SES-math score relation may be accounted for by school SES • variation in mean math score is not entirely accounted for by school SES

  21. MLM with person and time • When observations are repeated for the same units, we also have a nested structure. • Examining within-person changes over time – growth curve analysis. • Growth curves may be similar across persons within a class. • Example: Muthén and Muthén • Dependent variable: categorical, latent

  22. Muthen and Muthen • NLSY • N=7326 (part 1); N=924 (part 2); N=922 (part 3); N=1225 (part 4) • Dependent variables: antisocial behavior (excluding alcohol use) during past year, in 17 dichotomous items; alcohol use during past year, in 22 dichotomous items

  23. MLM with person and time • Part 1: latent class determination by latent class analysis and factor analysis • It’s a cross-sectional analysis of baseline data in 1980. • It found 4 latent classes.

  24. MLM with person and time • Part 2: growth curve determination by latent class growth curve analysis and growth mixture modeling • It uses longitudinal information. • Different growth curves are allowed and estimated for different latent classes. • Growth mixture modeling is a generalization of latent class growth analysis, in allowing growth variance within class • GMM yields a 4-class solution.

  25. MLM with person and time • Part 3: latent class relation to growth curve model by general growth mixture modeling (GGMM) • What’s new is to the ability to predict a categorical outcome variable from latent classes. • The example also illustrates how covariates that predict membership in classes (Table 4).

  26. MLM with person and time • Part 4: latent class relation to growth curve model by GGMM • Multiple (2) latent class variables. • The first one comes from Part 1; the second one comes from Part 2. • It bridges the two component parts, asking how the first class membership affects membership in the second class scheme.

  27. MLM with person, time & space • Example: Axinn and Yabiku • Dependent variable: dichotomous, observed • Hazard model with event history

  28. MLM with person, time & space • Chitwan Valley Family Study (CVFS) • 171 neighborhoods (5-15 household cluster) • Dependent variable: initiated contraception to terminate childbearing

  29. MLM with person, time & space Age 0 Age 12 Birth of 1st child Contraceptive use or end of observation Time-invariant childhood community context Time-varying contemporary community context Time-invariant early life nonfamily experiences Time-varying contemporary nonfamily experiences

  30. MLM with person, time & space • Level one: Logit(ptij) = b0j + b1Cj+ b2Xij +b3Djt + b4Zijt C: time-invariant community var. D: time-variant community var. X: time-invariant personal var. Z: time-variant personal var. (Note that there is no interaction across levels)

  31. Multi-level Hazard Models • There is a general problem with non-linear multi-level models. • Unbiasedness breaks down. • Special attention needs to be paid to estimation of hazard models in a multi-level setting. • See Barber et al (2000).

More Related